id	sid	tid	token	lemma	pos
cana-730	1	1	communications	communication	NOUN
cana-730	1	2	on	on	ADP
cana-730	1	3	applied	apply	VERB
cana-730	1	4	nonlinear	nonlinear	ADJ
cana-730	1	5	analysis	analysis	NOUN
cana-730	1	6	issn	issn	NOUN
cana-730	1	7	:	:	PUNCT
cana-730	1	8	1074	1074	NUM
cana-730	1	9	-	-	PUNCT
cana-730	1	10	133x	133x	NUM
cana-730	1	11	vol	vol	NOUN
cana-730	1	12	31	31	NUM
cana-730	1	13	no	no	NOUN
cana-730	1	14	.	.	PUNCT
cana-730	2	1	3s	3s	NUM
cana-730	2	2	(	(	PUNCT
cana-730	2	3	2024	2024	NUM
cana-730	2	4	)	)	PUNCT
cana-730	2	5	44	44	NUM
cana-730	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-730	2	7	cost	cost	VERB
cana-730	2	8	analysis	analysis	NOUN
cana-730	2	9	approach	approach	NOUN
cana-730	2	10	-	-	PUNCT
cana-730	2	11	the	the	DET
cana-730	2	12	𝑴𝒙/𝑴/𝟏	𝑴𝒙/𝑴/𝟏	NOUN
cana-730	2	13	queues	queue	NOUN
cana-730	2	14	with	with	ADP
cana-730	2	15	working	work	VERB
cana-730	2	16	breakdowns	breakdown	NOUN
cana-730	2	17	and	and	CCONJ
cana-730	2	18	interruptions	interruption	NOUN
cana-730	2	19	b.	b.	PROPN
cana-730	2	20	deepa1	deepa1	PROPN
cana-730	2	21	*	*	PROPN
cana-730	2	22	,	,	PUNCT
cana-730	2	23	k.	k.	PROPN
cana-730	2	24	kalidass2	kalidass2	PROPN
cana-730	3	1	and	and	CCONJ
cana-730	3	2	k.	k.	PROPN
cana-730	4	1	vijaya3	vijaya3	PROPN
cana-730	5	1	*	*	PROPN
cana-730	5	2	1department	1department	NUM
cana-730	5	3	of	of	ADP
cana-730	5	4	mathematics	mathematic	NOUN
cana-730	5	5	,	,	PUNCT
cana-730	5	6	faculty	faculty	NOUN
cana-730	5	7	of	of	ADP
cana-730	5	8	engineering	engineering	PROPN
cana-730	5	9	,	,	PUNCT
cana-730	5	10	karpagam	karpagam	PROPN
cana-730	5	11	academy	academy	PROPN
cana-730	5	12	of	of	ADP
cana-730	5	13	higher	high	ADJ
cana-730	5	14	education	education	NOUN
cana-730	5	15	,	,	PUNCT
cana-730	5	16	coimbatore-21	coimbatore-21	PROPN
cana-730	5	17	,	,	PUNCT
cana-730	5	18	tamil	tamil	PROPN
cana-730	5	19	nadu	nadu	NOUN
cana-730	5	20	,	,	PUNCT
cana-730	5	21	india.email	india.email	PROPN
cana-730	5	22	:	:	PUNCT
cana-730	5	23	deepa09pragu@gmail.com	deepa09pragu@gmail.com	NUM
cana-730	5	24	2department	2department	NUM
cana-730	5	25	of	of	ADP
cana-730	5	26	mathematics	mathematic	NOUN
cana-730	5	27	,	,	PUNCT
cana-730	5	28	chikkanna	chikkanna	NOUN
cana-730	5	29	government	government	NOUN
cana-730	5	30	arts	arts	PROPN
cana-730	5	31	college	college	PROPN
cana-730	5	32	,	,	PUNCT
cana-730	5	33	thirupur	thirupur	NOUN
cana-730	5	34	.	.	PUNCT
cana-730	6	1	3research	3research	NUM
cana-730	6	2	scholar	scholar	NOUN
cana-730	6	3	,	,	PUNCT
cana-730	6	4	karpagam	karpagam	PROPN
cana-730	6	5	academy	academy	PROPN
cana-730	6	6	of	of	ADP
cana-730	6	7	higher	high	ADJ
cana-730	6	8	education.email	education.email	NOUN
cana-730	6	9	:	:	PUNCT
cana-730	6	10	vijayakirubai@gmail.com	vijayakirubai@gmail.com	X
cana-730	6	11	article	article	NOUN
cana-730	6	12	history	history	NOUN
cana-730	6	13	:	:	PUNCT
cana-730	6	14	received	receive	VERB
cana-730	6	15	:	:	PUNCT
cana-730	6	16	10	10	NUM
cana-730	6	17	-	-	PUNCT
cana-730	6	18	04	04	NUM
cana-730	6	19	-	-	PUNCT
cana-730	6	20	2024	2024	NUM
cana-730	6	21	revised	revise	VERB
cana-730	6	22	:	:	PUNCT
cana-730	6	23	19	19	NUM
cana-730	6	24	-	-	PUNCT
cana-730	6	25	05	05	NUM
cana-730	6	26	-	-	PUNCT
cana-730	6	27	2024	2024	NUM
cana-730	6	28	accepted	accept	VERB
cana-730	6	29	:	:	PUNCT
cana-730	6	30	05	05	NUM
cana-730	6	31	-	-	PUNCT
cana-730	6	32	06	06	NUM
cana-730	6	33	-	-	PUNCT
cana-730	6	34	2024	2024	NUM
cana-730	6	35	abstract	abstract	NOUN
cana-730	6	36	in	in	ADP
cana-730	6	37	this	this	DET
cana-730	6	38	paper	paper	NOUN
cana-730	6	39	,	,	PUNCT
cana-730	6	40	we	we	PRON
cana-730	6	41	have	have	AUX
cana-730	6	42	studied	study	VERB
cana-730	6	43	the	the	DET
cana-730	6	44	steady	steady	ADJ
cana-730	6	45	-	-	PUNCT
cana-730	6	46	state	state	NOUN
cana-730	6	47	analysis	analysis	NOUN
cana-730	6	48	of	of	ADP
cana-730	6	49	single	single	ADJ
cana-730	6	50	-	-	PUNCT
cana-730	6	51	server	server	NOUN
cana-730	6	52	markovian	markovian	ADJ
cana-730	6	53	bulk	bulk	NOUN
cana-730	6	54	arrival	arrival	NOUN
cana-730	6	55	queueing	queue	VERB
cana-730	6	56	systems	system	NOUN
cana-730	6	57	with	with	ADP
cana-730	6	58	working	work	VERB
cana-730	6	59	breakdowns	breakdown	NOUN
cana-730	6	60	and	and	CCONJ
cana-730	6	61	interruptions	interruption	NOUN
cana-730	6	62	.	.	PUNCT
cana-730	7	1	for	for	ADP
cana-730	7	2	this	this	DET
cana-730	7	3	model	model	NOUN
cana-730	7	4	,	,	PUNCT
cana-730	7	5	the	the	DET
cana-730	7	6	probability	probability	NOUN
cana-730	7	7	-	-	PUNCT
cana-730	7	8	generating	generate	VERB
cana-730	7	9	functions	function	NOUN
cana-730	7	10	of	of	ADP
cana-730	7	11	the	the	DET
cana-730	7	12	system	system	NOUN
cana-730	7	13	size	size	NOUN
cana-730	7	14	distributions	distribution	NOUN
cana-730	7	15	in	in	ADP
cana-730	7	16	steady	steady	ADJ
cana-730	7	17	state	state	NOUN
cana-730	7	18	are	be	AUX
cana-730	7	19	obtained	obtain	VERB
cana-730	7	20	.	.	PUNCT
cana-730	8	1	various	various	ADJ
cana-730	8	2	important	important	ADJ
cana-730	8	3	characteristics	characteristic	NOUN
cana-730	8	4	of	of	ADP
cana-730	8	5	the	the	DET
cana-730	8	6	model	model	NOUN
cana-730	8	7	,	,	PUNCT
cana-730	8	8	like	like	ADP
cana-730	8	9	the	the	DET
cana-730	8	10	expected	expect	VERB
cana-730	8	11	number	number	NOUN
cana-730	8	12	of	of	ADP
cana-730	8	13	customers	customer	NOUN
cana-730	8	14	in	in	ADP
cana-730	8	15	the	the	DET
cana-730	8	16	system	system	NOUN
cana-730	8	17	,	,	PUNCT
cana-730	8	18	the	the	DET
cana-730	8	19	expected	expect	VERB
cana-730	8	20	waiting	waiting	NOUN
cana-730	8	21	time	time	NOUN
cana-730	8	22	of	of	ADP
cana-730	8	23	a	a	DET
cana-730	8	24	customer	customer	NOUN
cana-730	8	25	in	in	ADP
cana-730	8	26	the	the	DET
cana-730	8	27	system	system	NOUN
cana-730	8	28	,	,	PUNCT
cana-730	8	29	etc	etc	X
cana-730	8	30	.	.	X
cana-730	8	31	,	,	PUNCT
cana-730	8	32	are	be	AUX
cana-730	8	33	derived	derive	VERB
cana-730	8	34	.	.	PUNCT
cana-730	9	1	in	in	ADP
cana-730	9	2	steady	steady	ADJ
cana-730	9	3	state	state	NOUN
cana-730	9	4	,	,	PUNCT
cana-730	9	5	we	we	PRON
cana-730	9	6	have	have	AUX
cana-730	9	7	discussed	discuss	VERB
cana-730	9	8	some	some	DET
cana-730	9	9	important	important	ADJ
cana-730	9	10	performance	performance	NOUN
cana-730	9	11	measures	measure	NOUN
cana-730	9	12	of	of	ADP
cana-730	9	13	the	the	DET
cana-730	9	14	system	system	NOUN
cana-730	9	15	and	and	CCONJ
cana-730	9	16	provided	provide	VERB
cana-730	9	17	some	some	DET
cana-730	9	18	numerical	numerical	ADJ
cana-730	9	19	examples	example	NOUN
cana-730	9	20	to	to	PART
cana-730	9	21	show	show	VERB
cana-730	9	22	that	that	SCONJ
cana-730	9	23	our	our	PRON
cana-730	9	24	results	result	NOUN
cana-730	9	25	are	be	AUX
cana-730	9	26	computationally	computationally	ADV
cana-730	9	27	tractable	tractable	ADJ
cana-730	9	28	.	.	PUNCT
cana-730	10	1	the	the	DET
cana-730	10	2	suitability	suitability	NOUN
cana-730	10	3	of	of	ADP
cana-730	10	4	the	the	DET
cana-730	10	5	model	model	NOUN
cana-730	10	6	is	be	AUX
cana-730	10	7	tested	test	VERB
cana-730	10	8	in	in	ADP
cana-730	10	9	a	a	DET
cana-730	10	10	cost	cost	NOUN
cana-730	10	11	optimization	optimization	NOUN
cana-730	10	12	issue	issue	NOUN
cana-730	10	13	where	where	SCONJ
cana-730	10	14	the	the	DET
cana-730	10	15	mean	mean	ADJ
cana-730	10	16	number	number	NOUN
cana-730	10	17	of	of	ADP
cana-730	10	18	customers	customer	NOUN
cana-730	10	19	is	be	AUX
cana-730	10	20	optimized	optimize	VERB
cana-730	10	21	by	by	ADP
cana-730	10	22	reducing	reduce	VERB
cana-730	10	23	the	the	DET
cana-730	10	24	average	average	ADJ
cana-730	10	25	cost	cost	NOUN
cana-730	10	26	per	per	ADP
cana-730	10	27	unit	unit	NOUN
cana-730	10	28	hour	hour	NOUN
cana-730	10	29	using	use	VERB
cana-730	10	30	a	a	DET
cana-730	10	31	direct	direct	ADJ
cana-730	10	32	search	search	NOUN
cana-730	10	33	technique	technique	NOUN
cana-730	10	34	.	.	PUNCT
cana-730	11	1	keywords	keyword	NOUN
cana-730	11	2	:	:	PUNCT
cana-730	11	3	poisson	poisson	PROPN
cana-730	11	4	arrival	arrival	NOUN
cana-730	11	5	,	,	PUNCT
cana-730	11	6	markovian	markovian	PROPN
cana-730	11	7	queue	queue	NOUN
cana-730	11	8	,	,	PUNCT
cana-730	11	9	vacation	vacation	NOUN
cana-730	11	10	,	,	PUNCT
cana-730	11	11	single	single	ADJ
cana-730	11	12	server	server	NOUN
cana-730	11	13	,	,	PUNCT
cana-730	11	14	working	work	VERB
cana-730	11	15	breakdown	breakdown	NOUN
cana-730	11	16	,	,	PUNCT
cana-730	11	17	maintenance	maintenance	NOUN
cana-730	11	18	.	.	PUNCT
cana-730	12	1	1	1	NUM
cana-730	12	2	introduction	introduction	NOUN
cana-730	12	3	markovian	markovian	NOUN
cana-730	12	4	queues	queue	NOUN
cana-730	12	5	are	be	AUX
cana-730	12	6	a	a	DET
cana-730	12	7	major	major	ADJ
cana-730	12	8	subfield	subfield	NOUN
cana-730	12	9	of	of	ADP
cana-730	12	10	applied	apply	VERB
cana-730	12	11	probability	probability	NOUN
cana-730	12	12	.	.	PUNCT
cana-730	13	1	in	in	ADP
cana-730	13	2	fact	fact	NOUN
cana-730	13	3	,	,	PUNCT
cana-730	13	4	markovian	markovian	ADJ
cana-730	13	5	queues	queue	NOUN
cana-730	13	6	are	be	AUX
cana-730	13	7	crucial	crucial	ADJ
cana-730	13	8	to	to	ADP
cana-730	13	9	the	the	DET
cana-730	13	10	theory	theory	NOUN
cana-730	13	11	and	and	CCONJ
cana-730	13	12	practice	practice	NOUN
cana-730	13	13	of	of	ADP
cana-730	13	14	continuous	continuous	ADJ
cana-730	13	15	-	-	PUNCT
cana-730	13	16	time	time	NOUN
cana-730	13	17	markov	markov	NOUN
cana-730	13	18	chains	chain	NOUN
cana-730	13	19	as	as	ADV
cana-730	13	20	well	well	ADV
cana-730	13	21	as	as	ADP
cana-730	13	22	to	to	ADP
cana-730	13	23	the	the	DET
cana-730	13	24	creation	creation	NOUN
cana-730	13	25	of	of	ADP
cana-730	13	26	broader	broad	ADJ
cana-730	13	27	queueing	queue	VERB
cana-730	13	28	models	model	NOUN
cana-730	13	29	.	.	PUNCT
cana-730	14	1	the	the	DET
cana-730	14	2	current	current	ADJ
cana-730	14	3	analysis	analysis	NOUN
cana-730	14	4	considers	consider	VERB
cana-730	14	5	a	a	DET
cana-730	14	6	markovian	markovian	ADJ
cana-730	14	7	queue	queue	NOUN
cana-730	14	8	in	in	ADP
cana-730	14	9	which	which	PRON
cana-730	14	10	the	the	DET
cana-730	14	11	server	server	NOUN
cana-730	14	12	experiences	experience	NOUN
cana-730	14	13	failures	failure	NOUN
cana-730	14	14	while	while	SCONJ
cana-730	14	15	serving	serve	VERB
cana-730	14	16	customers	customer	NOUN
cana-730	14	17	.	.	PUNCT
cana-730	15	1	instead	instead	ADV
cana-730	15	2	of	of	ADP
cana-730	15	3	stopping	stop	VERB
cana-730	15	4	all	all	DET
cana-730	15	5	service	service	NOUN
cana-730	15	6	delivery	delivery	NOUN
cana-730	15	7	during	during	ADP
cana-730	15	8	a	a	DET
cana-730	15	9	breakdown	breakdown	ADJ
cana-730	15	10	phase	phase	NOUN
cana-730	15	11	,	,	PUNCT
cana-730	15	12	the	the	DET
cana-730	15	13	server	server	NOUN
cana-730	15	14	reduces	reduce	VERB
cana-730	15	15	the	the	DET
cana-730	15	16	service	service	NOUN
cana-730	15	17	pace	pace	NOUN
cana-730	15	18	.	.	PUNCT
cana-730	16	1	good	good	ADJ
cana-730	16	2	references	reference	NOUN
cana-730	16	3	are	be	AUX
cana-730	16	4	just	just	ADV
cana-730	16	5	one	one	NUM
cana-730	16	6	of	of	ADP
cana-730	16	7	several	several	ADJ
cana-730	16	8	that	that	SCONJ
cana-730	16	9	[	[	X
cana-730	16	10	1	1	X
cana-730	16	11	]	]	X
cana-730	16	12	v.	v.	PROPN
cana-730	16	13	jacob	jacob	PROPN
cana-730	16	14	,	,	PUNCT
cana-730	16	15	s.r	s.r	PROPN
cana-730	16	16	.	.	NOUN
cana-730	16	17	chakravarthy	chakravarthy	ADJ
cana-730	16	18	,	,	PUNCT
cana-730	16	19	and	and	CCONJ
cana-730	16	20	a.	a.	PROPN
cana-730	16	21	krishnamoorthy	krishnamoorthy	PROPN
cana-730	16	22	discussed	discuss	VERB
cana-730	16	23	the	the	DET
cana-730	16	24	interpretation	interpretation	NOUN
cana-730	16	25	of	of	ADP
cana-730	16	26	interruptions	interruption	NOUN
cana-730	16	27	caused	cause	VERB
cana-730	16	28	by	by	ADP
cana-730	16	29	customers	customer	NOUN
cana-730	16	30	and	and	CCONJ
cana-730	16	31	the	the	DET
cana-730	16	32	retrying	retrying	NOUN
cana-730	16	33	of	of	ADP
cana-730	16	34	those	those	DET
cana-730	16	35	consumers	consumer	NOUN
cana-730	16	36	.	.	PUNCT
cana-730	17	1	n.k	n.k	X
cana-730	17	2	.	.	PROPN
cana-730	17	3	jaiswal	jaiswal	PROPN
cana-730	17	4	conducted	conduct	VERB
cana-730	17	5	research	research	NOUN
cana-730	17	6	on	on	ADP
cana-730	17	7	the	the	DET
cana-730	17	8	preemptive	preemptive	ADJ
cana-730	17	9	resume	resume	NOUN
cana-730	17	10	priority	priority	NOUN
cana-730	17	11	queue	queue	NOUN
cana-730	17	12	in	in	ADP
cana-730	17	13	[	[	X
cana-730	17	14	3	3	NUM
cana-730	17	15	]	]	PUNCT
cana-730	17	16	.	.	PUNCT
cana-730	18	1	[	[	X
cana-730	18	2	4	4	NUM
cana-730	18	3	]	]	X
cana-730	18	4	jau	jau	PROPN
cana-730	18	5	-	-	PROPN
cana-730	18	6	chuan	chuan	PROPN
cana-730	18	7	ke	ke	PROPN
cana-730	18	8	used	use	VERB
cana-730	18	9	server	server	NOUN
cana-730	18	10	breakdown	breakdown	NOUN
cana-730	18	11	and	and	CCONJ
cana-730	18	12	startup	startup	NOUN
cana-730	18	13	/	/	SYM
cana-730	18	14	closedown	closedown	PROPN
cana-730	18	15	times	time	NOUN
cana-730	18	16	to	to	PART
cana-730	18	17	model	model	VERB
cana-730	18	18	the	the	DET
cana-730	18	19	batch	batch	NOUN
cana-730	18	20	arrival	arrival	NOUN
cana-730	18	21	queues	queue	NOUN
cana-730	18	22	under	under	ADP
cana-730	18	23	vacation	vacation	NOUN
cana-730	18	24	policies	policy	NOUN
cana-730	18	25	.	.	PUNCT
cana-730	19	1	[	[	X
cana-730	19	2	5	5	X
cana-730	19	3	]	]	X
cana-730	19	4	kim	kim	PROPN
cana-730	19	5	bk	bk	PROPN
cana-730	19	6	and	and	CCONJ
cana-730	19	7	lee	lee	PROPN
cana-730	19	8	dh	dh	PROPN
cana-730	19	9	investigated	investigate	VERB
cana-730	19	10	and	and	CCONJ
cana-730	19	11	examined	examine	VERB
cana-730	19	12	the	the	DET
cana-730	19	13	m	m	NOUN
cana-730	19	14	/	/	SYM
cana-730	19	15	g/1	g/1	NOUN
cana-730	19	16	queue	queue	NOUN
cana-730	19	17	that	that	PRON
cana-730	19	18	had	have	VERB
cana-730	19	19	malfunctions	malfunction	NOUN
cana-730	19	20	and	and	CCONJ
cana-730	19	21	catastrophic	catastrophic	ADJ
cana-730	19	22	events	event	NOUN
cana-730	19	23	.	.	PUNCT
cana-730	20	1	the	the	DET
cana-730	20	2	m	m	PROPN
cana-730	20	3	/	/	SYM
cana-730	20	4	g/1/1	g/1/1	PROPN
cana-730	20	5	queue	queue	NOUN
cana-730	20	6	modeled	model	VERB
cana-730	20	7	by	by	ADP
cana-730	20	8	b.	b.	PROPN
cana-730	20	9	krishna	krishna	PROPN
cana-730	20	10	kumar	kumar	PROPN
cana-730	20	11	,	,	PUNCT
cana-730	20	12	d.	d.	PROPN
cana-730	20	13	arivuadainambi	arivuadainambi	PROPN
cana-730	20	14	,	,	PUNCT
cana-730	20	15	and	and	CCONJ
cana-730	20	16	a.	a.	PROPN
cana-730	20	17	vijayakumar	vijayakumar	PROPN
cana-730	20	18	has	have	VERB
cana-730	20	19	an	an	DET
cana-730	20	20	unreliable	unreliable	ADJ
cana-730	20	21	server	server	NOUN
cana-730	20	22	and	and	CCONJ
cana-730	20	23	no	no	DET
cana-730	20	24	waiting	waiting	NOUN
cana-730	20	25	capacity	capacity	NOUN
cana-730	20	26	.	.	PUNCT
cana-730	21	1	[	[	X
cana-730	21	2	6	6	NUM
cana-730	21	3	]	]	PUNCT
cana-730	21	4	.	.	PUNCT
cana-730	22	1	[	[	X
cana-730	22	2	7	7	X
cana-730	22	3	]	]	PUNCT
cana-730	22	4	a	a	DET
cana-730	22	5	study	study	NOUN
cana-730	22	6	conducted	conduct	VERB
cana-730	22	7	by	by	ADP
cana-730	22	8	krishnamoorthy	krishnamoorthy	PROPN
cana-730	22	9	a	a	X
cana-730	22	10	,	,	PUNCT
cana-730	22	11	pramod	pramod	PROPN
cana-730	22	12	pk	pk	PROPN
cana-730	22	13	,	,	PUNCT
cana-730	22	14	and	and	CCONJ
cana-730	22	15	chakravarthy	chakravarthy	ADJ
cana-730	22	16	examined	examine	VERB
cana-730	22	17	interrupted	interrupted	ADJ
cana-730	22	18	lines	line	NOUN
cana-730	22	19	.	.	PUNCT
cana-730	23	1	[	[	X
cana-730	23	2	8	8	NUM
cana-730	23	3	]	]	PUNCT
cana-730	23	4	in	in	ADP
cana-730	23	5	stochastic	stochastic	ADJ
cana-730	23	6	models	model	NOUN
cana-730	23	7	,	,	PUNCT
cana-730	23	8	keilson	keilson	PROPN
cana-730	23	9	,	,	PUNCT
cana-730	23	10	j.	j.	PROPN
cana-730	23	11	,	,	PUNCT
cana-730	23	12	and	and	CCONJ
cana-730	23	13	servi	servi	ADJ
cana-730	23	14	,	,	PUNCT
cana-730	23	15	l.d	l.d	PROPN
cana-730	23	16	.	.	PROPN
cana-730	23	17	investigated	investigate	VERB
cana-730	23	18	the	the	DET
cana-730	23	19	queue	queue	NOUN
cana-730	23	20	as	as	ADP
cana-730	23	21	a	a	DET
cana-730	23	22	distributional	distributional	ADJ
cana-730	23	23	form	form	NOUN
cana-730	23	24	of	of	ADP
cana-730	23	25	matrix	matrix	NOUN
cana-730	23	26	-	-	PUNCT
cana-730	23	27	geometric	geometric	ADJ
cana-730	23	28	solutions	solution	NOUN
cana-730	23	29	for	for	ADP
cana-730	23	30	little	little	ADJ
cana-730	23	31	's	's	PART
cana-730	23	32	law	law	NOUN
cana-730	23	33	.	.	PUNCT
cana-730	24	1	[	[	X
cana-730	24	2	9	9	NUM
cana-730	24	3	]	]	X
cana-730	24	4	khalaf	khalaf	PROPN
cana-730	24	5	r.	r.	PROPN
cana-730	24	6	f.	f.	PROPN
cana-730	24	7	,	,	PUNCT
cana-730	24	8	madan	madan	PROPN
cana-730	24	9	k.	k.	PROPN
cana-730	24	10	c.	c.	PROPN
cana-730	24	11	,	,	PUNCT
cana-730	24	12	and	and	CCONJ
cana-730	24	13	lukas	lukas	PROPN
cana-730	24	14	c.	c.	PROPN
cana-730	24	15	a.	a.	PROPN
cana-730	24	16	were	be	AUX
cana-730	24	17	taken	take	VERB
cana-730	24	18	into	into	ADP
cana-730	24	19	consideration	consideration	NOUN
cana-730	24	20	as	as	ADP
cana-730	24	21	a	a	DET
cana-730	24	22	queue	queue	NOUN
cana-730	24	23	model	model	NOUN
cana-730	24	24	that	that	PRON
cana-730	24	25	included	include	VERB
cana-730	24	26	bernoulli	bernoulli	NOUN
cana-730	24	27	schedules	schedule	NOUN
cana-730	24	28	for	for	ADP
cana-730	24	29	random	random	ADJ
cana-730	24	30	breakdowns	breakdown	NOUN
cana-730	24	31	,	,	PUNCT
cana-730	24	32	general	general	ADJ
cana-730	24	33	repair	repair	PROPN
cana-730	24	34	times	time	NOUN
cana-730	24	35	,	,	PUNCT
cana-730	24	36	general	general	ADJ
cana-730	24	37	vacation	vacation	NOUN
cana-730	24	38	periods	period	NOUN
cana-730	24	39	,	,	PUNCT
cana-730	24	40	and	and	CCONJ
cana-730	24	41	general	general	ADJ
cana-730	24	42	prolonged	prolong	VERB
cana-730	24	43	vacation	vacation	NOUN
cana-730	24	44	times	time	NOUN
cana-730	24	45	.	.	PUNCT
cana-730	25	1	the	the	DET
cana-730	25	2	cost	cost	NOUN
cana-730	25	3	optimization	optimization	NOUN
cana-730	25	4	of	of	ADP
cana-730	25	5	a	a	DET
cana-730	25	6	singleserver	singleserver	NOUN
cana-730	25	7	queue	queue	NOUN
cana-730	25	8	with	with	ADP
cana-730	25	9	working	work	VERB
cana-730	25	10	breakdowns	breakdown	NOUN
cana-730	25	11	under	under	ADP
cana-730	25	12	the	the	DET
cana-730	25	13	n	n	PRON
cana-730	25	14	policy	policy	NOUN
cana-730	25	15	was	be	AUX
cana-730	25	16	examined	examine	VERB
cana-730	25	17	by	by	ADP
cana-730	25	18	chen	chen	PROPN
cana-730	25	19	,	,	PUNCT
cana-730	25	20	j.-y	j.-y	PROPN
cana-730	25	21	.	.	PROPN
cana-730	25	22	,	,	PUNCT
cana-730	25	23	yen	yen	NOUN
cana-730	25	24	,	,	PUNCT
cana-730	25	25	t.-c	t.-c	PROPN
cana-730	25	26	.	.	PROPN
cana-730	25	27	,	,	PUNCT
cana-730	25	28	and	and	CCONJ
cana-730	25	29	wang	wang	PROPN
cana-730	25	30	,	,	PUNCT
cana-730	25	31	k.-h	k.-h	PROPN
cana-730	25	32	.	.	PUNCT
cana-730	26	1	[	[	X
cana-730	26	2	10	10	NUM
cana-730	26	3	]	]	PUNCT
cana-730	26	4	.	.	PUNCT
cana-730	27	1	communications	communication	NOUN
cana-730	27	2	on	on	ADP
cana-730	27	3	applied	apply	VERB
cana-730	27	4	nonlinear	nonlinear	ADJ
cana-730	27	5	analysis	analysis	NOUN
cana-730	27	6	issn	issn	NOUN
cana-730	27	7	:	:	PUNCT
cana-730	27	8	1074	1074	NUM
cana-730	27	9	-	-	PUNCT
cana-730	27	10	133x	133x	NUM
cana-730	27	11	vol	vol	NOUN
cana-730	27	12	31	31	NUM
cana-730	27	13	no	no	NOUN
cana-730	27	14	.	.	PUNCT
cana-730	28	1	3s	3s	NUM
cana-730	28	2	(	(	PUNCT
cana-730	28	3	2024	2024	NUM
cana-730	28	4	)	)	PUNCT
cana-730	28	5	45	45	NUM
cana-730	28	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-730	28	7	the	the	DET
cana-730	28	8	article	article	NOUN
cana-730	28	9	has	have	VERB
cana-730	28	10	a	a	DET
cana-730	28	11	structure	structure	NOUN
cana-730	28	12	as	as	SCONJ
cana-730	28	13	follows	follow	VERB
cana-730	28	14	:	:	PUNCT
cana-730	28	15	the	the	DET
cana-730	28	16	model	model	NOUN
cana-730	28	17	is	be	AUX
cana-730	28	18	illustrated	illustrate	VERB
cana-730	28	19	in	in	ADP
cana-730	28	20	section	section	NOUN
cana-730	28	21	2	2	NUM
cana-730	28	22	.	.	PUNCT
cana-730	29	1	in	in	ADP
cana-730	29	2	section	section	NOUN
cana-730	29	3	3	3	NUM
cana-730	29	4	,	,	PUNCT
cana-730	29	5	we	we	PRON
cana-730	29	6	derive	derive	VERB
cana-730	29	7	the	the	DET
cana-730	29	8	stability	stability	NOUN
cana-730	29	9	condition	condition	NOUN
cana-730	29	10	through	through	ADP
cana-730	29	11	the	the	DET
cana-730	29	12	matrix	matrix	NOUN
cana-730	29	13	geometric	geometric	ADJ
cana-730	29	14	method	method	NOUN
cana-730	29	15	.	.	PUNCT
cana-730	30	1	for	for	ADP
cana-730	30	2	the	the	DET
cana-730	30	3	model	model	NOUN
cana-730	30	4	,	,	PUNCT
cana-730	30	5	the	the	DET
cana-730	30	6	probability	probability	NOUN
cana-730	30	7	-	-	PUNCT
cana-730	30	8	generating	generate	VERB
cana-730	30	9	functions	function	NOUN
cana-730	30	10	of	of	ADP
cana-730	30	11	the	the	DET
cana-730	30	12	system	system	NOUN
cana-730	30	13	size	size	NOUN
cana-730	30	14	distributions	distribution	NOUN
cana-730	30	15	in	in	ADP
cana-730	30	16	steady	steady	ADJ
cana-730	30	17	state	state	NOUN
cana-730	30	18	are	be	AUX
cana-730	30	19	obtained	obtain	VERB
cana-730	30	20	in	in	ADP
cana-730	30	21	section	section	NOUN
cana-730	30	22	4	4	NUM
cana-730	30	23	.	.	PUNCT
cana-730	31	1	stochastic	stochastic	ADJ
cana-730	31	2	decomposition	decomposition	NOUN
cana-730	31	3	is	be	AUX
cana-730	31	4	provided	provide	VERB
cana-730	31	5	in	in	ADP
cana-730	31	6	section	section	NOUN
cana-730	31	7	5	5	NUM
cana-730	31	8	.	.	PUNCT
cana-730	32	1	various	various	ADJ
cana-730	32	2	important	important	ADJ
cana-730	32	3	characteristics	characteristic	NOUN
cana-730	32	4	for	for	ADP
cana-730	32	5	the	the	DET
cana-730	32	6	model	model	NOUN
cana-730	32	7	,	,	PUNCT
cana-730	32	8	like	like	ADP
cana-730	32	9	the	the	DET
cana-730	32	10	expected	expect	VERB
cana-730	32	11	number	number	NOUN
cana-730	32	12	of	of	ADP
cana-730	32	13	customers	customer	NOUN
cana-730	32	14	in	in	ADP
cana-730	32	15	the	the	DET
cana-730	32	16	system	system	NOUN
cana-730	32	17	,	,	PUNCT
cana-730	32	18	the	the	DET
cana-730	32	19	expected	expect	VERB
cana-730	32	20	waiting	waiting	NOUN
cana-730	32	21	time	time	NOUN
cana-730	32	22	of	of	ADP
cana-730	32	23	a	a	DET
cana-730	32	24	customer	customer	NOUN
cana-730	32	25	in	in	ADP
cana-730	32	26	the	the	DET
cana-730	32	27	system	system	NOUN
cana-730	32	28	,	,	PUNCT
cana-730	32	29	etc	etc	X
cana-730	32	30	.	.	X
cana-730	32	31	,	,	PUNCT
cana-730	32	32	are	be	AUX
cana-730	32	33	derived	derive	VERB
cana-730	32	34	from	from	ADP
cana-730	32	35	section	section	NOUN
cana-730	32	36	6	6	NUM
cana-730	32	37	.	.	PUNCT
cana-730	33	1	section	section	NOUN
cana-730	33	2	7	7	NUM
cana-730	33	3	discusses	discuss	VERB
cana-730	33	4	the	the	DET
cana-730	33	5	reliability	reliability	NOUN
cana-730	33	6	measures	measure	NOUN
cana-730	33	7	of	of	ADP
cana-730	33	8	the	the	DET
cana-730	33	9	model	model	NOUN
cana-730	33	10	.	.	PUNCT
cana-730	34	1	practical	practical	ADJ
cana-730	34	2	applications	application	NOUN
cana-730	34	3	is	be	AUX
cana-730	34	4	provided	provide	VERB
cana-730	34	5	in	in	ADP
cana-730	34	6	section	section	NOUN
cana-730	34	7	8	8	NUM
cana-730	34	8	.	.	PUNCT
cana-730	35	1	numerical	numerical	ADJ
cana-730	35	2	examples	example	NOUN
cana-730	35	3	are	be	AUX
cana-730	35	4	exhibited	exhibit	VERB
cana-730	35	5	to	to	PART
cana-730	35	6	study	study	VERB
cana-730	35	7	the	the	DET
cana-730	35	8	parameters	parameter	NOUN
cana-730	35	9	and	and	CCONJ
cana-730	35	10	their	their	PRON
cana-730	35	11	effects	effect	NOUN
cana-730	35	12	on	on	ADP
cana-730	35	13	the	the	DET
cana-730	35	14	model	model	NOUN
cana-730	35	15	in	in	ADP
cana-730	35	16	section	section	NOUN
cana-730	35	17	9	9	NUM
cana-730	35	18	.	.	PUNCT
cana-730	36	1	in	in	ADP
cana-730	36	2	section	section	NOUN
cana-730	36	3	10	10	NUM
cana-730	36	4	,	,	PUNCT
cana-730	36	5	we	we	PRON
cana-730	36	6	have	have	AUX
cana-730	36	7	discussed	discuss	VERB
cana-730	36	8	the	the	DET
cana-730	36	9	cost	cost	NOUN
cana-730	36	10	model	model	NOUN
cana-730	36	11	and	and	CCONJ
cana-730	36	12	its	its	PRON
cana-730	36	13	optimization	optimization	NOUN
cana-730	36	14	through	through	ADP
cana-730	36	15	a	a	DET
cana-730	36	16	direct	direct	ADJ
cana-730	36	17	search	search	NOUN
cana-730	36	18	method	method	NOUN
cana-730	36	19	.	.	PUNCT
cana-730	37	1	2	2	NUM
cana-730	37	2	the	the	DET
cana-730	37	3	model	model	NOUN
cana-730	37	4	the	the	DET
cana-730	37	5	inter	inter	ADJ
cana-730	37	6	-	-	ADJ
cana-730	37	7	arrival	arrival	ADJ
cana-730	37	8	stream	stream	NOUN
cana-730	37	9	of	of	ADP
cana-730	37	10	customers	customer	NOUN
cana-730	37	11	constitutes	constitute	VERB
cana-730	37	12	a	a	DET
cana-730	37	13	compound	compound	NOUN
cana-730	37	14	poisson	poisson	NOUN
cana-730	37	15	process	process	NOUN
cana-730	37	16	with	with	ADP
cana-730	37	17	rate	rate	NOUN
cana-730	37	18	𝜆	𝜆	PRON
cana-730	37	19	.services	.service	NOUN
cana-730	37	20	are	be	AUX
cana-730	37	21	provided	provide	VERB
cana-730	37	22	to	to	ADP
cana-730	37	23	the	the	DET
cana-730	37	24	customer	customer	NOUN
cana-730	37	25	who	who	PRON
cana-730	37	26	is	be	AUX
cana-730	37	27	at	at	ADP
cana-730	37	28	the	the	DET
cana-730	37	29	head	head	NOUN
cana-730	37	30	of	of	ADP
cana-730	37	31	the	the	DET
cana-730	37	32	queue	queue	NOUN
cana-730	37	33	and	and	CCONJ
cana-730	37	34	the	the	DET
cana-730	37	35	service	service	NOUN
cana-730	37	36	is	be	AUX
cana-730	37	37	single	single	ADJ
cana-730	37	38	at	at	ADP
cana-730	37	39	a	a	DET
cana-730	37	40	time	time	NOUN
cana-730	37	41	according	accord	VERB
cana-730	37	42	to	to	ADP
cana-730	37	43	an	an	DET
cana-730	37	44	exponential	exponential	ADJ
cana-730	37	45	distribution	distribution	NOUN
cana-730	37	46	with	with	ADP
cana-730	37	47	rate	rate	NOUN
cana-730	37	48	𝜇	𝜇	ADP
cana-730	37	49	.the	.the	DET
cana-730	37	50	arrival	arrival	NOUN
cana-730	37	51	stream	stream	NOUN
cana-730	37	52	of	of	ADP
cana-730	37	53	customers	customer	NOUN
cana-730	37	54	joins	join	VERB
cana-730	37	55	the	the	DET
cana-730	37	56	system	system	NOUN
cana-730	37	57	in	in	ADP
cana-730	37	58	batches	batch	NOUN
cana-730	37	59	/	/	SYM
cana-730	37	60	bulks	bulk	NOUN
cana-730	37	61	.	.	PUNCT
cana-730	38	1	the	the	DET
cana-730	38	2	size	size	NOUN
cana-730	38	3	of	of	ADP
cana-730	38	4	batches	batch	NOUN
cana-730	38	5	is	be	AUX
cana-730	38	6	a	a	DET
cana-730	38	7	random	random	ADJ
cana-730	38	8	variable	variable	NOUN
cana-730	38	9	x	x	PUNCT
cana-730	38	10	of	of	ADP
cana-730	38	11	nonnegative	nonnegative	ADJ
cana-730	38	12	values	value	NOUN
cana-730	38	13	with	with	ADP
cana-730	38	14	a	a	DET
cana-730	38	15	probability	probability	NOUN
cana-730	38	16	distribution	distribution	NOUN
cana-730	38	17	𝑏𝑘	𝑏𝑘	NOUN
cana-730	38	18	=	=	PUNCT
cana-730	38	19	𝑃𝑟	𝑃𝑟	PROPN
cana-730	38	20	{	{	PUNCT
cana-730	38	21	𝑋	𝑋	PROPN
cana-730	38	22	=	=	PUNCT
cana-730	38	23	𝑘	𝑘	PROPN
cana-730	38	24	}	}	PUNCT
cana-730	38	25	,	,	PUNCT
cana-730	38	26	𝑘	𝑘	DET
cana-730	38	27	≥	≥	NOUN
cana-730	38	28	1	1	NUM
cana-730	38	29	.	.	PUNCT
cana-730	39	1	the	the	DET
cana-730	39	2	server	server	NOUN
cana-730	39	3	is	be	AUX
cana-730	39	4	possible	possible	ADJ
cana-730	39	5	to	to	ADP
cana-730	39	6	partial	partial	ADJ
cana-730	39	7	failures	failure	NOUN
cana-730	39	8	while	while	SCONJ
cana-730	39	9	providing	provide	VERB
cana-730	39	10	service	service	NOUN
cana-730	39	11	to	to	ADP
cana-730	39	12	the	the	DET
cana-730	39	13	customer	customer	NOUN
cana-730	39	14	.	.	PUNCT
cana-730	40	1	at	at	ADP
cana-730	40	2	the	the	DET
cana-730	40	3	time	time	NOUN
cana-730	40	4	of	of	ADP
cana-730	40	5	failure	failure	NOUN
cana-730	40	6	,	,	PUNCT
cana-730	40	7	the	the	DET
cana-730	40	8	server	server	NOUN
cana-730	40	9	continues	continue	VERB
cana-730	40	10	the	the	DET
cana-730	40	11	service	service	NOUN
cana-730	40	12	process	process	NOUN
cana-730	40	13	with	with	ADP
cana-730	40	14	slower	slow	ADJ
cana-730	40	15	service	service	NOUN
cana-730	40	16	rate	rate	NOUN
cana-730	40	17	𝜇𝑏(𝜇𝑏	𝜇𝑏(𝜇𝑏	PROPN
cana-730	40	18	<	<	X
cana-730	40	19	𝜇	𝜇	NOUN
cana-730	40	20	)	)	PUNCT
cana-730	40	21	.	.	PUNCT
cana-730	41	1	the	the	DET
cana-730	41	2	time	time	NOUN
cana-730	41	3	between	between	ADP
cana-730	41	4	failures	failure	NOUN
cana-730	41	5	and	and	CCONJ
cana-730	41	6	the	the	DET
cana-730	41	7	time	time	NOUN
cana-730	41	8	between	between	ADP
cana-730	41	9	repairs	repair	NOUN
cana-730	41	10	is	be	AUX
cana-730	41	11	assumed	assume	VERB
cana-730	41	12	to	to	PART
cana-730	41	13	be	be	AUX
cana-730	41	14	an	an	DET
cana-730	41	15	exponential	exponential	ADJ
cana-730	41	16	random	random	ADJ
cana-730	41	17	variable	variable	NOUN
cana-730	41	18	with	with	ADP
cana-730	41	19	rate	rate	NOUN
cana-730	41	20	𝛼	𝛼	NOUN
cana-730	41	21	and	and	CCONJ
cana-730	41	22	𝛾	𝛾	ADP
cana-730	41	23	respectively	respectively	ADV
cana-730	41	24	.	.	PUNCT
cana-730	42	1	after	after	ADP
cana-730	42	2	service	service	NOUN
cana-730	42	3	completion	completion	NOUN
cana-730	42	4	,	,	PUNCT
cana-730	42	5	the	the	DET
cana-730	42	6	server	server	NOUN
cana-730	42	7	is	be	AUX
cana-730	42	8	sent	send	VERB
cana-730	42	9	to	to	PART
cana-730	42	10	repair	repair	VERB
cana-730	42	11	.	.	PUNCT
cana-730	43	1	once	once	SCONJ
cana-730	43	2	the	the	DET
cana-730	43	3	repair	repair	NOUN
cana-730	43	4	process	process	NOUN
cana-730	43	5	completed	complete	VERB
cana-730	43	6	,	,	PUNCT
cana-730	43	7	the	the	DET
cana-730	43	8	server	server	NOUN
cana-730	43	9	starts	start	VERB
cana-730	43	10	to	to	PART
cana-730	43	11	provide	provide	VERB
cana-730	43	12	service	service	NOUN
cana-730	43	13	in	in	ADP
cana-730	43	14	regular	regular	ADJ
cana-730	43	15	service	service	NOUN
cana-730	43	16	rate	rate	NOUN
cana-730	43	17	𝜇.the	𝜇.the	PROPN
cana-730	43	18	arrival	arrival	NOUN
cana-730	43	19	process	process	NOUN
cana-730	43	20	,	,	PUNCT
cana-730	43	21	service	service	NOUN
cana-730	43	22	,	,	PUNCT
cana-730	43	23	breakdown	breakdown	NOUN
cana-730	43	24	and	and	CCONJ
cana-730	43	25	maintenance	maintenance	NOUN
cana-730	43	26	times	time	NOUN
cana-730	43	27	are	be	AUX
cana-730	43	28	assumed	assume	VERB
cana-730	43	29	to	to	PART
cana-730	43	30	be	be	AUX
cana-730	43	31	mutually	mutually	ADV
cana-730	43	32	independent	independent	ADJ
cana-730	43	33	.	.	PUNCT
cana-730	44	1	let	let	VERB
cana-730	44	2	c(t	c(t	PROPN
cana-730	44	3	)	)	PUNCT
cana-730	44	4	be	be	AUX
cana-730	44	5	the	the	DET
cana-730	44	6	state	state	NOUN
cana-730	44	7	of	of	ADP
cana-730	44	8	the	the	DET
cana-730	44	9	server	server	NOUN
cana-730	44	10	at	at	ADP
cana-730	44	11	time	time	NOUN
cana-730	44	12	t.	t.	PROPN
cana-730	44	13	then	then	ADV
cana-730	44	14	𝐶(𝑡	𝐶(𝑡	X
cana-730	44	15	)	)	PUNCT
cana-730	44	16	=	=	NOUN
cana-730	44	17	{	{	PUNCT
cana-730	44	18	0	0	NUM
cana-730	44	19	,	,	PUNCT
cana-730	44	20	𝑡ℎ𝑒	𝑡ℎ𝑒	ADJ
cana-730	44	21	𝑠𝑒𝑟𝑣𝑒𝑟	𝑠𝑒𝑟𝑣𝑒𝑟	NOUN
cana-730	44	22	𝑖𝑠	𝑖𝑠	ADP
cana-730	44	23	𝑖𝑛	𝑖𝑛	PRON
cana-730	44	24	𝑚𝑎𝑖𝑛𝑡𝑒𝑛𝑎𝑛𝑐𝑒	𝑚𝑎𝑖𝑛𝑡𝑒𝑛𝑎𝑛𝑐𝑒	PROPN
cana-730	44	25	𝑠𝑡𝑎𝑡𝑒	𝑠𝑡𝑎𝑡𝑒	NOUN
cana-730	44	26	,	,	PUNCT
cana-730	44	27	1	1	NUM
cana-730	44	28	,	,	PUNCT
cana-730	44	29	𝑡ℎ𝑒	𝑡ℎ𝑒	NUM
cana-730	44	30	𝑠𝑒𝑟𝑣𝑒𝑟	𝑠𝑒𝑟𝑣𝑒𝑟	NOUN
cana-730	45	1	𝑖𝑠	𝑖𝑠	ADP
cana-730	45	2	𝑖𝑛	𝑖𝑛	PROPN
cana-730	46	1	𝑛𝑜𝑟𝑚𝑎𝑙	𝑛𝑜𝑟𝑚𝑎𝑙	PROPN
cana-730	46	2	𝑠𝑡𝑎𝑡𝑒	𝑠𝑡𝑎𝑡𝑒	ADJ
cana-730	46	3	,	,	PUNCT
cana-730	46	4	2	2	NUM
cana-730	46	5	,	,	PUNCT
cana-730	46	6	𝑡ℎ𝑒	𝑡ℎ𝑒	ADJ
cana-730	46	7	𝑠𝑒𝑟𝑣𝑒𝑟	𝑠𝑒𝑟𝑣𝑒𝑟	NOUN
cana-730	47	1	𝑖𝑠	𝑖𝑠	INTJ
cana-730	48	1	𝑖𝑛	𝑖𝑛	PROPN
cana-730	48	2	𝑤𝑜𝑟𝑘𝑖𝑛𝑔	𝑤𝑜𝑟𝑘𝑖𝑛𝑔	PROPN
cana-730	48	3	𝑏𝑟𝑒𝑎𝑘𝑑𝑤𝑛	𝑏𝑟𝑒𝑎𝑘𝑑𝑤𝑛	VERB
cana-730	48	4	𝑠𝑡𝑎𝑡𝑒	𝑠𝑡𝑎𝑡𝑒	PROPN
cana-730	48	5	let	let	VERB
cana-730	48	6	x	x	SYM
cana-730	48	7	(	(	PUNCT
cana-730	48	8	t	t	NOUN
cana-730	48	9	)	)	PUNCT
cana-730	48	10	be	be	VERB
cana-730	48	11	the	the	DET
cana-730	48	12	number	number	NOUN
cana-730	48	13	of	of	ADP
cana-730	48	14	customers	customer	NOUN
cana-730	48	15	present	present	ADJ
cana-730	48	16	in	in	ADP
cana-730	48	17	the	the	DET
cana-730	48	18	system	system	NOUN
cana-730	48	19	at	at	ADP
cana-730	48	20	time	time	NOUN
cana-730	48	21	t.	t.	PROPN
cana-730	48	22	then	then	ADV
cana-730	48	23	{	{	PUNCT
cana-730	48	24	(	(	PUNCT
cana-730	48	25	𝐶(𝑡	𝐶(𝑡	NOUN
cana-730	48	26	)	)	PUNCT
cana-730	48	27	,	,	PUNCT
cana-730	48	28	𝑋(𝑡	𝑋(𝑡	PROPN
cana-730	48	29	)	)	PUNCT
cana-730	48	30	)	)	PUNCT
cana-730	48	31	,	,	PUNCT
cana-730	48	32	𝑡	𝑡	PROPN
cana-730	48	33	≥	≥	NOUN
cana-730	48	34	0	0	NUM
cana-730	48	35	}	}	PUNCT
cana-730	48	36	is	be	AUX
cana-730	48	37	a	a	DET
cana-730	48	38	ctmc	ctmc	NOUN
cana-730	48	39	.	.	PUNCT
cana-730	49	1	𝑃𝑖,𝑛(𝑡	𝑃𝑖,𝑛(𝑡	NOUN
cana-730	49	2	)	)	PUNCT
cana-730	50	1	=	=	SYM
cana-730	50	2	𝑃𝑟𝑜𝑏{𝐶(𝑡	𝑃𝑟𝑜𝑏{𝐶(𝑡	PRON
cana-730	50	3	)	)	PUNCT
cana-730	50	4	=	=	SYM
cana-730	50	5	𝑖	𝑖	PROPN
cana-730	50	6	,	,	PUNCT
cana-730	50	7	𝑋(𝑡	𝑋(𝑡	PROPN
cana-730	50	8	)	)	PUNCT
cana-730	50	9	=	=	SYM
cana-730	50	10	𝑛	𝑛	PROPN
cana-730	50	11	}	}	PUNCT
cana-730	50	12	,	,	PUNCT
cana-730	50	13	𝑖	𝑖	NOUN
cana-730	51	1	=	=	PUNCT
cana-730	51	2	0,1,2	0,1,2	NUM
cana-730	51	3	,	,	PUNCT
cana-730	51	4	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-730	51	5	𝑛	𝑛	PRON
cana-730	51	6	≥	≥	NOUN
cana-730	51	7	0	0	NUM
cana-730	51	8	.	.	NOUN
cana-730	51	9	3	3	NUM
cana-730	51	10	stability	stability	NOUN
cana-730	51	11	condition	condition	NOUN
cana-730	51	12	a	a	DET
cana-730	51	13	matrix	matrix	NOUN
cana-730	51	14	geometric	geometric	ADJ
cana-730	51	15	method	method	NOUN
cana-730	51	16	is	be	AUX
cana-730	51	17	applied	apply	VERB
cana-730	51	18	to	to	PART
cana-730	51	19	analyze	analyze	VERB
cana-730	51	20	the	the	DET
cana-730	51	21	problem	problem	NOUN
cana-730	51	22	and	and	CCONJ
cana-730	51	23	to	to	PART
cana-730	51	24	derive	derive	VERB
cana-730	51	25	the	the	DET
cana-730	51	26	stability	stability	NOUN
cana-730	51	27	condition	condition	NOUN
cana-730	51	28	of	of	ADP
cana-730	51	29	the	the	DET
cana-730	51	30	model	model	NOUN
cana-730	51	31	.	.	PUNCT
cana-730	52	1	using	use	VERB
cana-730	52	2	the	the	DET
cana-730	52	3	lexicographical	lexicographical	ADJ
cana-730	52	4	order	order	NOUN
cana-730	52	5	for	for	ADP
cana-730	52	6	the	the	DET
cana-730	52	7	states	state	NOUN
cana-730	52	8	,	,	PUNCT
cana-730	52	9	the	the	DET
cana-730	52	10	infinitesimal	infinitesimal	ADJ
cana-730	52	11	generator	generator	NOUN
cana-730	52	12	of	of	ADP
cana-730	52	13	the	the	DET
cana-730	52	14	process	process	NOUN
cana-730	52	15	{	{	PUNCT
cana-730	52	16	(	(	PUNCT
cana-730	52	17	𝑋(𝑡	𝑋(𝑡	PROPN
cana-730	52	18	)	)	PUNCT
cana-730	52	19	,	,	PUNCT
cana-730	52	20	𝐶(𝑡	𝐶(𝑡	NOUN
cana-730	52	21	)	)	PUNCT
cana-730	52	22	)	)	PUNCT
cana-730	52	23	,	,	PUNCT
cana-730	52	24	𝑡	𝑡	PROPN
cana-730	52	25	≥	≥	NOUN
cana-730	52	26	0	0	NUM
cana-730	52	27	}	}	PUNCT
cana-730	52	28	can	can	AUX
cana-730	52	29	be	be	AUX
cana-730	52	30	written	write	VERB
cana-730	52	31	as	as	ADP
cana-730	52	32	a	a	DET
cana-730	52	33	block	block	NOUN
cana-730	52	34	jacobi	jacobi	NOUN
cana-730	52	35	matrix	matrix	NOUN
cana-730	52	36	and	and	CCONJ
cana-730	52	37	is	be	AUX
cana-730	52	38	denoted	denote	VERB
cana-730	52	39	as	as	ADP
cana-730	52	40	𝑄	𝑄	PROPN
cana-730	52	41	=	=	PRON
cana-730	53	1	[	[	PUNCT
cana-730	53	2	𝐴00	𝐴00	PROPN
cana-730	53	3	𝐵00	𝐵00	PROPN
cana-730	53	4	⬚	⬚	PROPN
cana-730	53	5	⬚	⬚	PROPN
cana-730	53	6	⋮	⋮	NOUN
cana-730	53	7	𝐴1	𝐴1	PROPN
cana-730	53	8	𝐵0	𝐵0	VERB
cana-730	53	9	𝐶0	𝐶0	PROPN
cana-730	53	10	⬚	⬚	PROPN
cana-730	53	11	⋮	⋮	NOUN
cana-730	53	12	𝐴2	𝐴2	PROPN
cana-730	53	13	𝐵1	𝐵1	PROPN
cana-730	53	14	𝐵0	𝐵0	PROPN
cana-730	53	15	𝐶0	𝐶0	PROPN
cana-730	53	16	⋮	⋮	PROPN
cana-730	53	17	𝐴3	𝐴3	PROPN
cana-730	53	18	𝐵2	𝐵2	PROPN
cana-730	53	19	𝐵1	𝐵1	PROPN
cana-730	53	20	𝐵0	𝐵0	PROPN
cana-730	53	21	⋮	⋮	PROPN
cana-730	53	22	𝐴4	𝐴4	PROPN
cana-730	53	23	𝐵3	𝐵3	PROPN
cana-730	53	24	𝐵2	𝐵2	PROPN
cana-730	53	25	𝐵1	𝐵1	PROPN
cana-730	53	26	⋮	⋮	PROPN
cana-730	53	27	𝐴5	𝐴5	NOUN
cana-730	53	28	…	…	PUNCT
cana-730	53	29	𝐵4	𝐵4	NOUN
cana-730	53	30	…	…	PUNCT
cana-730	53	31	𝐵3	𝐵3	NOUN
cana-730	53	32	…	…	PUNCT
cana-730	53	33	𝐵2	𝐵2	NOUN
cana-730	53	34	…	…	SYM
cana-730	53	35	⋮	⋮	NOUN
cana-730	53	36	⋮	⋮	NOUN
cana-730	53	37	⋯	⋯	X
cana-730	53	38	]	]	PUNCT
cana-730	53	39	------(1	------(1	PROPN
cana-730	53	40	)	)	PUNCT
cana-730	53	41	where	where	SCONJ
cana-730	53	42	𝐶0	𝐶0	PROPN
cana-730	53	43	,	,	PUNCT
cana-730	53	44	𝐵0	𝐵0	NOUN
cana-730	53	45	and	and	CCONJ
cana-730	53	46	𝐵𝑖(𝑖	𝐵𝑖(𝑖	PROPN
cana-730	53	47	=	=	SYM
cana-730	53	48	1,2	1,2	NUM
cana-730	53	49	,	,	PUNCT
cana-730	53	50	.	.	PUNCT
cana-730	53	51	.	.	PUNCT
cana-730	53	52	.	.	PUNCT
cana-730	53	53	)	)	PUNCT
cana-730	54	1	are	be	AUX
cana-730	54	2	matrices	matrix	NOUN
cana-730	54	3	of	of	ADP
cana-730	54	4	order	order	NOUN
cana-730	54	5	m	m	INTJ
cana-730	54	6	(	(	PUNCT
cana-730	54	7	the	the	DET
cana-730	54	8	number	number	NOUN
cana-730	54	9	of	of	ADP
cana-730	54	10	environmental	environmental	ADJ
cana-730	54	11	states	state	NOUN
cana-730	54	12	,	,	PUNCT
cana-730	54	13	that	that	PRON
cana-730	54	14	is	be	AUX
cana-730	54	15	m=4	m=4	ADV
cana-730	54	16	in	in	ADP
cana-730	54	17	this	this	DET
cana-730	54	18	study	study	NOUN
cana-730	54	19	)	)	PUNCT
cana-730	54	20	.	.	PUNCT
cana-730	55	1	𝐵0	𝐵0	PROPN
cana-730	55	2	is	be	AUX
cana-730	55	3	the	the	DET
cana-730	55	4	generator	generator	NOUN
cana-730	55	5	of	of	ADP
cana-730	55	6	the	the	DET
cana-730	55	7	environmental	environmental	ADJ
cana-730	55	8	process	process	NOUN
cana-730	55	9	,	,	PUNCT
cana-730	55	10	𝐵𝑖(𝑖	𝐵𝑖(𝑖	NOUN
cana-730	55	11	=	=	SYM
cana-730	55	12	1,2	1,2	NUM
cana-730	55	13	,	,	PUNCT
cana-730	55	14	.	.	PUNCT
cana-730	55	15	.	.	PUNCT
cana-730	55	16	.	.	PUNCT
cana-730	56	1	)	)	PUNCT
cana-730	56	2	are	be	AUX
cana-730	56	3	diagonal	diagonal	ADJ
cana-730	56	4	matrices	matrix	NOUN
cana-730	56	5	.	.	PUNCT
cana-730	57	1	each	each	DET
cana-730	57	2	element	element	NOUN
cana-730	57	3	of	of	ADP
cana-730	57	4	the	the	DET
cana-730	57	5	matrix	matrix	NOUN
cana-730	57	6	q	q	NOUN
cana-730	57	7	is	be	AUX
cana-730	57	8	listed	list	VERB
cana-730	57	9	in	in	ADP
cana-730	57	10	the	the	DET
cana-730	57	11	following	following	NOUN
cana-730	57	12	.	.	PUNCT
cana-730	58	1	communications	communication	NOUN
cana-730	58	2	on	on	ADP
cana-730	58	3	applied	apply	VERB
cana-730	58	4	nonlinear	nonlinear	ADJ
cana-730	58	5	analysis	analysis	NOUN
cana-730	58	6	issn	issn	NOUN
cana-730	58	7	:	:	PUNCT
cana-730	58	8	1074	1074	NUM
cana-730	58	9	-	-	PUNCT
cana-730	58	10	133x	133x	NUM
cana-730	58	11	vol	vol	NOUN
cana-730	58	12	31	31	NUM
cana-730	58	13	no	no	NOUN
cana-730	58	14	.	.	PUNCT
cana-730	59	1	3s	3s	NUM
cana-730	59	2	(	(	PUNCT
cana-730	59	3	2024	2024	NUM
cana-730	59	4	)	)	PUNCT
cana-730	59	5	46	46	NUM
cana-730	59	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-730	60	1	𝐴00	𝐴00	PROPN
cana-730	60	2	=	=	PUNCT
cana-730	61	1	[	[	PUNCT
cana-730	61	2	−𝜆	−𝜆	NOUN
cana-730	61	3	+	+	CCONJ
cana-730	61	4	𝛾	𝛾	NOUN
cana-730	61	5	𝛾	𝛾	NOUN
cana-730	61	6	0	0	NUM
cana-730	61	7	−𝜆	−𝜆	PROPN
cana-730	61	8	]	]	X
cana-730	61	9	,	,	PUNCT
cana-730	61	10	𝐴𝑖	𝐴𝑖	PROPN
cana-730	61	11	=	=	PUNCT
cana-730	61	12	[	[	PUNCT
cana-730	61	13	𝜆𝑔𝑖	𝜆𝑔𝑖	NOUN
cana-730	61	14	0	0	NUM
cana-730	61	15	0	0	NUM
cana-730	61	16	0	0	NUM
cana-730	61	17	𝜆𝑔𝑖	𝜆𝑔𝑖	NOUN
cana-730	61	18	0	0	NUM
cana-730	61	19	]	]	PUNCT
cana-730	61	20	,	,	PUNCT
cana-730	61	21	𝐵00	𝐵00	PROPN
cana-730	61	22	=	=	PUNCT
cana-730	62	1	[	[	PUNCT
cana-730	62	2	0	0	NUM
cana-730	62	3	0	0	NUM
cana-730	62	4	0	0	NUM
cana-730	62	5	𝜇	𝜇	ADP
cana-730	62	6	𝜇𝑏	𝜇𝑏	NOUN
cana-730	62	7	0	0	NUM
cana-730	62	8	]	]	PUNCT
cana-730	62	9	,	,	PUNCT
cana-730	62	10	,	,	PUNCT
cana-730	62	11	𝐵0	𝐵0	NOUN
cana-730	62	12	=	=	PUNCT
cana-730	62	13	[	[	PUNCT
cana-730	62	14	−𝜆	−𝜆	NOUN
cana-730	62	15	+	+	CCONJ
cana-730	62	16	𝛾	𝛾	NOUN
cana-730	62	17	𝛾	𝛾	NOUN
cana-730	62	18	0	0	NUM
cana-730	62	19	0	0	NUM
cana-730	62	20	−𝜆	−𝜆	NOUN
cana-730	63	1	+	+	CCONJ
cana-730	63	2	𝛼	𝛼	PRON
cana-730	63	3	+	+	X
cana-730	63	4	𝜇	𝜇	ADP
cana-730	63	5	𝛾	𝛾	NOUN
cana-730	63	6	0	0	NUM
cana-730	63	7	0	0	NUM
cana-730	63	8	−𝜆	−𝜆	NOUN
cana-730	63	9	+	+	X
cana-730	63	10	𝜇𝑏	𝜇𝑏	X
cana-730	63	11	]	]	PUNCT
cana-730	64	1	𝐵𝑖	𝐵𝑖	PROPN
cana-730	64	2	=	=	PUNCT
cana-730	64	3	[	[	PUNCT
cana-730	64	4	𝜆𝑔𝑖	𝜆𝑔𝑖	NOUN
cana-730	64	5	0	0	NUM
cana-730	64	6	0	0	NUM
cana-730	64	7	0	0	NUM
cana-730	64	8	𝜆𝑔𝑖	𝜆𝑔𝑖	NOUN
cana-730	64	9	0	0	NUM
cana-730	64	10	0	0	NUM
cana-730	64	11	0	0	NUM
cana-730	64	12	𝜆𝑔𝑖	𝜆𝑔𝑖	NOUN
cana-730	64	13	]	]	PUNCT
cana-730	64	14	,	,	PUNCT
cana-730	64	15	𝐶0	𝐶0	X
cana-730	64	16	=	=	PUNCT
cana-730	65	1	[	[	PUNCT
cana-730	65	2	0	0	NUM
cana-730	65	3	0	0	NUM
cana-730	65	4	0	0	NUM
cana-730	65	5	0	0	NUM
cana-730	65	6	𝜇	𝜇	ADP
cana-730	65	7	0	0	NUM
cana-730	65	8	𝜇𝑏	𝜇𝑏	NOUN
cana-730	65	9	0	0	NUM
cana-730	65	10	0	0	NUM
cana-730	65	11	]	]	PUNCT
cana-730	65	12	,	,	PUNCT
cana-730	65	13	consider	consider	VERB
cana-730	65	14	𝑏	𝑏	NOUN
cana-730	65	15	=	=	PUNCT
cana-730	65	16	∑𝑖𝐵𝑖	∑𝑖𝐵𝑖	NOUN
cana-730	66	1	=	=	X
cana-730	66	2	[	[	PUNCT
cana-730	66	3	𝜆𝑔	𝜆𝑔	NOUN
cana-730	66	4	0	0	NUM
cana-730	66	5	0	0	NUM
cana-730	66	6	0	0	NUM
cana-730	66	7	𝜆𝑔	𝜆𝑔	NOUN
cana-730	66	8	0	0	NUM
cana-730	66	9	0	0	NUM
cana-730	66	10	0	0	NUM
cana-730	67	1	𝜆𝑔	𝜆𝑔	NOUN
cana-730	67	2	]	]	PUNCT
cana-730	67	3	∞	∞	PUNCT
cana-730	67	4	𝑖=1	𝑖=1	PROPN
cana-730	67	5	where	where	SCONJ
cana-730	67	6	g	g	PROPN
cana-730	67	7	is	be	AUX
cana-730	67	8	the	the	DET
cana-730	67	9	expectation	expectation	NOUN
cana-730	67	10	.	.	PUNCT
cana-730	68	1	from	from	ADP
cana-730	68	2	the	the	DET
cana-730	68	3	theorem	theorem	NOUN
cana-730	68	4	of	of	ADP
cana-730	68	5	neuts	neut	NOUN
cana-730	68	6	(	(	PUNCT
cana-730	68	7	1981	1981	NUM
cana-730	68	8	)	)	PUNCT
cana-730	68	9	,	,	PUNCT
cana-730	68	10	we	we	PRON
cana-730	68	11	know	know	VERB
cana-730	68	12	that	that	SCONJ
cana-730	68	13	the	the	DET
cana-730	68	14	steady	steady	ADJ
cana-730	68	15	-	-	PUNCT
cana-730	68	16	state	state	NOUN
cana-730	68	17	probability	probability	NOUN
cana-730	68	18	vector	vector	NOUN
cana-730	68	19	exists	exist	VERB
cana-730	68	20	if	if	SCONJ
cana-730	68	21	and	and	CCONJ
cana-730	68	22	only	only	ADV
cana-730	68	23	if	if	SCONJ
cana-730	68	24	𝑋𝑏𝑒	𝑋𝑏𝑒	PROPN
cana-730	68	25	<	<	X
cana-730	68	26	𝑋𝐶0𝑒	𝑋𝐶0𝑒	X
cana-730	68	27	------(2	------(2	NOUN
cana-730	68	28	)	)	PUNCT
cana-730	68	29	x	x	X
cana-730	68	30	is	be	AUX
cana-730	68	31	the	the	DET
cana-730	68	32	invariant	invariant	ADJ
cana-730	68	33	probability	probability	NOUN
cana-730	68	34	of	of	ADP
cana-730	68	35	the	the	DET
cana-730	68	36	matrix	matrix	NOUN
cana-730	68	37	𝐷	𝐷	NOUN
cana-730	68	38	=	=	PUNCT
cana-730	68	39	𝐶0	𝐶0	PROPN
cana-730	68	40	+	+	X
cana-730	68	41	𝐵0	𝐵0	NOUN
cana-730	68	42	+	+	CCONJ
cana-730	68	43	𝐵1	𝐵1	NOUN
cana-730	68	44	+	+	CCONJ
cana-730	68	45	⋯	⋯	NOUN
cana-730	68	46	𝐷	𝐷	NOUN
cana-730	68	47	=	=	PUNCT
cana-730	68	48	[	[	PUNCT
cana-730	68	49	−𝛾	−𝛾	ADJ
cana-730	68	50	𝛾	𝛾	NOUN
cana-730	68	51	0	0	NUM
cana-730	68	52	0	0	NUM
cana-730	69	1	−𝛼	−𝛼	PROPN
cana-730	69	2	𝛼	𝛼	PRON
cana-730	69	3	𝜇𝑏	𝜇𝑏	NOUN
cana-730	69	4	0	0	NUM
cana-730	69	5	−𝜇𝑏	−𝜇𝑏	NOUN
cana-730	69	6	]	]	PUNCT
cana-730	69	7	,	,	PUNCT
cana-730	69	8	the	the	DET
cana-730	69	9	vector	vector	NOUN
cana-730	69	10	x	x	NOUN
cana-730	69	11	satisfies	satisfy	VERB
cana-730	69	12	xd=0	xd=0	PROPN
cana-730	69	13	and	and	CCONJ
cana-730	69	14	xe=1	xe=1	PROPN
cana-730	69	15	,	,	PUNCT
cana-730	69	16	where	where	SCONJ
cana-730	69	17	𝑒	𝑒	VERB
cana-730	69	18	=	=	PRON
cana-730	69	19	[	[	PUNCT
cana-730	69	20	1	1	NUM
cana-730	69	21	1	1	NUM
cana-730	69	22	1	1	NUM
cana-730	69	23	]	]	PUNCT
cana-730	69	24	3𝑥1	3𝑥1	NUM
cana-730	69	25	.after	.after	NOUN
cana-730	70	1	some	some	DET
cana-730	70	2	calculations	calculation	NOUN
cana-730	70	3	,	,	PUNCT
cana-730	70	4	the	the	DET
cana-730	70	5	vector	vector	NOUN
cana-730	70	6	𝑋	𝑋	NOUN
cana-730	70	7	=	=	SYM
cana-730	70	8	1	1	NUM
cana-730	70	9	𝜇𝑏𝛼+𝜇𝑏𝛾+𝛼𝛾	𝜇𝑏𝛼+𝜇𝑏𝛾+𝛼𝛾	VERB
cana-730	70	10	[	[	X
cana-730	70	11	𝜇𝑏𝛼	𝜇𝑏𝛼	X
cana-730	70	12	𝜇𝑏𝛾	𝜇𝑏𝛾	ADJ
cana-730	70	13	𝜇𝑏𝛾]1𝑥3	𝜇𝑏𝛾]1𝑥3	NOUN
cana-730	70	14	----------------(3	----------------(3	PROPN
cana-730	70	15	)	)	PUNCT
cana-730	70	16	communications	communication	NOUN
cana-730	70	17	on	on	ADP
cana-730	70	18	applied	apply	VERB
cana-730	70	19	nonlinear	nonlinear	ADJ
cana-730	70	20	analysis	analysis	NOUN
cana-730	70	21	issn	issn	NOUN
cana-730	70	22	:	:	PUNCT
cana-730	70	23	1074	1074	NUM
cana-730	70	24	-	-	PUNCT
cana-730	70	25	133x	133x	NUM
cana-730	70	26	vol	vol	NOUN
cana-730	70	27	31	31	NUM
cana-730	70	28	no	no	NOUN
cana-730	70	29	.	.	PUNCT
cana-730	71	1	3s	3s	NUM
cana-730	71	2	(	(	PUNCT
cana-730	71	3	2024	2024	NUM
cana-730	71	4	)	)	PUNCT
cana-730	71	5	47	47	NUM
cana-730	71	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-730	71	7	can	can	AUX
cana-730	71	8	be	be	AUX
cana-730	71	9	obtained	obtain	VERB
cana-730	71	10	and	and	CCONJ
cana-730	71	11	substituting	substitute	VERB
cana-730	71	12	in	in	ADP
cana-730	71	13	the	the	DET
cana-730	71	14	condition	condition	NOUN
cana-730	71	15	(	(	PUNCT
cana-730	71	16	2	2	NUM
cana-730	71	17	)	)	PUNCT
cana-730	71	18	and	and	CCONJ
cana-730	71	19	doing	do	VERB
cana-730	71	20	some	some	DET
cana-730	71	21	algebraic	algebraic	ADJ
cana-730	71	22	manipulation	manipulation	NOUN
cana-730	71	23	leads	lead	VERB
cana-730	71	24	to	to	ADP
cana-730	71	25	𝜌	𝜌	X
cana-730	71	26	=	=	SYM
cana-730	71	27	𝜆𝑔[𝜇𝑏(𝛼+𝛾)+𝛼𝛾	𝜆𝑔[𝜇𝑏(𝛼+𝛾)+𝛼𝛾	PROPN
cana-730	71	28	]	]	X
cana-730	71	29	𝜇𝑏𝛾[𝜇+𝛼	𝜇𝑏𝛾[𝜇+𝛼	X
cana-730	71	30	]	]	X
cana-730	71	31	<	<	X
cana-730	71	32	1	1	NUM
cana-730	71	33	--------(4	--------(4	NOUN
cana-730	71	34	)	)	PUNCT
cana-730	71	35	4	4	NUM
cana-730	71	36	steady	steady	ADJ
cana-730	71	37	state	state	NOUN
cana-730	71	38	analysis	analysis	NOUN
cana-730	71	39	the	the	DET
cana-730	71	40	steady	steady	ADJ
cana-730	71	41	state	state	NOUN
cana-730	71	42	probabilities	probability	NOUN
cana-730	71	43	equations	equation	NOUN
cana-730	71	44	governing	govern	VERB
cana-730	71	45	the	the	DET
cana-730	71	46	model	model	NOUN
cana-730	71	47	are	be	AUX
cana-730	71	48	derived	derive	VERB
cana-730	71	49	as	as	SCONJ
cana-730	71	50	follows	follow	VERB
cana-730	71	51	:	:	PUNCT
cana-730	71	52	(	(	PUNCT
cana-730	72	1	𝜆	𝜆	X
cana-730	72	2	+	+	NUM
cana-730	72	3	𝛾)𝑃0,0	𝛾)𝑃0,0	NOUN
cana-730	72	4	=	=	SYM
cana-730	72	5	𝜇𝑏𝑃2,1	𝜇𝑏𝑃2,1	ADV
cana-730	72	6	,	,	PUNCT
cana-730	72	7	𝑛	𝑛	PRON
cana-730	72	8	=	=	SYM
cana-730	72	9	0	0	NUM
cana-730	72	10	---------------(5	---------------(5	NOUN
cana-730	72	11	)	)	PUNCT
cana-730	72	12	(	(	PUNCT
cana-730	72	13	𝜆	𝜆	X
cana-730	72	14	+	+	X
cana-730	72	15	𝛾)𝑃0,𝑛	𝛾)𝑃0,𝑛	NOUN
cana-730	72	16	=	=	SYM
cana-730	72	17	𝜆	𝜆	PRON
cana-730	72	18	∑	∑	PUNCT
cana-730	72	19	𝑔𝑖𝑃0,𝑛−𝑖	𝑔𝑖𝑃0,𝑛−𝑖	X
cana-730	72	20	+	+	X
cana-730	72	21	𝜇𝑏𝑃2,𝑛+1	𝜇𝑏𝑃2,𝑛+1	PROPN
cana-730	72	22	,	,	PUNCT
cana-730	72	23	𝑛	𝑛	PRON
cana-730	72	24	≥	≥	NOUN
cana-730	72	25	1𝑛	1𝑛	NOUN
cana-730	72	26	𝑖=1	𝑖=1	PROPN
cana-730	72	27	--------------(6	--------------(6	PROPN
cana-730	72	28	)	)	PUNCT
cana-730	72	29	𝜆𝑃1,0	𝜆𝑃1,0	NOUN
cana-730	73	1	=	=	PUNCT
cana-730	73	2	𝜇𝑃1,1	𝜇𝑃1,1	NOUN
cana-730	73	3	+	+	NUM
cana-730	73	4	𝛾𝑃0,0	𝛾𝑃0,0	NOUN
cana-730	73	5	,	,	PUNCT
cana-730	73	6	𝑛	𝑛	PRON
cana-730	73	7	=	=	SYM
cana-730	73	8	0	0	NUM
cana-730	73	9	-----------------(7	-----------------(7	NOUN
cana-730	73	10	)	)	PUNCT
cana-730	73	11	(	(	PUNCT
cana-730	73	12	𝜆	𝜆	X
cana-730	73	13	+	+	X
cana-730	73	14	𝜇	𝜇	ADP
cana-730	73	15	+	+	NOUN
cana-730	73	16	𝛼)𝑃1,𝑛	𝛼)𝑃1,𝑛	PROPN
cana-730	73	17	=	=	SYM
cana-730	73	18	𝜇𝑃1,𝑛+1	𝜇𝑃1,𝑛+1	PROPN
cana-730	74	1	+	+	CCONJ
cana-730	74	2	𝛾𝑃0,𝑛	𝛾𝑃0,𝑛	PROPN
cana-730	74	3	+	+	CCONJ
cana-730	74	4	𝜆	𝜆	ADP
cana-730	74	5	∑	∑	PUNCT
cana-730	74	6	𝑔𝑖𝑃1,𝑛−𝑖	𝑔𝑖𝑃1,𝑛−𝑖	NOUN
cana-730	74	7	,	,	PUNCT
cana-730	74	8	𝑛	𝑛	DET
cana-730	74	9	≥	≥	NOUN
cana-730	74	10	1𝑛	1𝑛	NOUN
cana-730	74	11	𝑖=1	𝑖=1	PROPN
cana-730	74	12	(	(	PUNCT
cana-730	74	13	8)	8)	NUM
cana-730	74	14	(	(	PUNCT
cana-730	74	15	𝜆	𝜆	NOUN
cana-730	74	16	+	+	CCONJ
cana-730	74	17	𝜇𝑏)𝑃2,1	𝜇𝑏)𝑃2,1	NOUN
cana-730	74	18	=	=	SYM
cana-730	74	19	𝛼𝑃1,1	𝛼𝑃1,1	NOUN
cana-730	74	20	,	,	PUNCT
cana-730	74	21	𝑛	𝑛	NOUN
cana-730	74	22	=	=	SYM
cana-730	74	23	1	1	NUM
cana-730	74	24	---------------(9	---------------(9	NUM
cana-730	74	25	)	)	PUNCT
cana-730	74	26	(	(	PUNCT
cana-730	74	27	𝜆	𝜆	X
cana-730	74	28	+	+	CCONJ
cana-730	74	29	𝜇𝑏)𝑃2,𝑛	𝜇𝑏)𝑃2,𝑛	NOUN
cana-730	74	30	=	=	SYM
cana-730	74	31	𝛼𝑃1,𝑛	𝛼𝑃1,𝑛	PROPN
cana-730	75	1	+	+	CCONJ
cana-730	75	2	𝜆	𝜆	ADP
cana-730	75	3	∑	∑	PUNCT
cana-730	75	4	𝑔𝑖𝑃2,𝑛−𝑖	𝑔𝑖𝑃2,𝑛−𝑖	NOUN
cana-730	75	5	,	,	PUNCT
cana-730	75	6	𝑛	𝑛	DET
cana-730	75	7	≥	≥	NUM
cana-730	75	8	2𝑛−1	2𝑛−1	NUM
cana-730	75	9	𝑖=1	𝑖=1	PROPN
cana-730	75	10	--------------(10	--------------(10	PROPN
cana-730	75	11	)	)	PUNCT
cana-730	75	12	define	define	VERB
cana-730	75	13	the	the	DET
cana-730	75	14	following	follow	VERB
cana-730	75	15	partial	partial	ADJ
cana-730	75	16	probability	probability	NOUN
cana-730	75	17	generating	generating	NOUN
cana-730	75	18	functions	function	NOUN
cana-730	75	19	:	:	PUNCT
cana-730	75	20	𝑃0(𝑍	𝑃0(𝑍	ADV
cana-730	75	21	)	)	PUNCT
cana-730	75	22	=	=	PUNCT
cana-730	76	1	∑	∑	PUNCT
cana-730	76	2	𝑃0,𝑛𝑍𝑛∞	𝑃0,𝑛𝑍𝑛∞	ADJ
cana-730	76	3	𝑛=0	𝑛=0	PROPN
cana-730	76	4	,	,	PUNCT
cana-730	76	5	𝑃1(𝑍	𝑃1(𝑍	PROPN
cana-730	76	6	)	)	PUNCT
cana-730	76	7	=	=	PUNCT
cana-730	76	8	∑	∑	PUNCT
cana-730	76	9	𝑃1,𝑛𝑍𝑛∞	𝑃1,𝑛𝑍𝑛∞	NOUN
cana-730	76	10	𝑛=1	𝑛=1	NOUN
cana-730	76	11	,	,	PUNCT
cana-730	76	12	𝑃2(𝑍	𝑃2(𝑍	NOUN
cana-730	76	13	)	)	PUNCT
cana-730	76	14	=	=	SYM
cana-730	76	15	∑	∑	PUNCT
cana-730	76	16	𝑃2,𝑛𝑍𝑛∞	𝑃2,𝑛𝑍𝑛∞	NOUN
cana-730	76	17	𝑛=1	𝑛=1	NOUN
cana-730	76	18	,	,	PUNCT
cana-730	76	19	𝐺(𝑧	𝐺(𝑧	NUM
cana-730	76	20	)	)	PUNCT
cana-730	76	21	=	=	SYM
cana-730	76	22	∑	∑	PROPN
cana-730	76	23	𝑔𝑖𝑧	𝑔𝑖𝑧	PROPN
cana-730	76	24	𝑛	𝑛	PROPN
cana-730	76	25	,	,	PUNCT
cana-730	76	26	𝑖	𝑖	DET
cana-730	76	27	≥	≥	NOUN
cana-730	76	28	1∞	1∞	NUM
cana-730	76	29	𝑛=1	𝑛=1	NOUN
cana-730	76	30	solving	solve	VERB
cana-730	76	31	the	the	DET
cana-730	76	32	above	above	ADJ
cana-730	76	33	equations	equation	NOUN
cana-730	76	34	along	along	ADP
cana-730	76	35	with	with	ADP
cana-730	76	36	the	the	DET
cana-730	76	37	corresponding	corresponding	ADJ
cana-730	76	38	probability	probability	NOUN
cana-730	76	39	generating	generating	NOUN
cana-730	76	40	functions	function	NOUN
cana-730	76	41	we	we	PRON
cana-730	76	42	get	get	VERB
cana-730	76	43	:	:	PUNCT
cana-730	77	1	[	[	X
cana-730	77	2	𝜆𝑍(1	𝜆𝑍(1	X
cana-730	77	3	−	−	NOUN
cana-730	77	4	𝐺(𝑍	𝐺(𝑍	NOUN
cana-730	77	5	)	)	PUNCT
cana-730	77	6	)	)	PUNCT
cana-730	78	1	+	+	CCONJ
cana-730	78	2	𝛾𝑍]𝑃0(𝑍	𝛾𝑍]𝑃0(𝑍	NOUN
cana-730	78	3	)	)	PUNCT
cana-730	78	4	−	−	PROPN
cana-730	78	5	𝜇𝑏𝑃2(𝑍	𝜇𝑏𝑃2(𝑍	NOUN
cana-730	78	6	)	)	PUNCT
cana-730	78	7	=	=	SYM
cana-730	78	8	0	0	NUM
cana-730	78	9	-----------(11	-----------(11	NOUN
cana-730	78	10	)	)	PUNCT
cana-730	78	11	−𝛾𝑃0(𝑍	−𝛾𝑃0(𝑍	PROPN
cana-730	78	12	)	)	PUNCT
cana-730	79	1	+	+	CCONJ
cana-730	80	1	[	[	X
cana-730	80	2	𝜆(1	𝜆(1	NOUN
cana-730	80	3	−	−	NOUN
cana-730	80	4	𝐺(𝑍	𝐺(𝑍	NUM
cana-730	80	5	)	)	PUNCT
cana-730	80	6	)	)	PUNCT
cana-730	81	1	+	+	NUM
cana-730	81	2	𝛼	𝛼	X
cana-730	82	1	+	+	CCONJ
cana-730	82	2	𝜇(1	𝜇(1	PROPN
cana-730	82	3	−	−	PROPN
cana-730	82	4	1/𝑍)]𝑃1(𝑍	1/𝑍)]𝑃1(𝑍	NUM
cana-730	82	5	)	)	PUNCT
cana-730	82	6	=	=	PUNCT
cana-730	83	1	[	[	X
cana-730	83	2	𝛼+𝜇(1	𝛼+𝜇(1	NOUN
cana-730	83	3	−	−	NOUN
cana-730	83	4	1/𝑍)]𝑃1,0	1/𝑍)]𝑃1,0	NUM
cana-730	83	5	---------(12	---------(12	NOUN
cana-730	83	6	)	)	PUNCT
cana-730	84	1	[	[	X
cana-730	84	2	𝜆𝑍(1	𝜆𝑍(1	X
cana-730	84	3	−	−	NOUN
cana-730	84	4	𝐺(𝑍	𝐺(𝑍	NOUN
cana-730	84	5	)	)	PUNCT
cana-730	84	6	)	)	PUNCT
cana-730	85	1	+	+	CCONJ
cana-730	85	2	𝜇𝑏]𝑃2(𝑍	𝜇𝑏]𝑃2(𝑍	NOUN
cana-730	85	3	)	)	PUNCT
cana-730	85	4	−	−	PROPN
cana-730	85	5	𝛼𝑃1(𝑍	𝛼𝑃1(𝑍	NOUN
cana-730	85	6	)	)	PUNCT
cana-730	86	1	=	=	PUNCT
cana-730	87	1	−𝛼𝑃1,0	−𝛼𝑃1,0	PROPN
cana-730	87	2	-------------(13	-------------(13	NOUN
cana-730	87	3	)	)	PUNCT
cana-730	87	4	which	which	PRON
cana-730	87	5	is	be	AUX
cana-730	87	6	turn	turn	NOUN
cana-730	87	7	yields	yield	VERB
cana-730	87	8	𝑃0(𝑍	𝑃0(𝑍	ADV
cana-730	87	9	)	)	PUNCT
cana-730	87	10	=	=	SYM
cana-730	87	11	𝐴0(𝑍	𝐴0(𝑍	PROPN
cana-730	87	12	)	)	PUNCT
cana-730	87	13	δ′(𝑍	δ′(𝑍	PROPN
cana-730	87	14	)	)	PUNCT
cana-730	87	15	-------------(14	-------------(14	NOUN
cana-730	87	16	)	)	PUNCT
cana-730	87	17	𝑃1(𝑍	𝑃1(𝑍	PROPN
cana-730	87	18	)	)	PUNCT
cana-730	87	19	=	=	SYM
cana-730	87	20	𝐴1(𝑍	𝐴1(𝑍	PROPN
cana-730	87	21	)	)	PUNCT
cana-730	87	22	δ′(𝑍	δ′(𝑍	PROPN
cana-730	87	23	)	)	PUNCT
cana-730	87	24	------------(15	------------(15	PROPN
cana-730	87	25	)	)	PUNCT
cana-730	87	26	𝑃2(𝑍	𝑃2(𝑍	NOUN
cana-730	87	27	)	)	PUNCT
cana-730	87	28	=	=	SYM
cana-730	87	29	𝐴2(𝑍	𝐴2(𝑍	PROPN
cana-730	87	30	)	)	PUNCT
cana-730	87	31	δ′(𝑍	δ′(𝑍	PROPN
cana-730	87	32	)	)	PUNCT
cana-730	87	33	-------------(16	-------------(16	NOUN
cana-730	87	34	)	)	PUNCT
cana-730	87	35	𝑃(𝑍	𝑃(𝑍	NOUN
cana-730	87	36	)	)	PUNCT
cana-730	87	37	=	=	SYM
cana-730	87	38	𝑃0(𝑍	𝑃0(𝑍	ADV
cana-730	87	39	)	)	PUNCT
cana-730	87	40	+	+	PUNCT
cana-730	88	1	𝑃1(𝑍	𝑃1(𝑍	NOUN
cana-730	88	2	)	)	PUNCT
cana-730	88	3	+	+	X
cana-730	88	4	𝑃2(𝑍	𝑃2(𝑍	NOUN
cana-730	88	5	)	)	PUNCT
cana-730	88	6	+	+	CCONJ
cana-730	89	1	𝑃3(𝑍	𝑃3(𝑍	X
cana-730	89	2	)	)	PUNCT
cana-730	89	3	----------(17	----------(17	VERB
cana-730	89	4	)	)	PUNCT
cana-730	89	5	where	where	SCONJ
cana-730	89	6	,	,	PUNCT
cana-730	89	7	𝐴0(𝑍	𝐴0(𝑍	PROPN
cana-730	89	8	)	)	PUNCT
cana-730	89	9	=	=	SYM
cana-730	89	10	𝜆𝜇𝑏𝛼𝐺′(𝑍)𝑃1,0	𝜆𝜇𝑏𝛼𝐺′(𝑍)𝑃1,0	PUNCT
cana-730	90	1	communications	communication	NOUN
cana-730	90	2	on	on	ADP
cana-730	90	3	applied	apply	VERB
cana-730	90	4	nonlinear	nonlinear	ADJ
cana-730	90	5	analysis	analysis	NOUN
cana-730	90	6	issn	issn	NOUN
cana-730	90	7	:	:	PUNCT
cana-730	90	8	1074	1074	NUM
cana-730	90	9	-	-	PUNCT
cana-730	90	10	133x	133x	NUM
cana-730	90	11	vol	vol	NOUN
cana-730	90	12	31	31	NUM
cana-730	90	13	no	no	NOUN
cana-730	90	14	.	.	PUNCT
cana-730	91	1	3s	3s	NUM
cana-730	91	2	(	(	PUNCT
cana-730	91	3	2024	2024	NUM
cana-730	91	4	)	)	PUNCT
cana-730	91	5	48	48	NUM
cana-730	91	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-730	91	7	𝐴1(𝑍	𝐴1(𝑍	PROPN
cana-730	91	8	)	)	PUNCT
cana-730	91	9	=	=	PUNCT
cana-730	92	1	[	[	X
cana-730	92	2	𝜆2𝛼[−2𝑍(1	𝜆2𝛼[−2𝑍(1	NOUN
cana-730	92	3	−	−	PROPN
cana-730	92	4	𝐺(𝑍))𝐺′(𝑍	𝐺(𝑍))𝐺′(𝑍	PROPN
cana-730	92	5	)	)	PUNCT
cana-730	93	1	+	+	CCONJ
cana-730	93	2	(	(	PUNCT
cana-730	93	3	1	1	NUM
cana-730	93	4	−	−	NOUN
cana-730	93	5	𝐺(𝑍)))2	𝐺(𝑍)))2	NOUN
cana-730	93	6	]	]	PUNCT
cana-730	94	1	+	+	CCONJ
cana-730	94	2	[	[	X
cana-730	94	3	𝜆𝛼𝜇𝑏	𝜆𝛼𝜇𝑏	X
cana-730	94	4	+	+	NUM
cana-730	94	5	𝛾𝛼𝜆][−𝑍𝐺′(𝑍	𝛾𝛼𝜆][−𝑍𝐺′(𝑍	NOUN
cana-730	94	6	)	)	PUNCT
cana-730	95	1	+	+	CCONJ
cana-730	95	2	(	(	PUNCT
cana-730	95	3	1	1	NUM
cana-730	95	4	−	−	NOUN
cana-730	95	5	𝐺(𝑍	𝐺(𝑍	NOUN
cana-730	95	6	)	)	PUNCT
cana-730	95	7	)	)	PUNCT
cana-730	95	8	]	]	PUNCT
cana-730	96	1	+	+	CCONJ
cana-730	96	2	[	[	X
cana-730	96	3	𝜆𝜇𝜇𝑏	𝜆𝜇𝜇𝑏	X
cana-730	96	4	+	+	CCONJ
cana-730	96	5	𝜆𝜇𝛾]𝑥[(1	𝜆𝜇𝛾]𝑥[(1	PROPN
cana-730	96	6	−	−	NOUN
cana-730	96	7	𝑍)𝐺′(𝑍	𝑍)𝐺′(𝑍	NOUN
cana-730	96	8	)	)	PUNCT
cana-730	96	9	+	+	CCONJ
cana-730	96	10	(	(	PUNCT
cana-730	96	11	1	1	NUM
cana-730	96	12	−	−	NOUN
cana-730	96	13	𝐺(𝑍	𝐺(𝑍	NOUN
cana-730	96	14	)	)	PUNCT
cana-730	96	15	)	)	PUNCT
cana-730	96	16	]	]	PUNCT
cana-730	97	1	+	+	CCONJ
cana-730	97	2	𝜆2𝜇(1	𝜆2𝜇(1	NUM
cana-730	98	1	−	−	PRON
cana-730	99	1	𝑍)2(1	𝑍)2(1	NOUN
cana-730	99	2	−	−	PROPN
cana-730	99	3	𝐺(𝑍))𝐺′(𝑍	𝐺(𝑍))𝐺′(𝑍	ADV
cana-730	99	4	)	)	PUNCT
cana-730	100	1	+	+	CCONJ
cana-730	100	2	(	(	PUNCT
cana-730	100	3	1	1	NUM
cana-730	100	4	−	−	NOUN
cana-730	100	5	𝐺(𝑍)))2	𝐺(𝑍)))2	NOUN
cana-730	100	6	]	]	PUNCT
cana-730	100	7	+	+	NUM
cana-730	100	8	𝛾𝛼𝜇𝑏	𝛾𝛼𝜇𝑏	NOUN
cana-730	100	9	+	+	X
cana-730	100	10	𝛾𝜇𝜇𝑏]𝑃1,0	𝛾𝜇𝜇𝑏]𝑃1,0	X
cana-730	100	11	𝐴2(𝑍	𝐴2(𝑍	NOUN
cana-730	100	12	)	)	PUNCT
cana-730	100	13	=	=	PUNCT
cana-730	101	1	[	[	X
cana-730	101	2	2𝜆2𝛼𝑍(1	2𝜆2𝛼𝑍(1	NUM
cana-730	101	3	−	−	ADP
cana-730	101	4	𝐺(𝑍))𝐺′(𝑍	𝐺(𝑍))𝐺′(𝑍	PROPN
cana-730	101	5	)	)	PUNCT
cana-730	101	6	−	−	ADP
cana-730	101	7	𝛼𝜆2(1	𝛼𝜆2(1	NOUN
cana-730	101	8	−	−	NOUN
cana-730	101	9	𝐺(𝑍)))2	𝐺(𝑍)))2	NOUN
cana-730	101	10	−	−	PROPN
cana-730	101	11	𝛾𝜆𝛼[(1	𝛾𝜆𝛼[(1	ADJ
cana-730	101	12	−	−	NOUN
cana-730	101	13	𝐺(𝑍	𝐺(𝑍	ADJ
cana-730	101	14	)	)	PUNCT
cana-730	101	15	−	−	PROPN
cana-730	101	16	𝑍𝐺′(𝑍)]]𝑃1,0	𝑍𝐺′(𝑍)]]𝑃1,0	SYM
cana-730	101	17	δ′(𝑍	δ′(𝑍	PROPN
cana-730	101	18	)	)	PUNCT
cana-730	101	19	=	=	SYM
cana-730	101	20	𝜆3(1	𝜆3(1	PROPN
cana-730	101	21	−	−	NOUN
cana-730	102	1	𝐺(𝑍)))3	𝐺(𝑍)))3	X
cana-730	102	2	+	+	PUNCT
cana-730	102	3	(	(	PUNCT
cana-730	102	4	1	1	NUM
cana-730	102	5	−	−	NOUN
cana-730	102	6	𝐺(𝑍)))2[−3𝜆3𝑍𝐺′(𝑍	𝐺(𝑍)))2[−3𝜆3𝑍𝐺′(𝑍	NOUN
cana-730	102	7	)	)	PUNCT
cana-730	103	1	+	+	CCONJ
cana-730	103	2	𝜆2(𝜇𝑏	𝜆2(𝜇𝑏	NUM
cana-730	104	1	+	+	NUM
cana-730	104	2	𝛼	𝛼	PRON
cana-730	104	3	+	+	X
cana-730	104	4	𝜇	𝜇	ADP
cana-730	104	5	+	+	NOUN
cana-730	104	6	𝛾	𝛾	NOUN
cana-730	104	7	)	)	PUNCT
cana-730	105	1	+	+	NUM
cana-730	105	2	𝜆(𝛼𝜇𝑏	𝜆(𝛼𝜇𝑏	NOUN
cana-730	106	1	+	+	CCONJ
cana-730	106	2	𝜇𝜇𝑏	𝜇𝜇𝑏	ADJ
cana-730	106	3	+	+	CCONJ
cana-730	106	4	𝛾𝜇𝑏	𝛾𝜇𝑏	NOUN
cana-730	106	5	+	+	CCONJ
cana-730	106	6	𝛾𝛼	𝛾𝛼	X
cana-730	106	7	+	+	NUM
cana-730	106	8	𝛾𝜇	𝛾𝜇	NOUN
cana-730	106	9	)	)	PUNCT
cana-730	106	10	]	]	PUNCT
cana-730	107	1	+	+	CCONJ
cana-730	107	2	𝐺′(𝑍)𝜆𝑍[−𝛾𝛼	𝐺′(𝑍)𝜆𝑍[−𝛾𝛼	PROPN
cana-730	107	3	−	−	PROPN
cana-730	107	4	𝛾𝜇	𝛾𝜇	ADP
cana-730	108	1	+	+	CCONJ
cana-730	108	2	𝛾𝜇	𝛾𝜇	ADP
cana-730	108	3	𝑍	𝑍	PROPN
cana-730	108	4	−	−	NOUN
cana-730	108	5	𝛾𝜇𝑏	𝛾𝜇𝑏	NOUN
cana-730	108	6	−	−	PROPN
cana-730	108	7	𝛼𝜇𝑏	𝛼𝜇𝑏	NOUN
cana-730	108	8	−	−	PROPN
cana-730	108	9	𝜇𝜇𝑏	𝜇𝜇𝑏	VERB
cana-730	108	10	+	+	CCONJ
cana-730	108	11	𝜇𝜇𝑏	𝜇𝜇𝑏	ADJ
cana-730	108	12	𝑍	𝑍	AUX
cana-730	108	13	]	]	PUNCT
cana-730	108	14	+	+	PUNCT
cana-730	108	15	𝛾𝜇𝑏[𝛼	𝛾𝜇𝑏[𝛼	NOUN
cana-730	108	16	+	+	CCONJ
cana-730	108	17	𝜇	𝜇	X
cana-730	108	18	]	]	X
cana-730	108	19	now	now	ADV
cana-730	108	20	letting	let	VERB
cana-730	108	21	z=1	z=1	PUNCT
cana-730	108	22	then	then	ADV
cana-730	108	23	the	the	DET
cana-730	108	24	above	above	ADJ
cana-730	108	25	equations	equation	NOUN
cana-730	108	26	can	can	AUX
cana-730	108	27	be	be	AUX
cana-730	108	28	rewritten	rewrite	VERB
cana-730	108	29	as	as	SCONJ
cana-730	108	30	follows	follow	VERB
cana-730	108	31	:	:	PUNCT
cana-730	108	32	𝑃0(1	𝑃0(1	NUM
cana-730	108	33	)	)	PUNCT
cana-730	109	1	=	=	PUNCT
cana-730	109	2	𝐺′(1)𝜇𝑏𝜆𝛼𝑃1,0	𝐺′(1)𝜇𝑏𝜆𝛼𝑃1,0	NUM
cana-730	109	3	−𝜆𝐺′′(1)[𝛾𝛼+𝛾𝜇𝑏+𝛼𝜇𝑏]+𝛾𝜇𝑏[𝛼+𝜇	−𝜆𝐺′′(1)[𝛾𝛼+𝛾𝜇𝑏+𝛼𝜇𝑏]+𝛾𝜇𝑏[𝛼+𝜇	NOUN
cana-730	109	4	]	]	X
cana-730	109	5	---------(18	---------(18	NOUN
cana-730	109	6	)	)	PUNCT
cana-730	109	7	𝑃1(1	𝑃1(1	ADJ
cana-730	109	8	)	)	PUNCT
cana-730	109	9	=	=	SYM
cana-730	109	10	−𝜆𝛼𝐺′(1)[𝜇𝑏+𝛾]+𝛾𝜇𝑏[𝜇+𝛼]𝑃1,0	−𝜆𝛼𝐺′(1)[𝜇𝑏+𝛾]+𝛾𝜇𝑏[𝜇+𝛼]𝑃1,0	NOUN
cana-730	109	11	−𝜆𝐺′(1)[𝜇𝑏𝛾+𝛼𝛾+𝛼𝜇𝑏]+𝜇𝑏𝛾[𝜇+𝛼	−𝜆𝐺′(1)[𝜇𝑏𝛾+𝛼𝛾+𝛼𝜇𝑏]+𝜇𝑏𝛾[𝜇+𝛼	X
cana-730	109	12	]	]	X
cana-730	109	13	------------(19	------------(19	ADJ
cana-730	109	14	)	)	PUNCT
cana-730	109	15	𝑃2(1	𝑃2(1	NOUN
cana-730	109	16	)	)	PUNCT
cana-730	110	1	=	=	PUNCT
cana-730	110	2	𝜆𝛼𝛾𝐺′(1)𝑃1,0	𝜆𝛼𝛾𝐺′(1)𝑃1,0	NOUN
cana-730	111	1	−𝜆𝐺′(1)[𝜇𝑏𝛾+𝛼𝛾+𝛼𝜇𝑏]+𝜇𝑏𝛾[𝜇+𝛼	−𝜆𝐺′(1)[𝜇𝑏𝛾+𝛼𝛾+𝛼𝜇𝑏]+𝜇𝑏𝛾[𝜇+𝛼	NOUN
cana-730	111	2	]	]	X
cana-730	111	3	------------(20	------------(20	NOUN
cana-730	111	4	)	)	PUNCT
cana-730	111	5	using	use	VERB
cana-730	111	6	the	the	DET
cana-730	111	7	normalization	normalization	NOUN
cana-730	111	8	condition	condition	NOUN
cana-730	111	9	and	and	CCONJ
cana-730	111	10	solving	solve	VERB
cana-730	111	11	the	the	DET
cana-730	111	12	above	above	ADJ
cana-730	111	13	equations	equation	NOUN
cana-730	111	14	:	:	PUNCT
cana-730	111	15	𝑃0(1	𝑃0(1	NUM
cana-730	111	16	)	)	PUNCT
cana-730	112	1	+	+	CCONJ
cana-730	112	2	𝑃1(1	𝑃1(1	ADJ
cana-730	112	3	)	)	PUNCT
cana-730	112	4	+	+	NUM
cana-730	112	5	𝑃2(1	𝑃2(1	NOUN
cana-730	112	6	)	)	PUNCT
cana-730	112	7	=	=	SYM
cana-730	113	1	1	1	NUM
cana-730	113	2	we	we	PRON
cana-730	113	3	obtain	obtain	VERB
cana-730	113	4	𝑃1,0	𝑃1,0	NUM
cana-730	113	5	=	=	SYM
cana-730	113	6	−𝜆𝐺′(1)[𝜇𝑏𝛾+𝛼𝛾+𝛼𝜇𝑏]+𝜇𝑏𝛾[𝜇+𝛼	−𝜆𝐺′(1)[𝜇𝑏𝛾+𝛼𝛾+𝛼𝜇𝑏]+𝜇𝑏𝛾[𝜇+𝛼	NOUN
cana-730	113	7	]	]	X
cana-730	113	8	𝛾𝜇𝑏[𝜇+𝛼	𝛾𝜇𝑏[𝜇+𝛼	PROPN
cana-730	113	9	]	]	X
cana-730	113	10	--------------(21	--------------(21	PROPN
cana-730	113	11	)	)	PUNCT
cana-730	113	12	from	from	ADP
cana-730	113	13	equation	equation	NOUN
cana-730	113	14	(	(	PUNCT
cana-730	113	15	5),(7	5),(7	NUM
cana-730	113	16	)	)	PUNCT
cana-730	113	17	and	and	CCONJ
cana-730	113	18	(	(	PUNCT
cana-730	113	19	9	9	X
cana-730	113	20	)	)	PUNCT
cana-730	113	21	the	the	DET
cana-730	113	22	other	other	ADJ
cana-730	113	23	probabilities	probability	NOUN
cana-730	113	24	are	be	AUX
cana-730	113	25	obtained	obtain	VERB
cana-730	113	26	as	as	ADP
cana-730	113	27	follows	follow	VERB
cana-730	113	28	:	:	PUNCT
cana-730	113	29	𝑃0,0	𝑃0,0	NOUN
cana-730	113	30	=	=	PUNCT
cana-730	113	31	𝜆𝛼𝜇𝑏𝑃1,0	𝜆𝛼𝜇𝑏𝑃1,0	NOUN
cana-730	114	1	[	[	X
cana-730	114	2	𝜇(𝜆+𝛾)(𝜆+𝜇𝑏)+𝛾𝛼𝜇𝑏	𝜇(𝜆+𝛾)(𝜆+𝜇𝑏)+𝛾𝛼𝜇𝑏	X
cana-730	114	3	]	]	X
cana-730	114	4	-------------(22	-------------(22	NOUN
cana-730	114	5	)	)	PUNCT
cana-730	114	6	𝑃2,1	𝑃2,1	PROPN
cana-730	114	7	=	=	SYM
cana-730	114	8	𝜆(𝜆+𝛾)(𝜇𝑏𝛼)𝑃1,0	𝜆(𝜆+𝛾)(𝜇𝑏𝛼)𝑃1,0	NOUN
cana-730	115	1	[	[	X
cana-730	115	2	𝜇(𝜆+𝛾)(𝜆+𝜇𝑏)+𝛾𝛼𝜇𝑏	𝜇(𝜆+𝛾)(𝜆+𝜇𝑏)+𝛾𝛼𝜇𝑏	NOUN
cana-730	115	3	]	]	SYM
cana-730	115	4	------(23	------(23	NOUN
cana-730	115	5	)	)	PUNCT
cana-730	115	6	5	5	NUM
cana-730	115	7	stochastic	stochastic	ADJ
cana-730	115	8	decomposition	decomposition	NOUN
cana-730	115	9	approach	approach	NOUN
cana-730	115	10	this	this	DET
cana-730	115	11	section	section	NOUN
cana-730	115	12	concerns	concern	VERB
cana-730	115	13	the	the	DET
cana-730	115	14	analysis	analysis	NOUN
cana-730	115	15	of	of	ADP
cana-730	115	16	the	the	DET
cana-730	115	17	stochastic	stochastic	ADJ
cana-730	115	18	decomposition	decomposition	NOUN
cana-730	115	19	property	property	NOUN
cana-730	115	20	of	of	ADP
cana-730	115	21	the	the	DET
cana-730	115	22	system	system	NOUN
cana-730	115	23	size	size	NOUN
cana-730	115	24	distribution	distribution	NOUN
cana-730	115	25	.	.	PUNCT
cana-730	116	1	the	the	DET
cana-730	116	2	literature	literature	NOUN
cana-730	116	3	on	on	ADP
cana-730	116	4	vacations	vacation	NOUN
cana-730	116	5	models	model	NOUN
cana-730	116	6	recognizes	recognize	VERB
cana-730	116	7	this	this	DET
cana-730	116	8	property	property	NOUN
cana-730	116	9	as	as	ADP
cana-730	116	10	one	one	NUM
cana-730	116	11	of	of	ADP
cana-730	116	12	the	the	DET
cana-730	116	13	most	most	ADV
cana-730	116	14	interesting	interesting	ADJ
cana-730	116	15	features	feature	NOUN
cana-730	116	16	on	on	ADP
cana-730	116	17	this	this	DET
cana-730	116	18	matter	matter	NOUN
cana-730	116	19	.	.	PUNCT
cana-730	117	1	yang	yang	PROPN
cana-730	117	2	and	and	CCONJ
cana-730	117	3	templeton	templeton	PROPN
cana-730	118	1	[	[	X
cana-730	118	2	11	11	NUM
cana-730	118	3	]	]	PUNCT
cana-730	118	4	studied	study	VERB
cana-730	118	5	the	the	DET
cana-730	118	6	stochastic	stochastic	ADJ
cana-730	118	7	decomposition	decomposition	NOUN
cana-730	118	8	of	of	ADP
cana-730	118	9	retrial	retrial	ADJ
cana-730	118	10	queues	queue	NOUN
cana-730	118	11	,	,	PUNCT
cana-730	118	12	whose	whose	DET
cana-730	118	13	applications	application	NOUN
cana-730	118	14	were	be	AUX
cana-730	118	15	discussed	discuss	VERB
cana-730	118	16	later	later	ADV
cana-730	118	17	by	by	ADP
cana-730	118	18	artalejo	artalejo	ADJ
cana-730	118	19	and	and	CCONJ
cana-730	118	20	falin	falin	NOUN
cana-730	118	21	[	[	X
cana-730	118	22	12	12	NUM
cana-730	118	23	]	]	PUNCT
cana-730	118	24	and	and	CCONJ
cana-730	118	25	yang	yang	PROPN
cana-730	119	1	[	[	X
cana-730	119	2	13].the	13].the	PRON
cana-730	119	3	classical	classical	ADJ
cana-730	119	4	interpretation	interpretation	NOUN
cana-730	119	5	of	of	ADP
cana-730	119	6	the	the	DET
cana-730	119	7	stochastic	stochastic	ADJ
cana-730	119	8	decomposition	decomposition	NOUN
cana-730	119	9	property	property	NOUN
cana-730	119	10	shows	show	VERB
cana-730	119	11	that	that	SCONJ
cana-730	119	12	the	the	DET
cana-730	119	13	system	system	NOUN
cana-730	119	14	size	size	NOUN
cana-730	119	15	distribution	distribution	NOUN
cana-730	119	16	decomposes	decompose	VERB
cana-730	119	17	into	into	ADP
cana-730	119	18	two	two	NUM
cana-730	119	19	random	random	ADJ
cana-730	119	20	variables	variable	NOUN
cana-730	119	21	one	one	NUM
cana-730	119	22	of	of	ADP
cana-730	119	23	which	which	PRON
cana-730	119	24	corresponds	correspond	VERB
cana-730	119	25	to	to	ADP
cana-730	119	26	the	the	DET
cana-730	119	27	system	system	NOUN
cana-730	119	28	size	size	NOUN
cana-730	119	29	of	of	ADP
cana-730	119	30	the	the	DET
cana-730	119	31	ordinary	ordinary	ADJ
cana-730	119	32	queue	queue	NOUN
cana-730	119	33	without	without	ADP
cana-730	119	34	working	work	VERB
cana-730	119	35	breakdowns	breakdown	NOUN
cana-730	119	36	and	and	CCONJ
cana-730	119	37	the	the	DET
cana-730	119	38	other	other	ADJ
cana-730	119	39	random	random	ADJ
cana-730	119	40	variable	variable	NOUN
cana-730	119	41	gives	give	VERB
cana-730	119	42	the	the	DET
cana-730	119	43	increase	increase	NOUN
cana-730	119	44	in	in	ADP
cana-730	119	45	the	the	DET
cana-730	119	46	system	system	NOUN
cana-730	119	47	size	size	NOUN
cana-730	119	48	due	due	ADP
cana-730	119	49	to	to	ADP
cana-730	119	50	the	the	DET
cana-730	119	51	presence	presence	NOUN
cana-730	119	52	of	of	ADP
cana-730	119	53	working	work	VERB
cana-730	119	54	breakdowns	breakdown	NOUN
cana-730	119	55	in	in	ADP
cana-730	119	56	the	the	DET
cana-730	119	57	system	system	NOUN
cana-730	119	58	.	.	PUNCT
cana-730	120	1	in	in	ADP
cana-730	120	2	particular	particular	ADJ
cana-730	120	3	,	,	PUNCT
cana-730	120	4	in	in	ADP
cana-730	120	5	the	the	DET
cana-730	120	6	context	context	NOUN
cana-730	120	7	of	of	ADP
cana-730	120	8	our	our	PRON
cana-730	120	9	system	system	NOUN
cana-730	120	10	,	,	PUNCT
cana-730	120	11	we	we	PRON
cana-730	120	12	observe	observe	VERB
cana-730	120	13	that	that	SCONJ
cana-730	120	14	the	the	DET
cana-730	120	15	probability	probability	NOUN
cana-730	120	16	generating	generate	VERB
cana-730	120	17	function	function	NOUN
cana-730	120	18	of	of	ADP
cana-730	120	19	the	the	DET
cana-730	120	20	system	system	NOUN
cana-730	120	21	size	size	NOUN
cana-730	120	22	p(z	p(z	NOUN
cana-730	120	23	)	)	PUNCT
cana-730	120	24	can	can	AUX
cana-730	120	25	be	be	AUX
cana-730	120	26	written	write	VERB
cana-730	120	27	as	as	ADP
cana-730	120	28	𝑃(𝑍	𝑃(𝑍	NUM
cana-730	120	29	)	)	PUNCT
cana-730	120	30	=	=	SYM
cana-730	121	1	𝑃𝑐(𝑍	𝑃𝑐(𝑍	X
cana-730	121	2	)	)	PUNCT
cana-730	121	3	𝑥	𝑥	DET
cana-730	121	4	𝑃𝑤𝑏(𝑍	𝑃𝑤𝑏(𝑍	X
cana-730	121	5	)	)	PUNCT
cana-730	121	6	where	where	SCONJ
cana-730	121	7	communications	communication	NOUN
cana-730	121	8	on	on	ADP
cana-730	121	9	applied	apply	VERB
cana-730	121	10	nonlinear	nonlinear	ADJ
cana-730	121	11	analysis	analysis	NOUN
cana-730	121	12	issn	issn	NOUN
cana-730	121	13	:	:	PUNCT
cana-730	121	14	1074	1074	NUM
cana-730	121	15	-	-	PUNCT
cana-730	121	16	133x	133x	NUM
cana-730	121	17	vol	vol	NOUN
cana-730	121	18	31	31	NUM
cana-730	121	19	no	no	NOUN
cana-730	121	20	.	.	PUNCT
cana-730	122	1	3s	3s	NUM
cana-730	122	2	(	(	PUNCT
cana-730	122	3	2024	2024	NUM
cana-730	122	4	)	)	PUNCT
cana-730	122	5	49	49	NUM
cana-730	122	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-730	122	7	𝑃𝑤𝑏(𝑍	𝑃𝑤𝑏(𝑍	X
cana-730	122	8	)	)	PUNCT
cana-730	122	9	=	=	NOUN
cana-730	122	10	𝑁(𝑍	𝑁(𝑍	X
cana-730	122	11	)	)	PUNCT
cana-730	122	12	𝑥	𝑥	PRON
cana-730	122	13	𝑈(𝑍	𝑈(𝑍	NUM
cana-730	122	14	)	)	PUNCT
cana-730	122	15	δ′(𝑍)𝛾𝜇𝑏[𝜇	δ′(𝑍)𝛾𝜇𝑏[𝜇	NOUN
cana-730	122	16	+	+	CCONJ
cana-730	122	17	𝛼][𝜆𝑔	𝛼][𝜆𝑔	NOUN
cana-730	122	18	−	−	NOUN
cana-730	122	19	𝜇][1	𝜇][1	NOUN
cana-730	122	20	−	−	PROPN
cana-730	122	21	𝑍	𝑍	NOUN
cana-730	122	22	]	]	PUNCT
cana-730	122	23	𝑃𝑐(𝑍	𝑃𝑐(𝑍	ADV
cana-730	122	24	)	)	PUNCT
cana-730	122	25	=	=	PUNCT
cana-730	122	26	(	(	PUNCT
cana-730	122	27	𝜆𝑔	𝜆𝑔	NOUN
cana-730	122	28	−	−	PROPN
cana-730	122	29	𝜇)(1	𝜇)(1	NOUN
cana-730	122	30	−	−	ADP
cana-730	122	31	𝑍	𝑍	NOUN
cana-730	122	32	)	)	PUNCT
cana-730	122	33	(	(	PUNCT
cana-730	122	34	𝜆	𝜆	X
cana-730	122	35	+	+	CCONJ
cana-730	122	36	𝜇)𝑍	𝜇)𝑍	NOUN
cana-730	122	37	−	−	NOUN
cana-730	122	38	𝜇	𝜇	ADP
cana-730	122	39	−	−	NOUN
cana-730	122	40	𝜆𝑍𝐺(𝑍	𝜆𝑍𝐺(𝑍	NOUN
cana-730	122	41	)	)	PUNCT
cana-730	122	42	where	where	SCONJ
cana-730	122	43	,	,	PUNCT
cana-730	122	44	𝑁(𝑍	𝑁(𝑍	NOUN
cana-730	122	45	)	)	PUNCT
cana-730	122	46	=	=	SYM
cana-730	122	47	𝜆2𝜇(1	𝜆2𝜇(1	NUM
cana-730	122	48	−	−	NOUN
cana-730	123	1	𝐺(𝑍))2	𝐺(𝑍))2	NOUN
cana-730	123	2	+	+	CCONJ
cana-730	124	1	𝜆(1	𝜆(1	NOUN
cana-730	124	2	−	−	NOUN
cana-730	124	3	𝐺(𝑍))[𝛼𝜇𝑏	𝐺(𝑍))[𝛼𝜇𝑏	VERB
cana-730	124	4	+	+	CCONJ
cana-730	124	5	𝜇𝜇𝑏	𝜇𝜇𝑏	NOUN
cana-730	124	6	+	+	CCONJ
cana-730	124	7	𝜇𝛾	𝜇𝛾	ADP
cana-730	124	8	+	+	X
cana-730	124	9	2𝜆𝜇(1	2𝜆𝜇(1	NOUN
cana-730	124	10	−	−	NOUN
cana-730	124	11	𝑍)𝐺′(𝑍	𝑍)𝐺′(𝑍	NOUN
cana-730	124	12	)	)	PUNCT
cana-730	124	13	]	]	PUNCT
cana-730	125	1	+	+	CCONJ
cana-730	125	2	𝐺′(𝑍)𝜆(1	𝐺′(𝑍)𝜆(1	PUNCT
cana-730	125	3	−	−	PROPN
cana-730	125	4	𝑍)[𝜇𝑏𝛼	𝑍)[𝜇𝑏𝛼	ADJ
cana-730	125	5	+	+	CCONJ
cana-730	125	6	𝜇𝜇𝑏	𝜇𝜇𝑏	ADJ
cana-730	125	7	+	+	CCONJ
cana-730	125	8	𝜇𝛾	𝜇𝛾	NOUN
cana-730	125	9	]	]	X
cana-730	125	10	+	+	CCONJ
cana-730	125	11	𝛾𝜇𝑏[𝛼	𝛾𝜇𝑏[𝛼	NOUN
cana-730	125	12	+	+	CCONJ
cana-730	125	13	𝜇	𝜇	X
cana-730	125	14	]	]	X
cana-730	125	15	𝑈(𝑍	𝑈(𝑍	NUM
cana-730	125	16	)	)	PUNCT
cana-730	125	17	=	=	NOUN
cana-730	125	18	−𝜇𝛾𝜇𝑏[𝛼	−𝜇𝛾𝜇𝑏[𝛼	NOUN
cana-730	125	19	+	+	CCONJ
cana-730	125	20	𝜇	𝜇	X
cana-730	125	21	]	]	X
cana-730	125	22	+	+	CCONJ
cana-730	125	23	𝜆2𝑍𝐺′(1)𝐺(𝑍)[𝛼𝛾	𝜆2𝑍𝐺′(1)𝐺(𝑍)[𝛼𝛾	NOUN
cana-730	125	24	+	+	NUM
cana-730	125	25	𝛾𝜇𝑏	𝛾𝜇𝑏	NOUN
cana-730	125	26	+	+	CCONJ
cana-730	125	27	𝛼𝜇𝑏	𝛼𝜇𝑏	NOUN
cana-730	125	28	]	]	X
cana-730	125	29	−	−	PROPN
cana-730	125	30	𝜆𝑍𝐺(𝑍)𝛾𝜇𝑏[𝛼	𝜆𝑍𝐺(𝑍)𝛾𝜇𝑏[𝛼	NOUN
cana-730	125	31	+	+	CCONJ
cana-730	125	32	𝜇	𝜇	X
cana-730	125	33	]	]	X
cana-730	125	34	−	−	PROPN
cana-730	125	35	𝜆𝐺′(1)𝑍(𝜆	𝜆𝐺′(1)𝑍(𝜆	NOUN
cana-730	125	36	+	+	CCONJ
cana-730	125	37	𝜇)[𝛼𝛾	𝜇)[𝛼𝛾	NOUN
cana-730	125	38	+	+	CCONJ
cana-730	125	39	𝛾𝜇𝑏	𝛾𝜇𝑏	NOUN
cana-730	125	40	+	+	CCONJ
cana-730	125	41	𝛼𝜇𝑏	𝛼𝜇𝑏	NOUN
cana-730	125	42	]	]	X
cana-730	126	1	+	+	CCONJ
cana-730	126	2	(	(	PUNCT
cana-730	126	3	𝜆	𝜆	PRON
cana-730	126	4	+	+	X
cana-730	126	5	𝜇)𝑍𝛾𝜇𝑏[𝛼	𝜇)𝑍𝛾𝜇𝑏[𝛼	NOUN
cana-730	126	6	+	+	CCONJ
cana-730	126	7	𝜇	𝜇	X
cana-730	126	8	]	]	X
cana-730	126	9	+	+	NUM
cana-730	126	10	𝜆𝐺′(1)𝜇)[𝛼𝛾	𝜆𝐺′(1)𝜇)[𝛼𝛾	X
cana-730	126	11	+	+	NUM
cana-730	126	12	𝛾𝜇𝑏	𝛾𝜇𝑏	NOUN
cana-730	126	13	+	+	CCONJ
cana-730	126	14	𝛼𝜇𝑏	𝛼𝜇𝑏	NOUN
cana-730	126	15	]	]	PUNCT
cana-730	126	16	𝑃𝑐(𝑍	𝑃𝑐(𝑍	PRON
cana-730	126	17	)	)	PUNCT
cana-730	126	18	is	be	AUX
cana-730	126	19	the	the	DET
cana-730	126	20	probability	probability	NOUN
cana-730	126	21	generating	generate	VERB
cana-730	126	22	function	function	NOUN
cana-730	126	23	of	of	ADP
cana-730	126	24	the	the	DET
cana-730	126	25	random	random	ADJ
cana-730	126	26	variable	variable	NOUN
cana-730	126	27	n	n	CCONJ
cana-730	126	28	which	which	PRON
cana-730	126	29	is	be	AUX
cana-730	126	30	the	the	DET
cana-730	126	31	number	number	NOUN
cana-730	126	32	in	in	ADP
cana-730	126	33	the	the	DET
cana-730	126	34	system	system	NOUN
cana-730	126	35	in	in	ADP
cana-730	126	36	the	the	DET
cana-730	126	37	classical	classical	ADJ
cana-730	126	38	𝑀𝑥/𝑀/1	𝑀𝑥/𝑀/1	NOUN
cana-730	126	39	queueing	queue	VERB
cana-730	126	40	model	model	NOUN
cana-730	126	41	.	.	PUNCT
cana-730	127	1	𝑃𝑤𝑏(𝑍	𝑃𝑤𝑏(𝑍	X
cana-730	127	2	)	)	PUNCT
cana-730	127	3	is	be	AUX
cana-730	127	4	the	the	DET
cana-730	127	5	probability	probability	NOUN
cana-730	127	6	generating	generate	VERB
cana-730	127	7	function	function	NOUN
cana-730	127	8	of	of	ADP
cana-730	127	9	the	the	DET
cana-730	127	10	extra	extra	ADJ
cana-730	127	11	load	load	NOUN
cana-730	127	12	in	in	ADP
cana-730	127	13	the	the	DET
cana-730	127	14	system	system	NOUN
cana-730	127	15	due	due	ADP
cana-730	127	16	to	to	ADP
cana-730	127	17	the	the	DET
cana-730	127	18	presence	presence	NOUN
cana-730	127	19	of	of	ADP
cana-730	127	20	working	work	VERB
cana-730	127	21	break	break	NOUN
cana-730	127	22	downs	down	NOUN
cana-730	127	23	.	.	PUNCT
cana-730	128	1	6	6	NUM
cana-730	128	2	performance	performance	NOUN
cana-730	128	3	measures	measure	NOUN
cana-730	128	4	according	accord	VERB
cana-730	128	5	to	to	ADP
cana-730	128	6	the	the	DET
cana-730	128	7	distribution	distribution	NOUN
cana-730	128	8	of	of	ADP
cana-730	128	9	the	the	DET
cana-730	128	10	steady	steady	ADJ
cana-730	128	11	state	state	NOUN
cana-730	128	12	,	,	PUNCT
cana-730	128	13	various	various	ADJ
cana-730	128	14	system	system	NOUN
cana-730	128	15	performance	performance	NOUN
cana-730	128	16	measures	measure	NOUN
cana-730	128	17	can	can	AUX
cana-730	128	18	be	be	AUX
cana-730	128	19	developed	develop	VERB
cana-730	128	20	.	.	PUNCT
cana-730	129	1	1.expected	1.expected	NUM
cana-730	129	2	number	number	NOUN
cana-730	129	3	of	of	ADP
cana-730	129	4	customers	customer	NOUN
cana-730	129	5	in	in	ADP
cana-730	129	6	the	the	DET
cana-730	129	7	system	system	NOUN
cana-730	129	8	:	:	PUNCT
cana-730	129	9	𝐸(𝑋	𝐸(𝑋	NOUN
cana-730	129	10	)	)	PUNCT
cana-730	129	11	=	=	SYM
cana-730	129	12	𝑃0′(1	𝑃0′(1	ADJ
cana-730	129	13	)	)	PUNCT
cana-730	129	14	+	+	CCONJ
cana-730	129	15	𝑃1′(1	𝑃1′(1	ADJ
cana-730	129	16	)	)	PUNCT
cana-730	129	17	+	+	SYM
cana-730	129	18	𝑃2′(1	𝑃2′(1	NOUN
cana-730	129	19	)	)	PUNCT
cana-730	129	20	[	[	PUNCT
cana-730	129	21	𝜃1𝜃4	𝜃1𝜃4	PUNCT
cana-730	129	22	−	−	NOUN
cana-730	129	23	𝜃3𝜃2	𝜃3𝜃2	SYM
cana-730	129	24	2θ1	2θ1	NUM
cana-730	129	25	2	2	NUM
cana-730	129	26	+	+	NUM
cana-730	129	27	𝜃1𝜃6	𝜃1𝜃6	X
cana-730	129	28	−	−	X
cana-730	129	29	𝜃5𝜃2	𝜃5𝜃2	X
cana-730	129	30	2θ1	2θ1	NUM
cana-730	129	31	2	2	NUM
cana-730	129	32	+	+	CCONJ
cana-730	129	33	𝜃1𝜃8	𝜃1𝜃8	VERB
cana-730	129	34	−	−	PRON
cana-730	129	35	𝜃7𝜃2	𝜃7𝜃2	SYM
cana-730	129	36	2θ1	2θ1	NUM
cana-730	129	37	2	2	NUM
cana-730	129	38	]	]	PUNCT
cana-730	129	39	where	where	SCONJ
cana-730	129	40	,	,	PUNCT
cana-730	129	41	𝜃1	𝜃1	NOUN
cana-730	129	42	=	=	PUNCT
cana-730	129	43	−𝜆𝐺′(1)[μbα	−𝜆𝐺′(1)[μbα	PROPN
cana-730	129	44	+	+	CCONJ
cana-730	129	45	γα	γα	ADP
cana-730	129	46	+	+	ADJ
cana-730	129	47	γμb	γμb	X
cana-730	129	48	]	]	X
cana-730	129	49	+	+	PUNCT
cana-730	129	50	μb𝛾[𝜇	μb𝛾[𝜇	NOUN
cana-730	129	51	+	+	CCONJ
cana-730	129	52	𝛼	𝛼	X
cana-730	129	53	]	]	X
cana-730	129	54	𝜃2	𝜃2	PROPN
cana-730	129	55	=	=	SYM
cana-730	129	56	−𝜆𝐺′′(1)[μbα	−𝜆𝐺′′(1)[μbα	PROPN
cana-730	129	57	+	+	CCONJ
cana-730	129	58	γα	γα	ADP
cana-730	129	59	+	+	ADJ
cana-730	129	60	γμb	γμb	X
cana-730	129	61	]	]	X
cana-730	129	62	+	+	CCONJ
cana-730	129	63	𝐺′(1)22𝜆2[𝛾	𝐺′(1)22𝜆2[𝛾	NOUN
cana-730	129	64	+	+	CCONJ
cana-730	129	65	μb	μb	PROPN
cana-730	129	66	+	+	NUM
cana-730	129	67	𝛼	𝛼	X
cana-730	129	68	]	]	X
cana-730	129	69	−	−	ADP
cana-730	129	70	2𝜆𝐺′(1)[𝛾𝜇	2𝜆𝐺′(1)[𝛾𝜇	NUM
cana-730	129	71	+	+	CCONJ
cana-730	129	72	𝛾𝛼	𝛾𝛼	X
cana-730	129	73	+	+	NOUN
cana-730	129	74	μb𝜇	μb𝜇	NOUN
cana-730	129	75	+	+	CCONJ
cana-730	129	76	𝛾μb	𝛾μb	X
cana-730	129	77	+	+	CCONJ
cana-730	129	78	𝛼μb	𝛼μb	ADJ
cana-730	129	79	]	]	PUNCT
cana-730	129	80	𝜃3	𝜃3	ADJ
cana-730	129	81	=	=	PUNCT
cana-730	129	82	μb𝜆𝛼𝐺′(1)𝑃1,0	μb𝜆𝛼𝐺′(1)𝑃1,0	NOUN
cana-730	129	83	𝜃4	𝜃4	NOUN
cana-730	129	84	=	=	PUNCT
cana-730	129	85	μb𝜆𝛼𝐺′′(1)𝑃1,0	μb𝜆𝛼𝐺′′(1)𝑃1,0	NUM
cana-730	129	86	𝜃5	𝜃5	NOUN
cana-730	129	87	=	=	PUNCT
cana-730	130	1	[	[	X
cana-730	130	2	−𝜆𝐺′(1)[𝛼μb	−𝜆𝐺′(1)[𝛼μb	PROPN
cana-730	130	3	+	+	CCONJ
cana-730	130	4	𝛼𝛾	𝛼𝛾	NOUN
cana-730	130	5	]	]	X
cana-730	130	6	+	+	CCONJ
cana-730	130	7	𝛾μb[𝜇	𝛾μb[𝜇	ADJ
cana-730	130	8	+	+	CCONJ
cana-730	130	9	𝛼]]𝑃1,0	𝛼]]𝑃1,0	NUM
cana-730	130	10	𝜃6	𝜃6	NOUN
cana-730	130	11	=	=	SYM
cana-730	130	12	𝑃1,0[−2𝜆𝐺′(1)[𝛼μb	𝑃1,0[−2𝜆𝐺′(1)[𝛼μb	PROPN
cana-730	130	13	+	+	NUM
cana-730	130	14	𝛼𝛾	𝛼𝛾	NOUN
cana-730	130	15	+	+	CCONJ
cana-730	130	16	𝜇μb	𝜇μb	NOUN
cana-730	130	17	+	+	CCONJ
cana-730	130	18	𝜇𝛾	𝜇𝛾	NOUN
cana-730	130	19	]	]	X
cana-730	130	20	+	+	CCONJ
cana-730	130	21	2𝜆2𝛼(𝐺′(1))2	2𝜆2𝛼(𝐺′(1))2	NUM
cana-730	130	22	−	−	NOUN
cana-730	130	23	𝜆𝐺′′(1)[𝛾μb	𝜆𝐺′′(1)[𝛾μb	ADJ
cana-730	130	24	+	+	CCONJ
cana-730	130	25	𝛾𝛼	𝛾𝛼	X
cana-730	130	26	]	]	X
cana-730	130	27	]	]	X
cana-730	130	28	𝜃7	𝜃7	X
cana-730	130	29	=	=	SYM
cana-730	130	30	𝛾𝜆𝛼𝐺′(1)𝑃1,0	𝛾𝜆𝛼𝐺′(1)𝑃1,0	PROPN
cana-730	130	31	𝜃8	𝜃8	PROPN
cana-730	130	32	=	=	PUNCT
cana-730	131	1	[	[	X
cana-730	131	2	−2𝛼𝜆2(𝐺′(1))2	−2𝛼𝜆2(𝐺′(1))2	X
cana-730	131	3	+	+	CCONJ
cana-730	131	4	2𝛾𝜆𝛼𝐺′(1	2𝛾𝜆𝛼𝐺′(1	NUM
cana-730	131	5	)	)	PUNCT
cana-730	132	1	+	+	NUM
cana-730	132	2	𝛾𝜆𝛼𝐺′′(1)]𝑃1,0	𝛾𝜆𝛼𝐺′′(1)]𝑃1,0	VERB
cana-730	132	3	2.expected	2.expected	NUM
cana-730	132	4	number	number	NOUN
cana-730	132	5	of	of	ADP
cana-730	132	6	customer	customer	NOUN
cana-730	132	7	customers	customer	NOUN
cana-730	132	8	in	in	ADP
cana-730	132	9	the	the	DET
cana-730	132	10	queue	queue	NOUN
cana-730	132	11	𝐸(𝑄	𝐸(𝑄	NOUN
cana-730	132	12	)	)	PUNCT
cana-730	132	13	=	=	PUNCT
cana-730	132	14	∑	∑	PUNCT
cana-730	132	15	(	(	PUNCT
cana-730	132	16	𝑛	𝑛	PROPN
cana-730	132	17	−	−	PROPN
cana-730	132	18	1)𝑃𝑛	1)𝑃𝑛	PROPN
cana-730	132	19	∞	∞	PROPN
cana-730	132	20	𝑛=1	𝑛=1	NOUN
cana-730	132	21	3.expected	3.expected	NUM
cana-730	132	22	waiting	waiting	NOUN
cana-730	132	23	time	time	NOUN
cana-730	132	24	in	in	ADP
cana-730	132	25	the	the	DET
cana-730	132	26	system	system	NOUN
cana-730	132	27	𝐸(𝑊𝑠	𝐸(𝑊𝑠	ADV
cana-730	132	28	)	)	PUNCT
cana-730	132	29	=	=	SYM
cana-730	132	30	𝐸(𝑋	𝐸(𝑋	NOUN
cana-730	132	31	)	)	PUNCT
cana-730	132	32	𝜆𝑔	𝜆𝑔	ADP
cana-730	132	33	4.expected	4.expecte	VERB
cana-730	132	34	waiting	waiting	NOUN
cana-730	132	35	time	time	NOUN
cana-730	132	36	in	in	ADP
cana-730	132	37	the	the	DET
cana-730	132	38	queue	queue	NOUN
cana-730	132	39	𝐸(𝑊𝑞	𝐸(𝑊𝑞	ADV
cana-730	132	40	)	)	PUNCT
cana-730	132	41	=	=	SYM
cana-730	132	42	𝐸(𝑄	𝐸(𝑄	NOUN
cana-730	132	43	)	)	PUNCT
cana-730	132	44	𝜆𝑔	𝜆𝑔	ADP
cana-730	132	45	communications	communication	NOUN
cana-730	132	46	on	on	ADP
cana-730	132	47	applied	apply	VERB
cana-730	132	48	nonlinear	nonlinear	ADJ
cana-730	132	49	analysis	analysis	NOUN
cana-730	132	50	issn	issn	NOUN
cana-730	132	51	:	:	PUNCT
cana-730	132	52	1074	1074	NUM
cana-730	132	53	-	-	PUNCT
cana-730	132	54	133x	133x	NUM
cana-730	132	55	vol	vol	NOUN
cana-730	132	56	31	31	NUM
cana-730	132	57	no	no	NOUN
cana-730	132	58	.	.	PUNCT
cana-730	133	1	3s	3s	NUM
cana-730	133	2	(	(	PUNCT
cana-730	133	3	2024	2024	NUM
cana-730	133	4	)	)	PUNCT
cana-730	133	5	50	50	NUM
cana-730	133	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-730	133	7	5.the	5.the	DET
cana-730	133	8	proportion	proportion	NOUN
cana-730	133	9	of	of	ADP
cana-730	133	10	time	time	NOUN
cana-730	133	11	,	,	PUNCT
cana-730	133	12	the	the	DET
cana-730	133	13	server	server	NOUN
cana-730	133	14	is	be	AUX
cana-730	133	15	busy=𝑃1(1	busy=𝑃1(1	PROPN
cana-730	133	16	)	)	PUNCT
cana-730	133	17	−	−	NOUN
cana-730	134	1	𝑃1,0	𝑃1,0	NUM
cana-730	134	2	6	6	NUM
cana-730	134	3	.	.	PUNCT
cana-730	135	1	the	the	DET
cana-730	135	2	proportion	proportion	NOUN
cana-730	135	3	of	of	ADP
cana-730	135	4	time	time	NOUN
cana-730	135	5	,	,	PUNCT
cana-730	135	6	the	the	DET
cana-730	135	7	server	server	NOUN
cana-730	135	8	being	be	AUX
cana-730	135	9	in	in	ADP
cana-730	135	10	maintenance	maintenance	NOUN
cana-730	135	11	𝑄0	𝑄0	PUNCT
cana-730	136	1	=	=	PUNCT
cana-730	136	2	𝑃0(1	𝑃0(1	NUM
cana-730	136	3	)	)	PUNCT
cana-730	136	4	7	7	NUM
cana-730	136	5	.	.	PUNCT
cana-730	137	1	the	the	DET
cana-730	137	2	proportion	proportion	NOUN
cana-730	137	3	of	of	ADP
cana-730	137	4	time	time	NOUN
cana-730	137	5	,	,	PUNCT
cana-730	137	6	the	the	DET
cana-730	137	7	server	server	NOUN
cana-730	137	8	being	be	AUX
cana-730	137	9	normal	normal	ADJ
cana-730	137	10	𝑄1	𝑄1	NOUN
cana-730	137	11	=	=	PUNCT
cana-730	137	12	𝑃1(1	𝑃1(1	X
cana-730	137	13	)	)	PUNCT
cana-730	137	14	8	8	NUM
cana-730	137	15	.	.	PUNCT
cana-730	138	1	the	the	DET
cana-730	138	2	proportion	proportion	NOUN
cana-730	138	3	of	of	ADP
cana-730	138	4	time	time	NOUN
cana-730	138	5	,	,	PUNCT
cana-730	138	6	the	the	DET
cana-730	138	7	server	server	NOUN
cana-730	138	8	being	be	AUX
cana-730	138	9	in	in	ADP
cana-730	138	10	non	non	ADJ
cana-730	138	11	-	-	ADJ
cana-730	138	12	reliable	reliable	ADJ
cana-730	138	13	state	state	NOUN
cana-730	138	14	𝑄2	𝑄2	PROPN
cana-730	139	1	=	=	SYM
cana-730	139	2	𝑃2(1	𝑃2(1	NOUN
cana-730	139	3	)	)	PUNCT
cana-730	139	4	7	7	NUM
cana-730	139	5	reliability	reliability	NOUN
cana-730	139	6	measures	measure	NOUN
cana-730	139	7	in	in	ADP
cana-730	139	8	queuing	queue	VERB
cana-730	139	9	theory	theory	NOUN
cana-730	139	10	literature	literature	NOUN
cana-730	139	11	,	,	PUNCT
cana-730	139	12	some	some	DET
cana-730	139	13	studies	study	NOUN
cana-730	139	14	are	be	AUX
cana-730	139	15	devoted	devote	VERB
cana-730	139	16	to	to	ADP
cana-730	139	17	reliability	reliability	NOUN
cana-730	139	18	measures	measure	NOUN
cana-730	139	19	under	under	ADP
cana-730	139	20	different	different	ADJ
cana-730	139	21	queuing	queuing	NOUN
cana-730	139	22	situations	situation	NOUN
cana-730	139	23	because	because	SCONJ
cana-730	139	24	of	of	ADP
cana-730	139	25	its	its	PRON
cana-730	139	26	importance	importance	NOUN
cana-730	139	27	.	.	PUNCT
cana-730	140	1	availability	availability	NOUN
cana-730	140	2	is	be	AUX
cana-730	140	3	defined	define	VERB
cana-730	140	4	as	as	ADP
cana-730	140	5	the	the	DET
cana-730	140	6	probability	probability	NOUN
cana-730	140	7	that	that	SCONJ
cana-730	140	8	the	the	DET
cana-730	140	9	system	system	NOUN
cana-730	140	10	is	be	AUX
cana-730	140	11	operating	operate	VERB
cana-730	140	12	properly	properly	ADV
cana-730	140	13	when	when	SCONJ
cana-730	140	14	it	it	PRON
cana-730	140	15	is	be	AUX
cana-730	140	16	requested	request	VERB
cana-730	140	17	for	for	ADP
cana-730	140	18	use	use	NOUN
cana-730	140	19	.	.	PUNCT
cana-730	141	1	on	on	ADP
cana-730	141	2	the	the	DET
cana-730	141	3	other	other	ADJ
cana-730	141	4	hand	hand	NOUN
cana-730	141	5	,	,	PUNCT
cana-730	141	6	failure	failure	NOUN
cana-730	141	7	frequency	frequency	NOUN
cana-730	141	8	of	of	ADP
cana-730	141	9	the	the	DET
cana-730	141	10	server	server	NOUN
cana-730	141	11	is	be	AUX
cana-730	141	12	the	the	DET
cana-730	141	13	probability	probability	NOUN
cana-730	141	14	when	when	SCONJ
cana-730	141	15	the	the	DET
cana-730	141	16	system	system	NOUN
cana-730	141	17	is	be	AUX
cana-730	141	18	not	not	PART
cana-730	141	19	operating	operate	VERB
cana-730	141	20	in	in	ADP
cana-730	141	21	normal	normal	ADJ
cana-730	141	22	condition	condition	NOUN
cana-730	141	23	.	.	PUNCT
cana-730	142	1	thus	thus	ADV
cana-730	142	2	,	,	PUNCT
cana-730	142	3	we	we	PRON
cana-730	142	4	obtain	obtain	VERB
cana-730	142	5	the	the	DET
cana-730	142	6	following	follow	VERB
cana-730	142	7	two	two	NUM
cana-730	142	8	important	important	ADJ
cana-730	142	9	reliability	reliability	NOUN
cana-730	142	10	measures	measure	NOUN
cana-730	142	11	,	,	PUNCT
cana-730	142	12	(	(	PUNCT
cana-730	142	13	i)the	i)the	DET
cana-730	142	14	availability	availability	NOUN
cana-730	142	15	of	of	ADP
cana-730	142	16	the	the	DET
cana-730	142	17	server	server	NOUN
cana-730	142	18	is	be	AUX
cana-730	142	19	𝑃1(1	𝑃1(1	ADJ
cana-730	142	20	)	)	PUNCT
cana-730	142	21	=	=	PUNCT
cana-730	142	22	−𝜆𝛼𝐺′(1)[μb	−𝜆𝛼𝐺′(1)[μb	NOUN
cana-730	142	23	+	+	CCONJ
cana-730	142	24	𝛾	𝛾	ADP
cana-730	142	25	]	]	X
cana-730	142	26	+	+	CCONJ
cana-730	142	27	𝛾μb[𝜇	𝛾μb[𝜇	X
cana-730	142	28	+	+	CCONJ
cana-730	142	29	𝛼	𝛼	X
cana-730	142	30	]	]	X
cana-730	142	31	−𝜆𝐺′(1)[𝛾𝛼	−𝜆𝐺′(1)[𝛾𝛼	NOUN
cana-730	143	1	+	+	CCONJ
cana-730	143	2	𝛾μb	𝛾μb	X
cana-730	143	3	+	+	CCONJ
cana-730	143	4	𝛼μb	𝛼μb	NOUN
cana-730	143	5	]	]	X
cana-730	143	6	+	+	CCONJ
cana-730	143	7	𝛾μb[𝛼	𝛾μb[𝛼	NOUN
cana-730	143	8	+	+	CCONJ
cana-730	143	9	𝜇	𝜇	X
cana-730	143	10	]	]	X
cana-730	143	11	(	(	PUNCT
cana-730	143	12	ii)the	ii)the	DET
cana-730	143	13	failure	failure	NOUN
cana-730	143	14	frequency	frequency	NOUN
cana-730	143	15	of	of	ADP
cana-730	143	16	the	the	DET
cana-730	143	17	server	server	NOUN
cana-730	143	18	is	be	AUX
cana-730	143	19	𝑃0(1	𝑃0(1	NUM
cana-730	143	20	)	)	PUNCT
cana-730	144	1	+	+	NUM
cana-730	144	2	𝑃2(1	𝑃2(1	NOUN
cana-730	144	3	)	)	PUNCT
cana-730	144	4	=	=	PUNCT
cana-730	145	1	𝑃1,0	𝑃1,0	NUM
cana-730	145	2	𝐺′(1)μb𝜆𝛼+𝜆𝛼𝛾𝐺′(1	𝐺′(1)μb𝜆𝛼+𝜆𝛼𝛾𝐺′(1	PROPN
cana-730	145	3	)	)	PUNCT
cana-730	145	4	−𝜆𝐺′(1)[𝛾𝛼+𝛾μb+𝛼μb]+𝛾μb[𝛼+𝜇	−𝜆𝐺′(1)[𝛾𝛼+𝛾μb+𝛼μb]+𝛾μb[𝛼+𝜇	PROPN
cana-730	145	5	]	]	PUNCT
cana-730	145	6	8	8	NUM
cana-730	145	7	practical	practical	ADJ
cana-730	145	8	application	application	NOUN
cana-730	145	9	in	in	ADP
cana-730	145	10	queueing	queue	VERB
cana-730	145	11	theory	theory	NOUN
cana-730	145	12	,	,	PUNCT
cana-730	145	13	a	a	DET
cana-730	145	14	breakdown	breakdown	ADJ
cana-730	145	15	time	time	NOUN
cana-730	145	16	refers	refer	VERB
cana-730	145	17	to	to	ADP
cana-730	145	18	a	a	DET
cana-730	145	19	period	period	NOUN
cana-730	145	20	when	when	SCONJ
cana-730	145	21	a	a	DET
cana-730	145	22	system	system	NOUN
cana-730	145	23	,	,	PUNCT
cana-730	145	24	such	such	ADJ
cana-730	145	25	as	as	ADP
cana-730	145	26	a	a	DET
cana-730	145	27	server	server	NOUN
cana-730	145	28	or	or	CCONJ
cana-730	145	29	a	a	DET
cana-730	145	30	machine	machine	NOUN
cana-730	145	31	,	,	PUNCT
cana-730	145	32	becomes	become	VERB
cana-730	145	33	unavailable	unavailable	ADJ
cana-730	145	34	due	due	ADP
cana-730	145	35	to	to	ADP
cana-730	145	36	maintenance	maintenance	NOUN
cana-730	145	37	,	,	PUNCT
cana-730	145	38	repair	repair	NOUN
cana-730	145	39	,	,	PUNCT
cana-730	145	40	or	or	CCONJ
cana-730	145	41	unexpected	unexpected	ADJ
cana-730	145	42	failure	failure	NOUN
cana-730	145	43	.	.	PUNCT
cana-730	146	1	during	during	ADP
cana-730	146	2	breakdown	breakdown	ADJ
cana-730	146	3	times	time	NOUN
cana-730	146	4	,	,	PUNCT
cana-730	146	5	the	the	DET
cana-730	146	6	service	service	NOUN
cana-730	146	7	provided	provide	VERB
cana-730	146	8	to	to	ADP
cana-730	146	9	customers	customer	NOUN
cana-730	146	10	may	may	AUX
cana-730	146	11	be	be	AUX
cana-730	146	12	affected	affect	VERB
cana-730	146	13	,	,	PUNCT
cana-730	146	14	leading	lead	VERB
cana-730	146	15	to	to	ADP
cana-730	146	16	delays	delay	NOUN
cana-730	146	17	and	and	CCONJ
cana-730	146	18	disruptions	disruption	NOUN
cana-730	146	19	in	in	ADP
cana-730	146	20	the	the	DET
cana-730	146	21	queueing	queue	VERB
cana-730	146	22	system	system	NOUN
cana-730	146	23	.	.	PUNCT
cana-730	147	1	one	one	NUM
cana-730	147	2	strategy	strategy	NOUN
cana-730	147	3	for	for	ADP
cana-730	147	4	managing	manage	VERB
cana-730	147	5	breakdown	breakdown	ADJ
cana-730	147	6	times	time	NOUN
cana-730	147	7	in	in	ADP
cana-730	147	8	queueing	queue	VERB
cana-730	147	9	systems	system	NOUN
cana-730	147	10	is	be	AUX
cana-730	147	11	to	to	PART
cana-730	147	12	continue	continue	VERB
cana-730	147	13	providing	provide	VERB
cana-730	147	14	service	service	NOUN
cana-730	147	15	at	at	ADP
cana-730	147	16	a	a	DET
cana-730	147	17	reduced	reduce	VERB
cana-730	147	18	rate	rate	NOUN
cana-730	147	19	rather	rather	ADV
cana-730	147	20	than	than	ADP
cana-730	147	21	stopping	stop	VERB
cana-730	147	22	work	work	NOUN
cana-730	147	23	immediately	immediately	ADV
cana-730	147	24	.	.	PUNCT
cana-730	148	1	this	this	DET
cana-730	148	2	approach	approach	NOUN
cana-730	148	3	can	can	AUX
cana-730	148	4	help	help	VERB
cana-730	148	5	in	in	ADP
cana-730	148	6	several	several	ADJ
cana-730	148	7	ways	way	NOUN
cana-730	148	8	:	:	PUNCT
cana-730	148	9	in	in	ADP
cana-730	148	10	a	a	DET
cana-730	148	11	restaurant	restaurant	NOUN
cana-730	148	12	setting	setting	NOUN
cana-730	148	13	,	,	PUNCT
cana-730	148	14	if	if	SCONJ
cana-730	148	15	a	a	DET
cana-730	148	16	piece	piece	NOUN
cana-730	148	17	of	of	ADP
cana-730	148	18	equipment	equipment	NOUN
cana-730	148	19	breaks	break	VERB
cana-730	148	20	down	down	ADP
cana-730	148	21	,	,	PUNCT
cana-730	148	22	like	like	ADP
cana-730	148	23	a	a	DET
cana-730	148	24	dishwasher	dishwasher	NOUN
cana-730	148	25	or	or	CCONJ
cana-730	148	26	oven	oven	NOUN
cana-730	148	27	,	,	PUNCT
cana-730	148	28	the	the	DET
cana-730	148	29	staff	staff	NOUN
cana-730	148	30	might	might	AUX
cana-730	148	31	continue	continue	VERB
cana-730	148	32	serving	serve	VERB
cana-730	148	33	customers	customer	NOUN
cana-730	148	34	but	but	CCONJ
cana-730	148	35	at	at	ADP
cana-730	148	36	a	a	DET
cana-730	148	37	slower	slow	ADJ
cana-730	148	38	pace	pace	NOUN
cana-730	148	39	,	,	PUNCT
cana-730	148	40	using	use	VERB
cana-730	148	41	alternative	alternative	ADJ
cana-730	148	42	methods	method	NOUN
cana-730	148	43	or	or	CCONJ
cana-730	148	44	equipment	equipment	NOUN
cana-730	148	45	until	until	SCONJ
cana-730	148	46	the	the	DET
cana-730	148	47	issue	issue	NOUN
cana-730	148	48	is	be	AUX
cana-730	148	49	resolved	resolve	VERB
cana-730	148	50	.	.	PUNCT
cana-730	149	1	this	this	DET
cana-730	149	2	way	way	NOUN
cana-730	149	3	,	,	PUNCT
cana-730	149	4	they	they	PRON
cana-730	149	5	can	can	AUX
cana-730	149	6	still	still	ADV
cana-730	149	7	provide	provide	VERB
cana-730	149	8	some	some	DET
cana-730	149	9	level	level	NOUN
cana-730	149	10	of	of	ADP
cana-730	149	11	service	service	NOUN
cana-730	149	12	to	to	ADP
cana-730	149	13	customers	customer	NOUN
cana-730	149	14	,	,	PUNCT
cana-730	149	15	rather	rather	ADV
cana-730	149	16	than	than	ADP
cana-730	149	17	abruptly	abruptly	ADV
cana-730	149	18	stopping	stop	VERB
cana-730	149	19	operations	operation	NOUN
cana-730	149	20	.	.	PUNCT
cana-730	150	1	customer	customer	NOUN
cana-730	150	2	service	service	NOUN
cana-730	150	3	centers	center	NOUN
cana-730	150	4	:	:	PUNCT
cana-730	150	5	in	in	ADP
cana-730	150	6	call	call	NOUN
cana-730	150	7	centers	center	NOUN
cana-730	150	8	or	or	CCONJ
cana-730	150	9	customer	customer	NOUN
cana-730	150	10	service	service	NOUN
cana-730	150	11	departments	department	NOUN
cana-730	150	12	,	,	PUNCT
cana-730	150	13	agents	agent	NOUN
cana-730	150	14	may	may	AUX
cana-730	150	15	continue	continue	VERB
cana-730	150	16	to	to	PART
cana-730	150	17	work	work	VERB
cana-730	150	18	but	but	CCONJ
cana-730	150	19	at	at	ADP
cana-730	150	20	a	a	DET
cana-730	150	21	reduced	reduced	ADJ
cana-730	150	22	capacity	capacity	NOUN
cana-730	150	23	during	during	ADP
cana-730	150	24	breakdowns	breakdown	NOUN
cana-730	150	25	,	,	PUNCT
cana-730	150	26	such	such	ADJ
cana-730	150	27	as	as	ADP
cana-730	150	28	when	when	SCONJ
cana-730	150	29	their	their	PRON
cana-730	150	30	computer	computer	NOUN
cana-730	150	31	systems	system	NOUN
cana-730	150	32	experience	experience	VERB
cana-730	150	33	technical	technical	ADJ
cana-730	150	34	issues	issue	NOUN
cana-730	150	35	or	or	CCONJ
cana-730	150	36	when	when	SCONJ
cana-730	150	37	they	they	PRON
cana-730	150	38	face	face	VERB
cana-730	150	39	disruptions	disruption	NOUN
cana-730	150	40	in	in	ADP
cana-730	150	41	internet	internet	NOUN
cana-730	150	42	connectivity	connectivity	NOUN
cana-730	150	43	.	.	PUNCT
cana-730	151	1	this	this	PRON
cana-730	151	2	can	can	AUX
cana-730	151	3	lead	lead	VERB
cana-730	151	4	to	to	AUX
cana-730	151	5	longer	long	ADV
cana-730	151	6	call	call	VERB
cana-730	151	7	handling	handling	NOUN
cana-730	151	8	times	time	NOUN
cana-730	151	9	and	and	CCONJ
cana-730	151	10	increased	increase	VERB
cana-730	151	11	queue	queue	NOUN
cana-730	151	12	lengths	length	NOUN
cana-730	151	13	,	,	PUNCT
cana-730	151	14	affecting	affect	VERB
cana-730	151	15	customer	customer	NOUN
cana-730	151	16	satisfaction	satisfaction	NOUN
cana-730	151	17	levels	level	NOUN
cana-730	151	18	.	.	PUNCT
cana-730	152	1	public	public	ADJ
cana-730	152	2	transportation	transportation	NOUN
cana-730	152	3	:	:	PUNCT
cana-730	152	4	during	during	ADP
cana-730	152	5	breakdowns	breakdown	NOUN
cana-730	152	6	or	or	CCONJ
cana-730	152	7	delays	delay	NOUN
cana-730	152	8	in	in	ADP
cana-730	152	9	public	public	ADJ
cana-730	152	10	transportation	transportation	NOUN
cana-730	152	11	systems	system	NOUN
cana-730	152	12	like	like	ADP
cana-730	152	13	buses	bus	NOUN
cana-730	152	14	or	or	CCONJ
cana-730	152	15	trains	train	NOUN
cana-730	152	16	,	,	PUNCT
cana-730	152	17	operators	operator	NOUN
cana-730	152	18	may	may	AUX
cana-730	152	19	still	still	ADV
cana-730	152	20	provide	provide	VERB
cana-730	152	21	service	service	NOUN
cana-730	152	22	,	,	PUNCT
cana-730	152	23	but	but	CCONJ
cana-730	152	24	at	at	ADP
cana-730	152	25	a	a	DET
cana-730	152	26	slower	slow	ADJ
cana-730	152	27	pace	pace	NOUN
cana-730	152	28	.	.	PUNCT
cana-730	153	1	for	for	ADP
cana-730	153	2	example	example	NOUN
cana-730	153	3	,	,	PUNCT
cana-730	153	4	a	a	DET
cana-730	153	5	bus	bus	NOUN
cana-730	153	6	experiencing	experience	VERB
cana-730	153	7	mechanical	mechanical	ADJ
cana-730	153	8	problems	problem	NOUN
cana-730	153	9	might	might	AUX
cana-730	153	10	continue	continue	VERB
cana-730	153	11	its	its	PRON
cana-730	153	12	route	route	NOUN
cana-730	153	13	but	but	CCONJ
cana-730	153	14	at	at	ADP
cana-730	153	15	reduced	reduced	ADJ
cana-730	153	16	speed	speed	NOUN
cana-730	153	17	,	,	PUNCT
cana-730	153	18	leading	lead	VERB
cana-730	153	19	to	to	ADP
cana-730	153	20	longer	long	ADV
cana-730	153	21	waiting	wait	VERB
cana-730	153	22	times	time	NOUN
cana-730	153	23	at	at	ADP
cana-730	153	24	bus	bus	NOUN
cana-730	153	25	stops	stop	NOUN
cana-730	153	26	and	and	CCONJ
cana-730	153	27	increased	increase	VERB
cana-730	153	28	passenger	passenger	NOUN
cana-730	153	29	frustration	frustration	NOUN
cana-730	153	30	.	.	PUNCT
cana-730	154	1	health	health	NOUN
cana-730	154	2	care	care	NOUN
cana-730	154	3	facilities	facility	NOUN
cana-730	154	4	:	:	PUNCT
cana-730	154	5	in	in	ADP
cana-730	154	6	hospitals	hospital	NOUN
cana-730	154	7	or	or	CCONJ
cana-730	154	8	clinics	clinic	NOUN
cana-730	154	9	,	,	PUNCT
cana-730	154	10	medical	medical	ADJ
cana-730	154	11	staff	staff	NOUN
cana-730	154	12	may	may	AUX
cana-730	154	13	continue	continue	VERB
cana-730	154	14	to	to	PART
cana-730	154	15	provide	provide	VERB
cana-730	154	16	care	care	NOUN
cana-730	154	17	during	during	ADP
cana-730	154	18	equipment	equipment	NOUN
cana-730	154	19	breakdowns	breakdown	NOUN
cana-730	154	20	or	or	CCONJ
cana-730	154	21	technical	technical	ADJ
cana-730	154	22	issues	issue	NOUN
cana-730	154	23	,	,	PUNCT
cana-730	154	24	but	but	CCONJ
cana-730	154	25	at	at	ADP
cana-730	154	26	a	a	DET
cana-730	154	27	slower	slow	ADJ
cana-730	154	28	pace	pace	NOUN
cana-730	154	29	or	or	CCONJ
cana-730	154	30	with	with	ADP
cana-730	154	31	limited	limited	ADJ
cana-730	154	32	functionality	functionality	NOUN
cana-730	154	33	.	.	PUNCT
cana-730	155	1	for	for	SCONJ
cana-730	155	2	communications	communication	NOUN
cana-730	155	3	on	on	ADP
cana-730	155	4	applied	apply	VERB
cana-730	155	5	nonlinear	nonlinear	ADJ
cana-730	155	6	analysis	analysis	NOUN
cana-730	155	7	issn	issn	NOUN
cana-730	155	8	:	:	PUNCT
cana-730	155	9	1074	1074	NUM
cana-730	155	10	-	-	PUNCT
cana-730	155	11	133x	133x	NUM
cana-730	155	12	vol	vol	NOUN
cana-730	155	13	31	31	NUM
cana-730	155	14	no	no	NOUN
cana-730	155	15	.	.	PUNCT
cana-730	156	1	3s	3s	NUM
cana-730	156	2	(	(	PUNCT
cana-730	156	3	2024	2024	NUM
cana-730	156	4	)	)	PUNCT
cana-730	156	5	51	51	NUM
cana-730	156	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-730	156	7	instance	instance	NOUN
cana-730	156	8	,	,	PUNCT
cana-730	156	9	a	a	DET
cana-730	156	10	medical	medical	ADJ
cana-730	156	11	imaging	imaging	NOUN
cana-730	156	12	machine	machine	NOUN
cana-730	156	13	experiencing	experience	VERB
cana-730	156	14	technical	technical	ADJ
cana-730	156	15	difficulties	difficulty	NOUN
cana-730	156	16	may	may	AUX
cana-730	156	17	still	still	ADV
cana-730	156	18	be	be	AUX
cana-730	156	19	operational	operational	ADJ
cana-730	156	20	but	but	CCONJ
cana-730	156	21	produce	produce	VERB
cana-730	156	22	scans	scan	NOUN
cana-730	156	23	at	at	ADP
cana-730	156	24	a	a	DET
cana-730	156	25	slower	slow	ADJ
cana-730	156	26	rate	rate	NOUN
cana-730	156	27	,	,	PUNCT
cana-730	156	28	affecting	affect	VERB
cana-730	156	29	patient	patient	ADJ
cana-730	156	30	throughput	throughput	NOUN
cana-730	156	31	and	and	CCONJ
cana-730	156	32	waiting	waiting	NOUN
cana-730	156	33	times	time	NOUN
cana-730	156	34	.	.	PUNCT
cana-730	157	1	manufacturing	manufacture	VERB
cana-730	157	2	plants	plant	NOUN
cana-730	157	3	:	:	PUNCT
cana-730	157	4	in	in	ADP
cana-730	157	5	manufacturing	manufacturing	NOUN
cana-730	157	6	settings	setting	NOUN
cana-730	157	7	,	,	PUNCT
cana-730	157	8	breakdowns	breakdown	NOUN
cana-730	157	9	of	of	ADP
cana-730	157	10	machinery	machinery	NOUN
cana-730	157	11	or	or	CCONJ
cana-730	157	12	equipment	equipment	NOUN
cana-730	157	13	can	can	AUX
cana-730	157	14	result	result	VERB
cana-730	157	15	in	in	ADP
cana-730	157	16	slower	slow	ADJ
cana-730	157	17	production	production	NOUN
cana-730	157	18	rates	rate	NOUN
cana-730	157	19	.	.	PUNCT
cana-730	158	1	workers	worker	NOUN
cana-730	158	2	may	may	AUX
cana-730	158	3	attempt	attempt	VERB
cana-730	158	4	to	to	PART
cana-730	158	5	continue	continue	VERB
cana-730	158	6	production	production	NOUN
cana-730	158	7	using	use	VERB
cana-730	158	8	alternative	alternative	ADJ
cana-730	158	9	methods	method	NOUN
cana-730	158	10	or	or	CCONJ
cana-730	158	11	manual	manual	ADJ
cana-730	158	12	processes	process	NOUN
cana-730	158	13	,	,	PUNCT
cana-730	158	14	but	but	CCONJ
cana-730	158	15	output	output	NOUN
cana-730	158	16	levels	level	NOUN
cana-730	158	17	are	be	AUX
cana-730	158	18	typically	typically	ADV
cana-730	158	19	reduced	reduce	VERB
cana-730	158	20	,	,	PUNCT
cana-730	158	21	leading	lead	VERB
cana-730	158	22	to	to	ADP
cana-730	158	23	bottlenecks	bottleneck	NOUN
cana-730	158	24	in	in	ADP
cana-730	158	25	the	the	DET
cana-730	158	26	production	production	NOUN
cana-730	158	27	line	line	NOUN
cana-730	158	28	and	and	CCONJ
cana-730	158	29	delays	delay	NOUN
cana-730	158	30	in	in	ADP
cana-730	158	31	fulfilling	fulfil	VERB
cana-730	158	32	orders	order	NOUN
cana-730	158	33	.	.	PUNCT
cana-730	159	1	information	information	NOUN
cana-730	159	2	technology	technology	NOUN
cana-730	159	3	services	service	NOUN
cana-730	159	4	:	:	PUNCT
cana-730	159	5	in	in	ADP
cana-730	159	6	it	it	PRON
cana-730	159	7	departments	department	NOUN
cana-730	159	8	or	or	CCONJ
cana-730	159	9	data	datum	NOUN
cana-730	159	10	centers	center	NOUN
cana-730	159	11	,	,	PUNCT
cana-730	159	12	slow	slow	ADJ
cana-730	159	13	work	work	NOUN
cana-730	159	14	during	during	ADP
cana-730	159	15	breakdown	breakdown	ADJ
cana-730	159	16	times	time	NOUN
cana-730	159	17	can	can	AUX
cana-730	159	18	occur	occur	VERB
cana-730	159	19	when	when	SCONJ
cana-730	159	20	servers	server	NOUN
cana-730	159	21	or	or	CCONJ
cana-730	159	22	network	network	NOUN
cana-730	159	23	infrastructure	infrastructure	NOUN
cana-730	159	24	experience	experience	NOUN
cana-730	159	25	performance	performance	NOUN
cana-730	159	26	degradation	degradation	NOUN
cana-730	159	27	or	or	CCONJ
cana-730	159	28	outages	outage	NOUN
cana-730	159	29	.	.	PUNCT
cana-730	160	1	it	it	PRON
cana-730	160	2	staff	staff	NOUN
cana-730	160	3	may	may	AUX
cana-730	160	4	implement	implement	VERB
cana-730	160	5	temporary	temporary	ADJ
cana-730	160	6	fixes	fix	NOUN
cana-730	160	7	or	or	CCONJ
cana-730	160	8	workarounds	workaround	NOUN
cana-730	160	9	to	to	PART
cana-730	160	10	maintain	maintain	VERB
cana-730	160	11	essential	essential	ADJ
cana-730	160	12	services	service	NOUN
cana-730	160	13	,	,	PUNCT
cana-730	160	14	but	but	CCONJ
cana-730	160	15	at	at	ADP
cana-730	160	16	a	a	DET
cana-730	160	17	reduced	reduced	ADJ
cana-730	160	18	capacity	capacity	NOUN
cana-730	160	19	,	,	PUNCT
cana-730	160	20	resulting	result	VERB
cana-730	160	21	in	in	ADP
cana-730	160	22	slower	slow	ADJ
cana-730	160	23	response	response	NOUN
cana-730	160	24	times	time	NOUN
cana-730	160	25	for	for	ADP
cana-730	160	26	user	user	NOUN
cana-730	160	27	requests	request	NOUN
cana-730	160	28	and	and	CCONJ
cana-730	160	29	increased	increase	VERB
cana-730	160	30	downtime	downtime	NOUN
cana-730	160	31	.	.	PUNCT
cana-730	161	1	however	however	ADV
cana-730	161	2	,	,	PUNCT
cana-730	161	3	it	it	PRON
cana-730	161	4	's	be	AUX
cana-730	161	5	important	important	ADJ
cana-730	161	6	to	to	PART
cana-730	161	7	communicate	communicate	VERB
cana-730	161	8	with	with	ADP
cana-730	161	9	customers	customer	NOUN
cana-730	161	10	about	about	ADP
cana-730	161	11	the	the	DET
cana-730	161	12	situation	situation	NOUN
cana-730	161	13	transparently	transparently	ADV
cana-730	161	14	.	.	PUNCT
cana-730	162	1	letting	let	VERB
cana-730	162	2	them	they	PRON
cana-730	162	3	know	know	VERB
cana-730	162	4	about	about	ADP
cana-730	162	5	the	the	DET
cana-730	162	6	issue	issue	NOUN
cana-730	162	7	,	,	PUNCT
cana-730	162	8	the	the	DET
cana-730	162	9	steps	step	NOUN
cana-730	162	10	being	be	AUX
cana-730	162	11	taken	take	VERB
cana-730	162	12	to	to	PART
cana-730	162	13	resolve	resolve	VERB
cana-730	162	14	it	it	PRON
cana-730	162	15	,	,	PUNCT
cana-730	162	16	and	and	CCONJ
cana-730	162	17	any	any	DET
cana-730	162	18	potential	potential	ADJ
cana-730	162	19	delays	delay	NOUN
cana-730	162	20	can	can	AUX
cana-730	162	21	help	help	VERB
cana-730	162	22	manage	manage	VERB
cana-730	162	23	expectations	expectation	NOUN
cana-730	162	24	and	and	CCONJ
cana-730	162	25	maintain	maintain	VERB
cana-730	162	26	customer	customer	NOUN
cana-730	162	27	satisfaction	satisfaction	NOUN
cana-730	162	28	.	.	PUNCT
cana-730	163	1	9	9	NUM
cana-730	163	2	numerical	numerical	ADJ
cana-730	163	3	results	result	NOUN
cana-730	163	4	in	in	ADP
cana-730	163	5	this	this	DET
cana-730	163	6	section	section	NOUN
cana-730	163	7	we	we	PRON
cana-730	163	8	discuss	discuss	VERB
cana-730	163	9	a	a	DET
cana-730	163	10	few	few	ADJ
cana-730	163	11	illustrative	illustrative	ADJ
cana-730	163	12	examples	example	NOUN
cana-730	163	13	to	to	PART
cana-730	163	14	show	show	VERB
cana-730	163	15	the	the	DET
cana-730	163	16	qualitative	qualitative	ADJ
cana-730	163	17	aspects	aspect	NOUN
cana-730	163	18	of	of	ADP
cana-730	163	19	the	the	DET
cana-730	163	20	queuing	queue	VERB
cana-730	163	21	model	model	NOUN
cana-730	163	22	under	under	ADP
cana-730	163	23	study	study	NOUN
cana-730	163	24	.	.	PUNCT
cana-730	164	1	we	we	PRON
cana-730	164	2	consider	consider	VERB
cana-730	164	3	rated	rate	VERB
cana-730	164	4	fifteen	fifteen	NUM
cana-730	164	5	examples	example	NOUN
cana-730	164	6	including	include	VERB
cana-730	164	7	4	4	NUM
cana-730	164	8	on	on	ADP
cana-730	164	9	reliability	reliability	NOUN
cana-730	164	10	measures	measure	NOUN
cana-730	164	11	.	.	PUNCT
cana-730	165	1	the	the	DET
cana-730	165	2	purpose	purpose	NOUN
cana-730	165	3	of	of	ADP
cana-730	165	4	the	the	DET
cana-730	165	5	following	follow	VERB
cana-730	165	6	four	four	NUM
cana-730	165	7	examples	example	NOUN
cana-730	165	8	are	be	AUX
cana-730	165	9	to	to	PART
cana-730	165	10	study	study	VERB
cana-730	165	11	the	the	DET
cana-730	165	12	reliability	reliability	NOUN
cana-730	165	13	measures	measure	NOUN
cana-730	165	14	,	,	PUNCT
cana-730	165	15	varying	vary	VERB
cana-730	165	16	some	some	DET
cana-730	165	17	selected	select	VERB
cana-730	165	18	parameters	parameter	NOUN
cana-730	165	19	(	(	PUNCT
cana-730	165	20	the	the	DET
cana-730	165	21	failure	failure	NOUN
cana-730	165	22	rate	rate	NOUN
cana-730	165	23	and	and	CCONJ
cana-730	165	24	repair	repair	NOUN
cana-730	165	25	rate	rate	NOUN
cana-730	165	26	)	)	PUNCT
cana-730	165	27	.	.	PUNCT
cana-730	166	1	we	we	PRON
cana-730	166	2	fix	fix	VERB
cana-730	166	3	𝜆	𝜆	PRON
cana-730	166	4	=	=	SYM
cana-730	166	5	5	5	NUM
cana-730	166	6	,	,	PUNCT
cana-730	166	7	𝜇	𝜇	X
cana-730	166	8	=	=	NOUN
cana-730	166	9	15	15	NUM
cana-730	166	10	,	,	PUNCT
cana-730	166	11	𝜇𝑏	𝜇𝑏	NOUN
cana-730	166	12	=	=	NOUN
cana-730	166	13	10	10	NUM
cana-730	166	14	.	.	PUNCT
cana-730	166	15	example	example	NOUN
cana-730	166	16	1	1	NUM
cana-730	166	17	figure	figure	NOUN
cana-730	166	18	1	1	NUM
cana-730	166	19	illustrate	illustrate	VERB
cana-730	166	20	the	the	DET
cana-730	166	21	availability	availability	NOUN
cana-730	166	22	of	of	ADP
cana-730	166	23	the	the	DET
cana-730	166	24	server	server	NOUN
cana-730	166	25	against	against	ADP
cana-730	166	26	the	the	DET
cana-730	166	27	failure	failure	NOUN
cana-730	166	28	rate	rate	NOUN
cana-730	166	29	𝛼.	𝛼.	NOUN
cana-730	166	30	we	we	PRON
cana-730	166	31	observe	observe	VERB
cana-730	166	32	that	that	SCONJ
cana-730	166	33	the	the	DET
cana-730	166	34	availability	availability	NOUN
cana-730	166	35	of	of	ADP
cana-730	166	36	the	the	DET
cana-730	166	37	server	server	NOUN
cana-730	166	38	under	under	ADP
cana-730	166	39	study	study	NOUN
cana-730	166	40	state	state	NOUN
cana-730	166	41	decreases	decrease	NOUN
cana-730	166	42	with	with	ADP
cana-730	166	43	increase	increase	NOUN
cana-730	166	44	in	in	ADP
cana-730	166	45	the	the	DET
cana-730	166	46	failure	failure	NOUN
cana-730	166	47	rate	rate	NOUN
cana-730	166	48	𝛼	𝛼	NOUN
cana-730	166	49	for	for	ADP
cana-730	166	50	the	the	DET
cana-730	166	51	different	different	ADJ
cana-730	166	52	repair	repair	NOUN
cana-730	166	53	rates	rate	NOUN
cana-730	166	54	𝛾	𝛾	NOUN
cana-730	166	55	=	=	SYM
cana-730	166	56	2,2.5	2,2.5	NOUN
cana-730	166	57	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-730	166	58	3	3	NUM
cana-730	166	59	as	as	SCONJ
cana-730	166	60	expected	expect	VERB
cana-730	166	61	.	.	PUNCT
cana-730	167	1	figure	figure	NOUN
cana-730	167	2	1	1	NUM
cana-730	167	3	:	:	PUNCT
cana-730	167	4	the	the	DET
cana-730	167	5	effect	effect	NOUN
cana-730	167	6	of	of	ADP
cana-730	167	7	𝛼	𝛼	PRON
cana-730	167	8	on	on	ADP
cana-730	167	9	the	the	DET
cana-730	167	10	server	server	NOUN
cana-730	167	11	availability	availability	NOUN
cana-730	167	12	example	example	NOUN
cana-730	167	13	2	2	NUM
cana-730	167	14	figure	figure	NOUN
cana-730	167	15	2	2	NUM
cana-730	167	16	tells	tell	VERB
cana-730	167	17	the	the	DET
cana-730	167	18	effect	effect	NOUN
cana-730	167	19	of	of	ADP
cana-730	167	20	the	the	DET
cana-730	167	21	repair	repair	NOUN
cana-730	167	22	rate	rate	NOUN
cana-730	167	23	𝛾	𝛾	NOUN
cana-730	167	24	for	for	ADP
cana-730	167	25	three	three	NUM
cana-730	167	26	different	different	ADJ
cana-730	167	27	values	value	NOUN
cana-730	167	28	of	of	ADP
cana-730	167	29	the	the	DET
cana-730	167	30	failure	failure	NOUN
cana-730	167	31	rate	rate	NOUN
cana-730	167	32	𝛼	𝛼	NOUN
cana-730	167	33	=	=	NOUN
cana-730	167	34	1.2	1.2	NUM
cana-730	167	35	,	,	PUNCT
cana-730	167	36	1.4	1.4	NUM
cana-730	167	37	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-730	167	38	1.6	1.6	NUM
cana-730	167	39	on	on	ADP
cana-730	167	40	the	the	DET
cana-730	167	41	availability	availability	NOUN
cana-730	167	42	of	of	ADP
cana-730	167	43	the	the	DET
cana-730	167	44	server	server	NOUN
cana-730	167	45	.	.	PUNCT
cana-730	168	1	it	it	PRON
cana-730	168	2	is	be	AUX
cana-730	168	3	seen	see	VERB
cana-730	168	4	that	that	SCONJ
cana-730	168	5	the	the	DET
cana-730	168	6	availability	availability	NOUN
cana-730	168	7	of	of	ADP
cana-730	168	8	the	the	DET
cana-730	168	9	server	server	NOUN
cana-730	168	10	increases	increase	NOUN
cana-730	168	11	with	with	ADP
cana-730	168	12	increasing	increase	VERB
cana-730	168	13	𝛾	𝛾	ADP
cana-730	168	14	.this	.this	PRON
cana-730	168	15	is	be	AUX
cana-730	168	16	because	because	SCONJ
cana-730	168	17	the	the	DET
cana-730	168	18	increasing	increase	VERB
cana-730	168	19	repair	repair	NOUN
cana-730	168	20	rate	rate	NOUN
cana-730	168	21	brings	bring	VERB
cana-730	168	22	the	the	DET
cana-730	168	23	server	server	NOUN
cana-730	168	24	to	to	PART
cana-730	168	25	available	available	ADJ
cana-730	168	26	.	.	PUNCT
cana-730	169	1	communications	communication	NOUN
cana-730	169	2	on	on	ADP
cana-730	169	3	applied	apply	VERB
cana-730	169	4	nonlinear	nonlinear	ADJ
cana-730	169	5	analysis	analysis	NOUN
cana-730	169	6	issn	issn	NOUN
cana-730	169	7	:	:	PUNCT
cana-730	169	8	1074	1074	NUM
cana-730	169	9	-	-	PUNCT
cana-730	169	10	133x	133x	NUM
cana-730	169	11	vol	vol	NOUN
cana-730	169	12	31	31	NUM
cana-730	169	13	no	no	NOUN
cana-730	169	14	.	.	PUNCT
cana-730	170	1	3s	3s	NUM
cana-730	170	2	(	(	PUNCT
cana-730	170	3	2024	2024	NUM
cana-730	170	4	)	)	PUNCT
cana-730	170	5	52	52	NUM
cana-730	170	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-730	170	7	figure	figure	NOUN
cana-730	170	8	2	2	NUM
cana-730	170	9	:	:	PUNCT
cana-730	170	10	the	the	DET
cana-730	170	11	effect	effect	NOUN
cana-730	170	12	of	of	ADP
cana-730	170	13	𝛾	𝛾	NOUN
cana-730	170	14	on	on	ADP
cana-730	170	15	the	the	DET
cana-730	170	16	server	server	NOUN
cana-730	170	17	availability	availability	NOUN
cana-730	170	18	example	example	NOUN
cana-730	170	19	3	3	NUM
cana-730	170	20	figure	figure	NOUN
cana-730	170	21	3	3	NUM
cana-730	170	22	.	.	NOUN
cana-730	170	23	depicts	depict	VERB
cana-730	170	24	variation	variation	NOUN
cana-730	170	25	of	of	ADP
cana-730	170	26	the	the	DET
cana-730	170	27	failure	failure	NOUN
cana-730	170	28	frequency	frequency	NOUN
cana-730	170	29	of	of	ADP
cana-730	170	30	the	the	DET
cana-730	170	31	server	server	NOUN
cana-730	170	32	against	against	ADP
cana-730	170	33	the	the	DET
cana-730	170	34	failure	failure	NOUN
cana-730	170	35	rate	rate	NOUN
cana-730	170	36	𝛼	𝛼	NOUN
cana-730	170	37	for	for	ADP
cana-730	170	38	three	three	NUM
cana-730	170	39	different	different	ADJ
cana-730	170	40	values	value	NOUN
cana-730	170	41	of	of	ADP
cana-730	170	42	the	the	DET
cana-730	170	43	arrival	arrival	NOUN
cana-730	170	44	rate	rate	NOUN
cana-730	170	45	𝜆	𝜆	PROPN
cana-730	171	1	=	=	NOUN
cana-730	171	2	4,5	4,5	NOUN
cana-730	171	3	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-730	171	4	6	6	NUM
cana-730	171	5	.	.	PUNCT
cana-730	172	1	as	as	SCONJ
cana-730	172	2	we	we	PRON
cana-730	172	3	expect	expect	VERB
cana-730	172	4	,	,	PUNCT
cana-730	172	5	the	the	DET
cana-730	172	6	failure	failure	NOUN
cana-730	172	7	frequency	frequency	NOUN
cana-730	172	8	of	of	ADP
cana-730	172	9	the	the	DET
cana-730	172	10	server	server	NOUN
cana-730	172	11	increases	increase	NOUN
cana-730	172	12	with	with	ADP
cana-730	172	13	increasing	increase	VERB
cana-730	172	14	in	in	ADP
cana-730	172	15	the	the	DET
cana-730	172	16	failure	failure	NOUN
cana-730	172	17	rate	rate	NOUN
cana-730	172	18	𝛼.	𝛼.	NOUN
cana-730	172	19	figure	figure	NOUN
cana-730	172	20	3	3	NUM
cana-730	172	21	:	:	PUNCT
cana-730	172	22	the	the	DET
cana-730	172	23	effect	effect	NOUN
cana-730	172	24	of	of	ADP
cana-730	172	25	𝛼	𝛼	PRON
cana-730	172	26	on	on	ADP
cana-730	172	27	the	the	DET
cana-730	172	28	server	server	NOUN
cana-730	172	29	failure	failure	NOUN
cana-730	172	30	example	example	NOUN
cana-730	172	31	4	4	NUM
cana-730	172	32	figure	figure	NOUN
cana-730	172	33	4	4	NUM
cana-730	172	34	displays	display	VERB
cana-730	172	35	the	the	DET
cana-730	172	36	effect	effect	NOUN
cana-730	172	37	of	of	ADP
cana-730	172	38	the	the	DET
cana-730	172	39	repair	repair	NOUN
cana-730	172	40	rate	rate	NOUN
cana-730	172	41	𝛾	𝛾	NOUN
cana-730	172	42	on	on	ADP
cana-730	172	43	the	the	DET
cana-730	172	44	failure	failure	NOUN
cana-730	172	45	frequency	frequency	NOUN
cana-730	172	46	of	of	ADP
cana-730	172	47	the	the	DET
cana-730	172	48	server	server	NOUN
cana-730	172	49	for	for	ADP
cana-730	172	50	three	three	NUM
cana-730	172	51	different	different	ADJ
cana-730	172	52	values	value	NOUN
cana-730	172	53	of	of	ADP
cana-730	172	54	𝜆	𝜆	DET
cana-730	172	55	.the	.the	DET
cana-730	172	56	failure	failure	NOUN
cana-730	172	57	frequency	frequency	NOUN
cana-730	172	58	of	of	ADP
cana-730	172	59	the	the	DET
cana-730	172	60	server	server	NOUN
cana-730	172	61	decreases	decrease	VERB
cana-730	172	62	with	with	ADP
cana-730	172	63	increase	increase	NOUN
cana-730	172	64	in	in	ADP
cana-730	172	65	the	the	DET
cana-730	172	66	repair	repair	NOUN
cana-730	172	67	rate	rate	NOUN
cana-730	172	68	𝛾	𝛾	PROPN
cana-730	172	69	as	as	SCONJ
cana-730	172	70	it	it	PRON
cana-730	172	71	is	be	AUX
cana-730	172	72	quite	quite	ADV
cana-730	172	73	natural	natural	ADJ
cana-730	172	74	.	.	PUNCT
cana-730	173	1	figure	figure	NOUN
cana-730	173	2	4	4	NUM
cana-730	173	3	:	:	PUNCT
cana-730	173	4	the	the	DET
cana-730	173	5	effect	effect	NOUN
cana-730	173	6	of	of	ADP
cana-730	173	7	𝛾	𝛾	NOUN
cana-730	173	8	on	on	ADP
cana-730	173	9	the	the	DET
cana-730	173	10	server	server	NOUN
cana-730	173	11	failure	failure	NOUN
cana-730	173	12	example	example	NOUN
cana-730	173	13	5	5	NUM
cana-730	173	14	in	in	ADP
cana-730	173	15	this	this	DET
cana-730	173	16	example	example	NOUN
cana-730	173	17	,	,	PUNCT
cana-730	173	18	we	we	PRON
cana-730	173	19	study	study	VERB
cana-730	173	20	the	the	DET
cana-730	173	21	effect	effect	NOUN
cana-730	173	22	of	of	ADP
cana-730	173	23	varying	vary	VERB
cana-730	173	24	𝜆	𝜆	ADP
cana-730	173	25	and	and	CCONJ
cana-730	173	26	𝜇	𝜇	X
cana-730	173	27	on	on	ADP
cana-730	173	28	the	the	DET
cana-730	173	29	probability	probability	NOUN
cana-730	173	30	𝑃1,0	𝑃1,0	NUM
cana-730	173	31	.	.	PUNCT
cana-730	174	1	we	we	PRON
cana-730	174	2	fix	fix	VERB
cana-730	174	3	𝛼	𝛼	NOUN
cana-730	174	4	=	=	SYM
cana-730	174	5	2	2	NUM
cana-730	174	6	𝜇𝑏	𝜇𝑏	NOUN
cana-730	174	7	=	=	NOUN
cana-730	174	8	50	50	NUM
cana-730	174	9	,	,	PUNCT
cana-730	174	10	𝛾	𝛾	NOUN
cana-730	174	11	=	=	SYM
cana-730	174	12	3	3	NUM
cana-730	174	13	,	,	PUNCT
cana-730	174	14	𝐺′(1	𝐺′(1	NOUN
cana-730	174	15	)	)	PUNCT
cana-730	174	16	=	=	SYM
cana-730	174	17	0.4	0.4	NUM
cana-730	174	18	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-730	174	19	𝐺′′(1	𝐺′′(1	PROPN
cana-730	174	20	)	)	PUNCT
cana-730	174	21	=	=	NUM
cana-730	174	22	0.03	0.03	NUM
cana-730	174	23	.	.	PUNCT
cana-730	175	1	as	as	SCONJ
cana-730	175	2	we	we	PRON
cana-730	175	3	expected	expect	VERB
cana-730	175	4	,	,	PUNCT
cana-730	175	5	in	in	ADP
cana-730	175	6	figure	figure	NOUN
cana-730	175	7	5	5	NUM
cana-730	175	8	we	we	PRON
cana-730	175	9	notice	notice	VERB
cana-730	175	10	that	that	SCONJ
cana-730	175	11	the	the	DET
cana-730	175	12	probability	probability	NOUN
cana-730	175	13	𝑃1,0	𝑃1,0	NUM
cana-730	175	14	appears	appear	VERB
cana-730	175	15	to	to	PART
cana-730	175	16	decrease	decrease	VERB
cana-730	175	17	as	as	ADP
cana-730	175	18	a	a	DET
cana-730	175	19	function	function	NOUN
cana-730	175	20	𝜆	𝜆	ADP
cana-730	175	21	for	for	ADP
cana-730	175	22	fixed	fix	VERB
cana-730	175	23	𝜇	𝜇	ADP
cana-730	175	24	and	and	CCONJ
cana-730	175	25	for	for	SCONJ
cana-730	175	26	fixed	fix	VERB
cana-730	175	27	𝜆	𝜆	ADP
cana-730	175	28	the	the	DET
cana-730	175	29	probability	probability	NOUN
cana-730	175	30	measure	measure	NOUN
cana-730	175	31	𝑃1,0	𝑃1,0	NUM
cana-730	175	32	increases	increase	NOUN
cana-730	175	33	as	as	ADP
cana-730	175	34	a	a	DET
cana-730	175	35	function	function	NOUN
cana-730	175	36	of	of	ADP
cana-730	175	37	the	the	DET
cana-730	175	38	service	service	NOUN
cana-730	175	39	rate	rate	NOUN
cana-730	175	40	𝜇.	𝜇.	NOUN
cana-730	175	41	communications	communication	NOUN
cana-730	175	42	on	on	ADP
cana-730	175	43	applied	apply	VERB
cana-730	175	44	nonlinear	nonlinear	ADJ
cana-730	175	45	analysis	analysis	NOUN
cana-730	175	46	issn	issn	NOUN
cana-730	175	47	:	:	PUNCT
cana-730	175	48	1074	1074	NUM
cana-730	175	49	-	-	PUNCT
cana-730	175	50	133x	133x	NUM
cana-730	175	51	vol	vol	NOUN
cana-730	175	52	31	31	NUM
cana-730	175	53	no	no	NOUN
cana-730	175	54	.	.	PUNCT
cana-730	176	1	3s	3s	NUM
cana-730	176	2	(	(	PUNCT
cana-730	176	3	2024	2024	NUM
cana-730	176	4	)	)	PUNCT
cana-730	176	5	53	53	NUM
cana-730	176	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-730	176	7	figure	figure	NOUN
cana-730	176	8	5	5	NUM
cana-730	176	9	:	:	PUNCT
cana-730	176	10	the	the	DET
cana-730	176	11	effect	effect	NOUN
cana-730	176	12	of	of	ADP
cana-730	176	13	𝜆	𝜆	DET
cana-730	176	14	𝑎𝑛𝑑	𝑎𝑛𝑑	NOUN
cana-730	176	15	𝜇	𝜇	X
cana-730	176	16	on	on	ADP
cana-730	176	17	𝑃1,0	𝑃1,0	NUM
cana-730	176	18	example	example	NOUN
cana-730	176	19	6	6	NUM
cana-730	176	20	in	in	ADP
cana-730	176	21	this	this	DET
cana-730	176	22	example	example	NOUN
cana-730	176	23	,	,	PUNCT
cana-730	176	24	we	we	PRON
cana-730	176	25	study	study	VERB
cana-730	176	26	the	the	DET
cana-730	176	27	effect	effect	NOUN
cana-730	176	28	of	of	ADP
cana-730	176	29	varying	vary	VERB
cana-730	176	30	𝜆	𝜆	ADP
cana-730	176	31	and	and	CCONJ
cana-730	176	32	𝜇	𝜇	X
cana-730	176	33	on	on	ADP
cana-730	176	34	the	the	DET
cana-730	176	35	probability	probability	NOUN
cana-730	176	36	𝑃0,0	𝑃0,0	NOUN
cana-730	176	37	as	as	SCONJ
cana-730	176	38	we	we	PRON
cana-730	176	39	expected	expect	VERB
cana-730	176	40	,	,	PUNCT
cana-730	176	41	figure	figure	VERB
cana-730	176	42	6	6	NUM
cana-730	176	43	shows	show	VERB
cana-730	176	44	that	that	SCONJ
cana-730	176	45	the	the	DET
cana-730	176	46	probability	probability	NOUN
cana-730	176	47	measure	measure	NOUN
cana-730	176	48	𝑃0,0	𝑃0,0	VERB
cana-730	176	49	decreases	decrease	NOUN
cana-730	176	50	as	as	ADP
cana-730	176	51	a	a	DET
cana-730	176	52	function	function	NOUN
cana-730	176	53	of	of	ADP
cana-730	176	54	𝜇	𝜇	ADP
cana-730	176	55	for	for	ADP
cana-730	176	56	fixed	fix	VERB
cana-730	176	57	𝜆	𝜆	PRON
cana-730	176	58	.for	.for	ADV
cana-730	176	59	fixed	fix	VERB
cana-730	176	60	𝜇	𝜇	ADP
cana-730	176	61	the	the	DET
cana-730	176	62	probability	probability	NOUN
cana-730	176	63	measure	measure	NOUN
cana-730	176	64	𝑃0,0	𝑃0,0	VERB
cana-730	176	65	decreases	decrease	NOUN
cana-730	176	66	as	as	ADP
cana-730	176	67	function	function	NOUN
cana-730	176	68	of	of	ADP
cana-730	176	69	the	the	DET
cana-730	176	70	arrival	arrival	NOUN
cana-730	176	71	rate	rate	NOUN
cana-730	176	72	𝜆.	𝜆.	PROPN
cana-730	176	73	figure	figure	VERB
cana-730	176	74	6	6	NUM
cana-730	176	75	:	:	PUNCT
cana-730	176	76	the	the	DET
cana-730	176	77	effect	effect	NOUN
cana-730	176	78	of	of	ADP
cana-730	176	79	𝜆	𝜆	DET
cana-730	176	80	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-730	176	81	𝜇	𝜇	X
cana-730	176	82	on	on	ADP
cana-730	176	83	𝑃0,0	𝑃0,0	NOUN
cana-730	176	84	example	example	NOUN
cana-730	176	85	7	7	NUM
cana-730	176	86	in	in	ADP
cana-730	176	87	this	this	DET
cana-730	176	88	example	example	NOUN
cana-730	176	89	,	,	PUNCT
cana-730	176	90	we	we	PRON
cana-730	176	91	study	study	VERB
cana-730	176	92	the	the	DET
cana-730	176	93	effect	effect	NOUN
cana-730	176	94	of	of	ADP
cana-730	176	95	service	service	NOUN
cana-730	176	96	rate	rate	NOUN
cana-730	176	97	𝜇	𝜇	ADP
cana-730	176	98	and	and	CCONJ
cana-730	176	99	the	the	DET
cana-730	176	100	arrival	arrival	NOUN
cana-730	176	101	rate	rate	NOUN
cana-730	176	102	𝜆	𝜆	NOUN
cana-730	176	103	on	on	ADP
cana-730	176	104	the	the	DET
cana-730	176	105	probability	probability	NOUN
cana-730	176	106	measure	measure	NOUN
cana-730	176	107	𝑃0(1	𝑃0(1	NOUN
cana-730	176	108	)	)	PUNCT
cana-730	176	109	and	and	CCONJ
cana-730	176	110	the	the	DET
cana-730	176	111	results	result	NOUN
cana-730	176	112	are	be	AUX
cana-730	176	113	plotted	plot	VERB
cana-730	176	114	in	in	ADP
cana-730	176	115	the	the	DET
cana-730	176	116	figure	figure	NOUN
cana-730	176	117	7	7	NUM
cana-730	176	118	.	.	PUNCT
cana-730	177	1	it	it	PRON
cana-730	177	2	is	be	AUX
cana-730	177	3	seen	see	VERB
cana-730	177	4	that	that	SCONJ
cana-730	177	5	the	the	DET
cana-730	177	6	probability	probability	NOUN
cana-730	177	7	measure	measure	NOUN
cana-730	177	8	𝑃0(1	𝑃0(1	NOUN
cana-730	177	9	)	)	PUNCT
cana-730	177	10	increases	increase	NOUN
cana-730	177	11	as	as	ADP
cana-730	177	12	a	a	DET
cana-730	177	13	function	function	NOUN
cana-730	177	14	of	of	ADP
cana-730	177	15	the	the	DET
cana-730	177	16	arrival	arrival	NOUN
cana-730	177	17	rate	rate	NOUN
cana-730	177	18	𝜆	𝜆	ADP
cana-730	177	19	for	for	ADP
cana-730	177	20	fixed	fixed	ADJ
cana-730	177	21	𝜇	𝜇	ADP
cana-730	177	22	.also	.also	NOUN
cana-730	177	23	,	,	PUNCT
cana-730	177	24	we	we	PRON
cana-730	177	25	observe	observe	VERB
cana-730	177	26	that	that	SCONJ
cana-730	177	27	the	the	DET
cana-730	177	28	probability	probability	NOUN
cana-730	177	29	measure	measure	NOUN
cana-730	177	30	𝑃0(1	𝑃0(1	NOUN
cana-730	177	31	)	)	PUNCT
cana-730	177	32	decreases	decrease	NOUN
cana-730	177	33	as	as	ADP
cana-730	177	34	a	a	DET
cana-730	177	35	function	function	NOUN
cana-730	177	36	of	of	ADP
cana-730	177	37	the	the	DET
cana-730	177	38	service	service	NOUN
cana-730	177	39	rate	rate	NOUN
cana-730	177	40	𝜇	𝜇	ADP
cana-730	177	41	for	for	ADP
cana-730	177	42	fixed	fix	VERB
cana-730	177	43	𝜆	𝜆	PRON
cana-730	177	44	.	.	PUNCT
cana-730	178	1	figure	figure	NOUN
cana-730	178	2	7	7	NUM
cana-730	178	3	:	:	PUNCT
cana-730	178	4	the	the	DET
cana-730	178	5	effect	effect	NOUN
cana-730	178	6	of	of	ADP
cana-730	178	7	𝜆	𝜆	DET
cana-730	178	8	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-730	178	9	𝜇	𝜇	X
cana-730	178	10	on	on	ADP
cana-730	178	11	𝑃0(1	𝑃0(1	NOUN
cana-730	178	12	)	)	PUNCT
cana-730	178	13	example	example	NOUN
cana-730	178	14	8	8	NUM
cana-730	178	15	this	this	DET
cana-730	178	16	example	example	NOUN
cana-730	178	17	,	,	PUNCT
cana-730	178	18	clearly	clearly	ADV
cana-730	178	19	shows	show	VERB
cana-730	178	20	the	the	DET
cana-730	178	21	effect	effect	NOUN
cana-730	178	22	of	of	ADP
cana-730	178	23	varying	vary	VERB
cana-730	178	24	arrival	arrival	NOUN
cana-730	178	25	rate	rate	NOUN
cana-730	178	26	𝜆	𝜆	ADP
cana-730	179	1	and	and	CCONJ
cana-730	179	2	the	the	DET
cana-730	179	3	service	service	NOUN
cana-730	179	4	rate	rate	NOUN
cana-730	179	5	𝜇	𝜇	ADP
cana-730	179	6	on	on	ADP
cana-730	179	7	the	the	DET
cana-730	179	8	probability	probability	NOUN
cana-730	179	9	measure	measure	NOUN
cana-730	179	10	𝑃1(1)here	𝑃1(1)here	PRON
cana-730	179	11	figure	figure	VERB
cana-730	179	12	8	8	NUM
cana-730	179	13	shows	show	VERB
cana-730	179	14	that	that	SCONJ
cana-730	179	15	the	the	DET
cana-730	179	16	probability	probability	NOUN
cana-730	179	17	measure	measure	NOUN
cana-730	179	18	𝑃1(1	𝑃1(1	NOUN
cana-730	179	19	)	)	PUNCT
cana-730	179	20	decreases	decrease	NOUN
cana-730	179	21	as	as	ADP
cana-730	179	22	a	a	DET
cana-730	179	23	function	function	NOUN
cana-730	179	24	of	of	ADP
cana-730	179	25	the	the	DET
cana-730	179	26	arrival	arrival	NOUN
cana-730	179	27	rate	rate	NOUN
cana-730	179	28	𝜆	𝜆	ADP
cana-730	179	29	for	for	ADP
cana-730	179	30	fixed	fix	VERB
cana-730	179	31	𝜇	𝜇	ADP
cana-730	179	32	and	and	CCONJ
cana-730	179	33	for	for	ADP
cana-730	179	34	fixed	fix	VERB
cana-730	179	35	𝜆	𝜆	PUNCT
cana-730	179	36	we	we	PRON
cana-730	179	37	observe	observe	VERB
cana-730	179	38	that	that	SCONJ
cana-730	179	39	the	the	DET
cana-730	179	40	probability	probability	NOUN
cana-730	179	41	measure	measure	NOUN
cana-730	179	42	𝑃1(1)decreases	𝑃1(1)decrease	NOUN
cana-730	179	43	as	as	ADP
cana-730	179	44	a	a	DET
cana-730	179	45	function	function	NOUN
cana-730	179	46	of	of	ADP
cana-730	179	47	the	the	DET
cana-730	179	48	service	service	NOUN
cana-730	179	49	rate	rate	NOUN
cana-730	179	50	𝜇	𝜇	ADP
cana-730	179	51	for	for	ADP
cana-730	179	52	fixed	fix	VERB
cana-730	179	53	𝜆	𝜆	PRON
cana-730	179	54	.	.	PUNCT
cana-730	180	1	communications	communication	NOUN
cana-730	180	2	on	on	ADP
cana-730	180	3	applied	apply	VERB
cana-730	180	4	nonlinear	nonlinear	ADJ
cana-730	180	5	analysis	analysis	NOUN
cana-730	180	6	issn	issn	NOUN
cana-730	180	7	:	:	PUNCT
cana-730	180	8	1074	1074	NUM
cana-730	180	9	-	-	PUNCT
cana-730	180	10	133x	133x	NUM
cana-730	180	11	vol	vol	NOUN
cana-730	180	12	31	31	NUM
cana-730	180	13	no	no	NOUN
cana-730	180	14	.	.	PUNCT
cana-730	181	1	3s	3s	NUM
cana-730	181	2	(	(	PUNCT
cana-730	181	3	2024	2024	NUM
cana-730	181	4	)	)	PUNCT
cana-730	181	5	54	54	NUM
cana-730	181	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-730	181	7	figure	figure	NOUN
cana-730	181	8	8	8	NUM
cana-730	181	9	:	:	PUNCT
cana-730	181	10	the	the	DET
cana-730	181	11	effect	effect	NOUN
cana-730	181	12	of	of	ADP
cana-730	181	13	𝜆	𝜆	DET
cana-730	181	14	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-730	181	15	𝜇	𝜇	X
cana-730	181	16	on	on	ADP
cana-730	181	17	𝑃1(1	𝑃1(1	ADJ
cana-730	181	18	)	)	PUNCT
cana-730	181	19	example	example	NOUN
cana-730	181	20	9	9	NUM
cana-730	181	21	in	in	ADP
cana-730	181	22	this	this	DET
cana-730	181	23	example	example	NOUN
cana-730	181	24	,	,	PUNCT
cana-730	181	25	we	we	PRON
cana-730	181	26	study	study	VERB
cana-730	181	27	the	the	DET
cana-730	181	28	effect	effect	NOUN
cana-730	181	29	of	of	ADP
cana-730	181	30	varying	vary	VERB
cana-730	181	31	𝜆	𝜆	ADP
cana-730	181	32	and	and	CCONJ
cana-730	181	33	𝜇	𝜇	X
cana-730	181	34	on	on	ADP
cana-730	181	35	the	the	DET
cana-730	181	36	probability	probability	NOUN
cana-730	181	37	measure	measure	NOUN
cana-730	181	38	𝑃2(1	𝑃2(1	NOUN
cana-730	181	39	)	)	PUNCT
cana-730	181	40	.as	.as	PUNCT
cana-730	182	1	we	we	PRON
cana-730	182	2	expected	expect	VERB
cana-730	182	3	,	,	PUNCT
cana-730	182	4	in	in	ADP
cana-730	182	5	figure	figure	NOUN
cana-730	182	6	9	9	NUM
cana-730	182	7	we	we	PRON
cana-730	182	8	notice	notice	VERB
cana-730	182	9	that	that	SCONJ
cana-730	182	10	the	the	DET
cana-730	182	11	probability	probability	NOUN
cana-730	182	12	measure	measure	NOUN
cana-730	182	13	𝑃2(1)appears	𝑃2(1)appear	NOUN
cana-730	182	14	to	to	PART
cana-730	182	15	increase	increase	VERB
cana-730	182	16	as	as	ADP
cana-730	182	17	a	a	DET
cana-730	182	18	function	function	NOUN
cana-730	182	19	of	of	ADP
cana-730	182	20	𝜆	𝜆	PRON
cana-730	182	21	for	for	ADP
cana-730	182	22	fixed	fix	VERB
cana-730	182	23	𝜇	𝜇	NOUN
cana-730	182	24	and	and	CCONJ
cana-730	182	25	it	it	PRON
cana-730	182	26	decreases	decrease	VERB
cana-730	182	27	as	as	ADP
cana-730	182	28	a	a	DET
cana-730	182	29	function	function	NOUN
cana-730	182	30	of	of	ADP
cana-730	182	31	the	the	DET
cana-730	182	32	service	service	NOUN
cana-730	182	33	rate	rate	NOUN
cana-730	182	34	𝜇	𝜇	ADP
cana-730	182	35	for	for	ADP
cana-730	182	36	fixed	fix	VERB
cana-730	182	37	𝜆	𝜆	PRON
cana-730	182	38	.	.	PUNCT
cana-730	183	1	figure	figure	NOUN
cana-730	183	2	9	9	NUM
cana-730	183	3	:	:	PUNCT
cana-730	183	4	the	the	DET
cana-730	183	5	effect	effect	NOUN
cana-730	183	6	of	of	ADP
cana-730	183	7	𝜆	𝜆	DET
cana-730	183	8	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-730	183	9	𝜇	𝜇	X
cana-730	183	10	on	on	ADP
cana-730	183	11	𝑃2(1	𝑃2(1	NOUN
cana-730	183	12	)	)	PUNCT
cana-730	183	13	example	example	NOUN
cana-730	183	14	10	10	NUM
cana-730	183	15	in	in	ADP
cana-730	183	16	this	this	DET
cana-730	183	17	example	example	NOUN
cana-730	183	18	,	,	PUNCT
cana-730	183	19	we	we	PRON
cana-730	183	20	investigate	investigate	VERB
cana-730	183	21	the	the	DET
cana-730	183	22	impact	impact	NOUN
cana-730	183	23	of	of	ADP
cana-730	183	24	the	the	DET
cana-730	183	25	normal	normal	ADJ
cana-730	183	26	service	service	NOUN
cana-730	183	27	rate	rate	NOUN
cana-730	183	28	𝜇	𝜇	ADP
cana-730	183	29	and	and	CCONJ
cana-730	183	30	partial	partial	ADJ
cana-730	183	31	service	service	NOUN
cana-730	183	32	rate	rate	NOUN
cana-730	183	33	𝜇𝑏	𝜇𝑏	NOUN
cana-730	183	34	on	on	ADP
cana-730	183	35	the	the	DET
cana-730	183	36	study	study	NOUN
cana-730	183	37	state	state	NOUN
cana-730	183	38	mean	mean	NOUN
cana-730	183	39	number	number	NOUN
cana-730	183	40	of	of	ADP
cana-730	183	41	customers	customer	NOUN
cana-730	183	42	in	in	ADP
cana-730	183	43	the	the	DET
cana-730	183	44	system	system	NOUN
cana-730	183	45	under	under	ADP
cana-730	183	46	the	the	DET
cana-730	183	47	ergodicity	ergodicity	NOUN
cana-730	183	48	condition	condition	NOUN
cana-730	183	49	.	.	PUNCT
cana-730	184	1	in	in	ADP
cana-730	184	2	figure	figure	NOUN
cana-730	184	3	10	10	NUM
cana-730	184	4	,	,	PUNCT
cana-730	184	5	we	we	PRON
cana-730	184	6	notice	notice	VERB
cana-730	184	7	that	that	SCONJ
cana-730	184	8	the	the	DET
cana-730	184	9	study	study	NOUN
cana-730	184	10	state	state	NOUN
cana-730	184	11	mean	mean	VERB
cana-730	184	12	number	number	NOUN
cana-730	184	13	of	of	ADP
cana-730	184	14	customer	customer	NOUN
cana-730	184	15	e(x	e(x	NUM
cana-730	184	16	)	)	PUNCT
cana-730	184	17	increases	increase	NOUN
cana-730	184	18	as	as	ADP
cana-730	184	19	the	the	DET
cana-730	184	20	partial	partial	ADJ
cana-730	184	21	service	service	NOUN
cana-730	184	22	rate	rate	NOUN
cana-730	184	23	𝜇𝑏for	𝜇𝑏for	ADP
cana-730	184	24	fixed	fix	VERB
cana-730	184	25	normal	normal	ADJ
cana-730	184	26	service	service	NOUN
cana-730	184	27	rate	rate	NOUN
cana-730	184	28	𝜇	𝜇	ADP
cana-730	184	29	and	and	CCONJ
cana-730	184	30	it	it	PRON
cana-730	184	31	also	also	ADV
cana-730	184	32	increases	increase	VERB
cana-730	184	33	for	for	ADP
cana-730	184	34	the	the	DET
cana-730	184	35	normal	normal	ADJ
cana-730	184	36	service	service	NOUN
cana-730	184	37	rate	rate	NOUN
cana-730	184	38	𝜇	𝜇	ADP
cana-730	184	39	for	for	ADP
cana-730	184	40	the	the	DET
cana-730	184	41	fixed	fix	VERB
cana-730	184	42	partial	partial	ADJ
cana-730	184	43	service	service	NOUN
cana-730	184	44	rate	rate	NOUN
cana-730	184	45	𝜇𝑏.	𝜇𝑏.	PROPN
cana-730	184	46	figure	figure	NOUN
cana-730	184	47	10	10	NUM
cana-730	184	48	:	:	PUNCT
cana-730	184	49	the	the	DET
cana-730	184	50	effect	effect	NOUN
cana-730	184	51	of	of	ADP
cana-730	184	52	𝜇	𝜇	ADP
cana-730	184	53	𝑎𝑛𝑑	𝑎𝑛𝑑	X
cana-730	184	54	𝜇𝑏	𝜇𝑏	VERB
cana-730	184	55	on	on	ADP
cana-730	184	56	e(x	e(x	NUM
cana-730	184	57	)	)	PUNCT
cana-730	184	58	example	example	NOUN
cana-730	184	59	11	11	NUM
cana-730	184	60	we	we	PRON
cana-730	184	61	study	study	VERB
cana-730	184	62	the	the	DET
cana-730	184	63	effect	effect	NOUN
cana-730	184	64	of	of	ADP
cana-730	184	65	the	the	DET
cana-730	184	66	varying	vary	VERB
cana-730	184	67	arrival	arrival	NOUN
cana-730	184	68	rate	rate	NOUN
cana-730	184	69	𝜆	𝜆	ADP
cana-730	184	70	and	and	CCONJ
cana-730	184	71	the	the	DET
cana-730	184	72	repair	repair	NOUN
cana-730	184	73	rate	rate	NOUN
cana-730	184	74	𝛾	𝛾	NOUN
cana-730	184	75	on	on	ADP
cana-730	184	76	the	the	DET
cana-730	184	77	probability	probability	NOUN
cana-730	184	78	measure	measure	NOUN
cana-730	184	79	𝑃0(1)and	𝑃0(1)and	ADP
cana-730	184	80	the	the	DET
cana-730	184	81	results	result	NOUN
cana-730	184	82	are	be	AUX
cana-730	184	83	plotted	plot	VERB
cana-730	184	84	in	in	ADP
cana-730	184	85	the	the	DET
cana-730	184	86	figure	figure	NOUN
cana-730	184	87	11	11	NUM
cana-730	184	88	.	.	PUNCT
cana-730	185	1	it	it	PRON
cana-730	185	2	is	be	AUX
cana-730	185	3	seen	see	VERB
cana-730	185	4	that	that	SCONJ
cana-730	185	5	the	the	DET
cana-730	185	6	probability	probability	NOUN
cana-730	185	7	measure	measure	NOUN
cana-730	185	8	𝑃0(1	𝑃0(1	NOUN
cana-730	185	9	)	)	PUNCT
cana-730	185	10	increases	increase	NOUN
cana-730	185	11	as	as	ADP
cana-730	185	12	the	the	DET
cana-730	185	13	function	function	NOUN
cana-730	185	14	of	of	ADP
cana-730	185	15	the	the	DET
cana-730	185	16	arrival	arrival	NOUN
cana-730	185	17	rate	rate	NOUN
cana-730	185	18	𝜆	𝜆	ADP
cana-730	185	19	for	for	ADP
cana-730	185	20	fixed	fix	VERB
cana-730	185	21	repair	repair	NOUN
cana-730	185	22	rate	rate	NOUN
cana-730	185	23	𝛾	𝛾	PROPN
cana-730	185	24	and	and	CCONJ
cana-730	185	25	we	we	PRON
cana-730	185	26	also	also	ADV
cana-730	185	27	observe	observe	VERB
cana-730	185	28	that	that	SCONJ
cana-730	185	29	the	the	DET
cana-730	185	30	probability	probability	NOUN
cana-730	185	31	measure	measure	NOUN
cana-730	185	32	𝑃0(1	𝑃0(1	NOUN
cana-730	185	33	)	)	PUNCT
cana-730	185	34	decreases	decrease	NOUN
cana-730	185	35	as	as	SCONJ
cana-730	185	36	the	the	DET
cana-730	185	37	function	function	NOUN
cana-730	185	38	of	of	ADP
cana-730	185	39	the	the	DET
cana-730	185	40	repair	repair	NOUN
cana-730	185	41	rate	rate	NOUN
cana-730	185	42	𝛾	𝛾	NOUN
cana-730	185	43	for	for	ADP
cana-730	185	44	fixed	fix	VERB
cana-730	185	45	arrival	arrival	NOUN
cana-730	185	46	rate	rate	NOUN
cana-730	185	47	𝜆.	𝜆.	NOUN
cana-730	185	48	communications	communication	NOUN
cana-730	185	49	on	on	ADP
cana-730	185	50	applied	apply	VERB
cana-730	185	51	nonlinear	nonlinear	ADJ
cana-730	185	52	analysis	analysis	NOUN
cana-730	185	53	issn	issn	NOUN
cana-730	185	54	:	:	PUNCT
cana-730	185	55	1074	1074	NUM
cana-730	185	56	-	-	PUNCT
cana-730	185	57	133x	133x	NUM
cana-730	185	58	vol	vol	NOUN
cana-730	185	59	31	31	NUM
cana-730	185	60	no	no	NOUN
cana-730	185	61	.	.	PUNCT
cana-730	186	1	3s	3s	NUM
cana-730	186	2	(	(	PUNCT
cana-730	186	3	2024	2024	NUM
cana-730	186	4	)	)	PUNCT
cana-730	186	5	55	55	NUM
cana-730	186	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-730	186	7	figure	figure	NOUN
cana-730	186	8	11	11	NUM
cana-730	186	9	:	:	PUNCT
cana-730	186	10	the	the	DET
cana-730	186	11	effect	effect	NOUN
cana-730	186	12	of	of	ADP
cana-730	186	13	𝜆	𝜆	DET
cana-730	186	14	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-730	186	15	𝛾	𝛾	PROPN
cana-730	186	16	on	on	ADP
cana-730	186	17	𝑃0(1	𝑃0(1	NOUN
cana-730	186	18	)	)	PUNCT
cana-730	186	19	example	example	NOUN
cana-730	186	20	12	12	NUM
cana-730	186	21	this	this	DET
cana-730	186	22	example	example	NOUN
cana-730	186	23	,	,	PUNCT
cana-730	186	24	clearly	clearly	ADV
cana-730	186	25	shows	show	VERB
cana-730	186	26	the	the	DET
cana-730	186	27	effect	effect	NOUN
cana-730	186	28	of	of	ADP
cana-730	186	29	varying	vary	VERB
cana-730	186	30	𝜆	𝜆	PRON
cana-730	186	31	and	and	CCONJ
cana-730	186	32	the	the	DET
cana-730	186	33	failure	failure	NOUN
cana-730	186	34	rate	rate	NOUN
cana-730	186	35	𝛼	𝛼	X
cana-730	186	36	on	on	ADP
cana-730	186	37	the	the	DET
cana-730	186	38	probability	probability	NOUN
cana-730	186	39	measure	measure	NOUN
cana-730	186	40	𝑃1(1	𝑃1(1	VERB
cana-730	186	41	)	)	PUNCT
cana-730	186	42	.	.	PUNCT
cana-730	187	1	as	as	SCONJ
cana-730	187	2	we	we	PRON
cana-730	187	3	expected	expect	VERB
cana-730	187	4	,	,	PUNCT
cana-730	187	5	in	in	ADP
cana-730	187	6	figure	figure	NOUN
cana-730	187	7	12	12	NUM
cana-730	187	8	we	we	PRON
cana-730	187	9	notice	notice	VERB
cana-730	187	10	that	that	SCONJ
cana-730	187	11	the	the	DET
cana-730	187	12	probability	probability	NOUN
cana-730	187	13	measure	measure	NOUN
cana-730	187	14	𝑃1(1	𝑃1(1	NOUN
cana-730	187	15	)	)	PUNCT
cana-730	187	16	appears	appear	VERB
cana-730	187	17	to	to	PART
cana-730	187	18	decrease	decrease	VERB
cana-730	187	19	as	as	ADP
cana-730	187	20	a	a	DET
cana-730	187	21	function	function	NOUN
cana-730	187	22	of	of	ADP
cana-730	187	23	arrival	arrival	NOUN
cana-730	187	24	rate	rate	NOUN
cana-730	187	25	𝜆	𝜆	ADP
cana-730	187	26	for	for	ADP
cana-730	187	27	fixed	fix	VERB
cana-730	187	28	failure	failure	NOUN
cana-730	187	29	rate	rate	NOUN
cana-730	187	30	𝛼	𝛼	NOUN
cana-730	187	31	for	for	ADP
cana-730	187	32	fixed	fix	VERB
cana-730	187	33	𝜆	𝜆	DET
cana-730	187	34	the	the	DET
cana-730	187	35	probability	probability	NOUN
cana-730	187	36	measure	measure	NOUN
cana-730	187	37	𝑃1(1	𝑃1(1	NOUN
cana-730	187	38	)	)	PUNCT
cana-730	187	39	decreases	decrease	NOUN
cana-730	187	40	as	as	ADP
cana-730	187	41	a	a	DET
cana-730	187	42	function	function	NOUN
cana-730	187	43	of	of	ADP
cana-730	187	44	the	the	DET
cana-730	187	45	failure	failure	NOUN
cana-730	187	46	rate	rate	NOUN
cana-730	187	47	𝛼	𝛼	PROPN
cana-730	187	48	.	.	PUNCT
cana-730	188	1	figure	figure	NOUN
cana-730	188	2	12	12	NUM
cana-730	188	3	:	:	PUNCT
cana-730	188	4	the	the	DET
cana-730	188	5	effect	effect	NOUN
cana-730	188	6	of	of	ADP
cana-730	188	7	𝜆	𝜆	DET
cana-730	188	8	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-730	188	9	𝛼	𝛼	NOUN
cana-730	188	10	on	on	ADP
cana-730	188	11	𝑃1(1	𝑃1(1	ADJ
cana-730	188	12	)	)	PUNCT
cana-730	188	13	example	example	NOUN
cana-730	188	14	13	13	NUM
cana-730	188	15	in	in	ADP
cana-730	188	16	this	this	DET
cana-730	188	17	example	example	NOUN
cana-730	188	18	,	,	PUNCT
cana-730	188	19	we	we	PRON
cana-730	188	20	study	study	VERB
cana-730	188	21	the	the	DET
cana-730	188	22	effect	effect	NOUN
cana-730	188	23	of	of	ADP
cana-730	188	24	the	the	DET
cana-730	188	25	varying	vary	VERB
cana-730	188	26	service	service	NOUN
cana-730	188	27	rate	rate	NOUN
cana-730	188	28	𝜇	𝜇	ADP
cana-730	188	29	and	and	CCONJ
cana-730	188	30	the	the	DET
cana-730	188	31	failure	failure	NOUN
cana-730	188	32	rate	rate	NOUN
cana-730	188	33	𝛼	𝛼	X
cana-730	188	34	on	on	ADP
cana-730	188	35	the	the	DET
cana-730	188	36	probability	probability	NOUN
cana-730	188	37	measure	measure	NOUN
cana-730	188	38	𝑃1(1	𝑃1(1	VERB
cana-730	188	39	)	)	PUNCT
cana-730	188	40	.	.	PUNCT
cana-730	189	1	it	it	PRON
cana-730	189	2	is	be	AUX
cana-730	189	3	clearly	clearly	ADV
cana-730	189	4	noticed	notice	VERB
cana-730	189	5	in	in	ADP
cana-730	189	6	figure	figure	NOUN
cana-730	189	7	13	13	NUM
cana-730	189	8	that	that	SCONJ
cana-730	189	9	the	the	DET
cana-730	189	10	probability	probability	NOUN
cana-730	189	11	measure	measure	NOUN
cana-730	189	12	𝑃1(1)increases	𝑃1(1)increase	NOUN
cana-730	189	13	as	as	ADP
cana-730	189	14	a	a	DET
cana-730	189	15	function	function	NOUN
cana-730	189	16	𝜇	𝜇	ADP
cana-730	189	17	for	for	ADP
cana-730	189	18	fixed	fix	VERB
cana-730	189	19	failure	failure	NOUN
cana-730	189	20	rate	rate	NOUN
cana-730	189	21	𝛼	𝛼	NOUN
cana-730	189	22	and	and	CCONJ
cana-730	189	23	the	the	DET
cana-730	189	24	same	same	ADJ
cana-730	189	25	probability	probability	NOUN
cana-730	189	26	measure𝑃1(1	measure𝑃1(1	NOUN
cana-730	189	27	)	)	PUNCT
cana-730	189	28	decreases	decrease	NOUN
cana-730	189	29	as	as	ADP
cana-730	189	30	a	a	DET
cana-730	189	31	function	function	NOUN
cana-730	189	32	of	of	ADP
cana-730	189	33	the	the	DET
cana-730	189	34	failure	failure	NOUN
cana-730	189	35	rate	rate	NOUN
cana-730	189	36	𝛼	𝛼	NOUN
cana-730	189	37	for	for	ADP
cana-730	189	38	fixed	fix	VERB
cana-730	189	39	service	service	NOUN
cana-730	189	40	rate	rate	NOUN
cana-730	189	41	𝜇.	𝜇.	NOUN
cana-730	189	42	figure	figure	NOUN
cana-730	189	43	13	13	NUM
cana-730	189	44	:	:	PUNCT
cana-730	189	45	the	the	DET
cana-730	189	46	effect	effect	NOUN
cana-730	189	47	of	of	ADP
cana-730	189	48	𝜇	𝜇	ADP
cana-730	189	49	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-730	189	50	𝛼	𝛼	NOUN
cana-730	189	51	on	on	ADP
cana-730	189	52	𝑃1(1	𝑃1(1	ADJ
cana-730	189	53	)	)	PUNCT
cana-730	189	54	example	example	NOUN
cana-730	189	55	14	14	NUM
cana-730	189	56	we	we	PRON
cana-730	189	57	study	study	VERB
cana-730	189	58	the	the	DET
cana-730	189	59	effect	effect	NOUN
cana-730	189	60	of	of	ADP
cana-730	189	61	varying	vary	VERB
cana-730	189	62	arrival	arrival	NOUN
cana-730	189	63	rate	rate	NOUN
cana-730	189	64	𝜆	𝜆	ADP
cana-730	189	65	and	and	CCONJ
cana-730	189	66	the	the	DET
cana-730	189	67	failure	failure	NOUN
cana-730	189	68	rate	rate	NOUN
cana-730	189	69	𝛼	𝛼	X
cana-730	189	70	on	on	ADP
cana-730	189	71	the	the	DET
cana-730	189	72	probability	probability	NOUN
cana-730	189	73	measure	measure	NOUN
cana-730	189	74	𝑃2(1	𝑃2(1	NOUN
cana-730	189	75	)	)	PUNCT
cana-730	189	76	and	and	CCONJ
cana-730	189	77	the	the	DET
cana-730	189	78	results	result	NOUN
cana-730	189	79	are	be	AUX
cana-730	189	80	plotted	plot	VERB
cana-730	189	81	in	in	ADP
cana-730	189	82	figure	figure	NOUN
cana-730	189	83	14	14	NUM
cana-730	189	84	.	.	PUNCT
cana-730	190	1	it	it	PRON
cana-730	190	2	is	be	AUX
cana-730	190	3	seen	see	VERB
cana-730	190	4	that	that	SCONJ
cana-730	190	5	the	the	DET
cana-730	190	6	probability	probability	NOUN
cana-730	190	7	measure	measure	NOUN
cana-730	190	8	𝑃2(1	𝑃2(1	NOUN
cana-730	190	9	)	)	PUNCT
cana-730	190	10	increases	increase	NOUN
cana-730	190	11	as	as	ADP
cana-730	190	12	the	the	DET
cana-730	190	13	function	function	NOUN
cana-730	190	14	of	of	ADP
cana-730	190	15	the	the	DET
cana-730	190	16	arrival	arrival	NOUN
cana-730	190	17	rate	rate	NOUN
cana-730	190	18	𝜆	𝜆	ADP
cana-730	190	19	for	for	ADP
cana-730	190	20	fixed	fix	VERB
cana-730	190	21	failure	failure	NOUN
cana-730	190	22	rate	rate	NOUN
cana-730	190	23	𝛼.	𝛼.	NOUN
cana-730	190	24	also	also	ADV
cana-730	190	25	observed	observe	VERB
cana-730	190	26	that	that	SCONJ
cana-730	190	27	the	the	DET
cana-730	190	28	probability	probability	NOUN
cana-730	190	29	measure	measure	NOUN
cana-730	190	30	𝑃2(1	𝑃2(1	NOUN
cana-730	190	31	)	)	PUNCT
cana-730	190	32	increases	increase	NOUN
cana-730	190	33	as	as	ADP
cana-730	190	34	the	the	DET
cana-730	190	35	function	function	NOUN
cana-730	190	36	of	of	ADP
cana-730	190	37	the	the	DET
cana-730	190	38	failure	failure	NOUN
cana-730	190	39	rate	rate	NOUN
cana-730	190	40	𝛼	𝛼	NOUN
cana-730	190	41	for	for	ADP
cana-730	190	42	fixed	fix	VERB
cana-730	190	43	𝜆	𝜆	PRON
cana-730	190	44	.	.	PUNCT
cana-730	191	1	communications	communication	NOUN
cana-730	191	2	on	on	ADP
cana-730	191	3	applied	apply	VERB
cana-730	191	4	nonlinear	nonlinear	ADJ
cana-730	191	5	analysis	analysis	NOUN
cana-730	191	6	issn	issn	NOUN
cana-730	191	7	:	:	PUNCT
cana-730	191	8	1074	1074	NUM
cana-730	191	9	-	-	PUNCT
cana-730	191	10	133x	133x	NUM
cana-730	191	11	vol	vol	NOUN
cana-730	191	12	31	31	NUM
cana-730	191	13	no	no	NOUN
cana-730	191	14	.	.	PUNCT
cana-730	192	1	3s	3s	NUM
cana-730	192	2	(	(	PUNCT
cana-730	192	3	2024	2024	NUM
cana-730	192	4	)	)	PUNCT
cana-730	192	5	56	56	NUM
cana-730	192	6	https://internationalpubls.com	https://internationalpubls.com	NUM
cana-730	192	7	figure	figure	NOUN
cana-730	192	8	14	14	NUM
cana-730	192	9	:	:	PUNCT
cana-730	192	10	the	the	DET
cana-730	192	11	effect	effect	NOUN
cana-730	192	12	of	of	ADP
cana-730	192	13	𝜆	𝜆	DET
cana-730	192	14	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-730	192	15	𝛼	𝛼	PROPN
cana-730	192	16	on	on	ADP
cana-730	192	17	𝑃2(1	𝑃2(1	NOUN
cana-730	192	18	)	)	PUNCT
cana-730	192	19	10	10	NUM
cana-730	192	20	the	the	DET
cana-730	192	21	cost	cost	NOUN
cana-730	192	22	model	model	NOUN
cana-730	192	23	and	and	CCONJ
cana-730	192	24	its	its	PRON
cana-730	192	25	optimization	optimization	NOUN
cana-730	192	26	in	in	ADP
cana-730	192	27	this	this	DET
cana-730	192	28	section	section	NOUN
cana-730	192	29	,	,	PUNCT
cana-730	192	30	we	we	PRON
cana-730	192	31	study	study	VERB
cana-730	192	32	the	the	DET
cana-730	192	33	total	total	ADJ
cana-730	192	34	expected	expect	VERB
cana-730	192	35	cost	cost	NOUN
cana-730	192	36	function	function	NOUN
cana-730	192	37	with	with	ADP
cana-730	192	38	decision	decision	NOUN
cana-730	192	39	variable	variable	NOUN
cana-730	192	40	𝜇	𝜇	ADV
cana-730	192	41	and	and	CCONJ
cana-730	192	42	𝜇𝑏	𝜇𝑏	VERB
cana-730	192	43	for	for	ADP
cana-730	192	44	the	the	DET
cana-730	192	45	above	above	ADJ
cana-730	192	46	discussed	discuss	VERB
cana-730	192	47	model	model	NOUN
cana-730	192	48	.	.	PUNCT
cana-730	193	1	our	our	PRON
cana-730	193	2	main	main	ADJ
cana-730	193	3	aim	aim	NOUN
cana-730	193	4	is	be	AUX
cana-730	193	5	to	to	PART
cana-730	193	6	obtain	obtain	VERB
cana-730	193	7	the	the	DET
cana-730	193	8	optimal	optimal	ADJ
cana-730	193	9	values	value	NOUN
cana-730	193	10	for	for	ADP
cana-730	193	11	the	the	DET
cana-730	193	12	continuous	continuous	ADJ
cana-730	193	13	random	random	ADJ
cana-730	193	14	variables	variable	NOUN
cana-730	193	15	say	say	VERB
cana-730	193	16	(	(	PUNCT
cana-730	193	17	𝜇∗	𝜇∗	NOUN
cana-730	193	18	,	,	PUNCT
cana-730	193	19	𝜇𝑏	𝜇𝑏	NOUN
cana-730	193	20	∗	∗	NOUN
cana-730	193	21	)	)	PUNCT
cana-730	193	22	in	in	ADP
cana-730	193	23	order	order	NOUN
cana-730	193	24	to	to	PART
cana-730	193	25	minimize	minimize	VERB
cana-730	193	26	the	the	DET
cana-730	193	27	cost	cost	NOUN
cana-730	193	28	.	.	PUNCT
cana-730	194	1	cost	cost	NOUN
cana-730	194	2	function	function	NOUN
cana-730	194	3	:	:	PUNCT
cana-730	194	4	let	let	VERB
cana-730	194	5	us	we	PRON
cana-730	194	6	define	define	VERB
cana-730	194	7	the	the	DET
cana-730	194	8	following	follow	VERB
cana-730	194	9	cost	cost	NOUN
cana-730	194	10	elements	element	NOUN
cana-730	194	11	:	:	PUNCT
cana-730	194	12	𝐶0	𝐶0	NOUN
cana-730	194	13	:	:	PUNCT
cana-730	194	14	cost	cost	NOUN
cana-730	194	15	per	per	ADP
cana-730	194	16	unit	unit	NOUN
cana-730	194	17	time	time	NOUN
cana-730	194	18	when	when	SCONJ
cana-730	194	19	the	the	DET
cana-730	194	20	server	server	NOUN
cana-730	194	21	is	be	AUX
cana-730	194	22	in	in	ADP
cana-730	194	23	maintenance	maintenance	NOUN
cana-730	194	24	state	state	NOUN
cana-730	194	25	.	.	PUNCT
cana-730	195	1	𝐶1	𝐶1	ADV
cana-730	195	2	:	:	PUNCT
cana-730	195	3	cost	cost	NOUN
cana-730	195	4	per	per	ADP
cana-730	195	5	unit	unit	NOUN
cana-730	195	6	time	time	NOUN
cana-730	195	7	for	for	ADP
cana-730	195	8	when	when	SCONJ
cana-730	195	9	the	the	DET
cana-730	195	10	server	server	NOUN
cana-730	195	11	is	be	AUX
cana-730	195	12	busy	busy	ADJ
cana-730	195	13	during	during	ADP
cana-730	195	14	the	the	DET
cana-730	195	15	normal	normal	ADJ
cana-730	195	16	service	service	NOUN
cana-730	195	17	period	period	NOUN
cana-730	195	18	.	.	PUNCT
cana-730	196	1	𝐶2	𝐶2	ADJ
cana-730	196	2	:	:	PUNCT
cana-730	196	3	break	break	VERB
cana-730	196	4	down	down	ADP
cana-730	196	5	cost	cost	NOUN
cana-730	196	6	per	per	ADP
cana-730	196	7	unit	unit	NOUN
cana-730	196	8	time	time	NOUN
cana-730	196	9	for	for	ADP
cana-730	196	10	a	a	DET
cana-730	196	11	broken	broken	ADJ
cana-730	196	12	server	server	NOUN
cana-730	196	13	.	.	PUNCT
cana-730	197	1	𝐶3	𝐶3	PROPN
cana-730	197	2	:	:	PUNCT
cana-730	197	3	fixed	fix	VERB
cana-730	197	4	cost	cost	NOUN
cana-730	197	5	for	for	ADP
cana-730	197	6	fast	fast	ADJ
cana-730	197	7	service	service	NOUN
cana-730	197	8	rate	rate	NOUN
cana-730	197	9	and	and	CCONJ
cana-730	197	10	𝐶4	𝐶4	NOUN
cana-730	197	11	:	:	PUNCT
cana-730	197	12	fixed	fix	VERB
cana-730	197	13	cost	cost	NOUN
cana-730	197	14	for	for	ADP
cana-730	197	15	slow	slow	ADJ
cana-730	197	16	service	service	NOUN
cana-730	197	17	rate	rate	NOUN
cana-730	197	18	.	.	PUNCT
cana-730	198	1	using	use	VERB
cana-730	198	2	the	the	DET
cana-730	198	3	definition	definition	NOUN
cana-730	198	4	of	of	ADP
cana-730	198	5	these	these	DET
cana-730	198	6	cost	cost	NOUN
cana-730	198	7	elements	element	NOUN
cana-730	198	8	listed	list	VERB
cana-730	198	9	above	above	ADV
cana-730	198	10	,	,	PUNCT
cana-730	198	11	the	the	DET
cana-730	198	12	expected	expect	VERB
cana-730	198	13	cost	cost	NOUN
cana-730	198	14	function	function	NOUN
cana-730	198	15	per	per	ADP
cana-730	198	16	unit	unit	NOUN
cana-730	198	17	time	time	NOUN
cana-730	198	18	is	be	AUX
cana-730	198	19	given	give	VERB
cana-730	198	20	by	by	ADP
cana-730	198	21	𝐹(𝜇	𝐹(𝜇	NUM
cana-730	198	22	,	,	PUNCT
cana-730	198	23	𝜇𝑏	𝜇𝑏	NOUN
cana-730	198	24	)	)	PUNCT
cana-730	199	1	=	=	SYM
cana-730	199	2	𝐶0𝑃0′(1	𝐶0𝑃0′(1	PROPN
cana-730	199	3	)	)	PUNCT
cana-730	199	4	+	+	NUM
cana-730	199	5	𝐶1𝑃1′(1	𝐶1𝑃1′(1	NOUN
cana-730	199	6	)	)	PUNCT
cana-730	199	7	+	+	NUM
cana-730	199	8	𝐶2𝑃2′(1	𝐶2𝑃2′(1	NUM
cana-730	199	9	)	)	PUNCT
cana-730	200	1	+	+	CCONJ
cana-730	200	2	𝐶3𝜇	𝐶3𝜇	PROPN
cana-730	200	3	+	+	NUM
cana-730	200	4	𝐶4𝜇𝑏	𝐶4𝜇𝑏	NOUN
cana-730	200	5	-------(24	-------(24	ADJ
cana-730	200	6	)	)	PUNCT
cana-730	200	7	the	the	DET
cana-730	200	8	cost	cost	NOUN
cana-730	200	9	minimization	minimization	NOUN
cana-730	200	10	problem	problem	NOUN
cana-730	200	11	can	can	AUX
cana-730	200	12	be	be	AUX
cana-730	200	13	formulated	formulate	VERB
cana-730	200	14	as	as	ADP
cana-730	200	15	𝐹(𝜇∗	𝐹(𝜇∗	NOUN
cana-730	200	16	,	,	PUNCT
cana-730	200	17	𝜇𝑏	𝜇𝑏	NOUN
cana-730	200	18	∗	∗	NOUN
cana-730	200	19	)	)	PUNCT
cana-730	201	1	=	=	SYM
cana-730	201	2	𝑀𝑖𝑛𝑖𝑚𝑖𝑧𝑒𝐹(𝜇	𝑀𝑖𝑛𝑖𝑚𝑖𝑧𝑒𝐹(𝜇	NOUN
cana-730	201	3	,	,	PUNCT
cana-730	201	4	𝜇𝑏),subject	𝜇𝑏),subject	NOUN
cana-730	201	5	to	to	ADP
cana-730	201	6	𝜇	𝜇	X
cana-730	201	7	>	>	X
cana-730	201	8	𝜇𝑏	𝜇𝑏	NOUN
cana-730	201	9	and	and	CCONJ
cana-730	201	10	𝜌	𝜌	X
cana-730	201	11	<	<	X
cana-730	201	12	1	1	NUM
cana-730	201	13	---------------------(25	---------------------(25	NOUN
cana-730	201	14	)	)	PUNCT
cana-730	201	15	the	the	DET
cana-730	201	16	complexity	complexity	NOUN
cana-730	201	17	of	of	ADP
cana-730	201	18	expressions	expression	NOUN
cana-730	201	19	𝑃1′(1	𝑃1′(1	ADJ
cana-730	201	20	)	)	PUNCT
cana-730	201	21	,	,	PUNCT
cana-730	201	22	𝑃2′(1	𝑃2′(1	PROPN
cana-730	201	23	)	)	PUNCT
cana-730	201	24	and	and	CCONJ
cana-730	201	25	𝑃0′(1	𝑃0′(1	ADJ
cana-730	201	26	)	)	PUNCT
cana-730	201	27	complicate	complicate	VERB
cana-730	201	28	the	the	DET
cana-730	201	29	cost	cost	NOUN
cana-730	201	30	function	function	NOUN
cana-730	201	31	in	in	ADP
cana-730	201	32	equation	equation	NOUN
cana-730	201	33	.	.	PUNCT
cana-730	202	1	unfortunately	unfortunately	ADV
cana-730	202	2	,	,	PUNCT
cana-730	202	3	it	it	PRON
cana-730	202	4	is	be	AUX
cana-730	202	5	impossible	impossible	ADJ
cana-730	202	6	to	to	PART
cana-730	202	7	derive	derive	VERB
cana-730	202	8	the	the	DET
cana-730	202	9	analytic	analytic	ADJ
cana-730	202	10	solutions	solution	NOUN
cana-730	202	11	for	for	ADP
cana-730	202	12	the	the	DET
cana-730	202	13	optimal	optimal	ADJ
cana-730	202	14	service	service	NOUN
cana-730	202	15	rates	rate	NOUN
cana-730	202	16	at	at	ADP
cana-730	202	17	the	the	DET
cana-730	202	18	minimum	minimum	ADJ
cana-730	202	19	expected	expect	VERB
cana-730	202	20	cost	cost	NOUN
cana-730	202	21	.	.	PUNCT
cana-730	203	1	thus	thus	ADV
cana-730	203	2	,	,	PUNCT
cana-730	203	3	we	we	PRON
cana-730	203	4	sought	seek	VERB
cana-730	203	5	to	to	PART
cana-730	203	6	compute	compute	VERB
cana-730	203	7	the	the	DET
cana-730	203	8	numerical	numerical	ADJ
cana-730	203	9	results	result	NOUN
cana-730	203	10	of	of	ADP
cana-730	203	11	the	the	DET
cana-730	203	12	optimal	optimal	ADJ
cana-730	203	13	service	service	NOUN
cana-730	203	14	rates	rate	NOUN
cana-730	203	15	𝜇∗	𝜇∗	PROPN
cana-730	203	16	and	and	CCONJ
cana-730	203	17	𝜇𝑏	𝜇𝑏	NOUN
cana-730	203	18	∗	∗	NOUN
cana-730	203	19	using	use	VERB
cana-730	203	20	direct	direct	ADJ
cana-730	203	21	search	search	NOUN
cana-730	203	22	method	method	NOUN
cana-730	203	23	.	.	PUNCT
cana-730	204	1	direct	direct	ADJ
cana-730	204	2	search	search	NOUN
cana-730	204	3	method	method	NOUN
cana-730	204	4	:	:	PUNCT
cana-730	204	5	we	we	PRON
cana-730	204	6	assume	assume	VERB
cana-730	204	7	the	the	DET
cana-730	204	8	following	follow	VERB
cana-730	204	9	cost	cost	NOUN
cana-730	204	10	parameters	parameter	NOUN
cana-730	204	11	as	as	ADP
cana-730	204	12	𝐶0	𝐶0	NOUN
cana-730	204	13	=	=	NOUN
cana-730	204	14	200	200	NUM
cana-730	204	15	,	,	PUNCT
cana-730	204	16	𝐶1	𝐶1	NOUN
cana-730	204	17	=	=	SYM
cana-730	204	18	500	500	NUM
cana-730	204	19	,	,	PUNCT
cana-730	204	20	𝐶2	𝐶2	X
cana-730	204	21	=	=	SYM
cana-730	204	22	300	300	NUM
cana-730	204	23	,	,	PUNCT
cana-730	204	24	𝐶3	𝐶3	NOUN
cana-730	204	25	=	=	SYM
cana-730	204	26	20	20	NUM
cana-730	204	27	,	,	PUNCT
cana-730	204	28	𝐶4	𝐶4	NOUN
cana-730	204	29	=	=	SYM
cana-730	204	30	10	10	NUM
cana-730	204	31	numerical	numerical	ADJ
cana-730	204	32	examples	example	NOUN
cana-730	204	33	are	be	AUX
cana-730	204	34	presented	present	VERB
cana-730	204	35	to	to	PART
cana-730	204	36	determine	determine	VERB
cana-730	204	37	the	the	DET
cana-730	204	38	optimal	optimal	ADJ
cana-730	204	39	value	value	NOUN
cana-730	204	40	𝜇	𝜇	X
cana-730	204	41	by	by	ADP
cana-730	204	42	means	mean	NOUN
cana-730	204	43	of	of	ADP
cana-730	204	44	the	the	DET
cana-730	204	45	direct	direct	ADJ
cana-730	204	46	search	search	NOUN
cana-730	204	47	method	method	NOUN
cana-730	204	48	.	.	PUNCT
cana-730	205	1	also	also	ADV
cana-730	205	2	,	,	PUNCT
cana-730	205	3	we	we	PRON
cana-730	205	4	fix	fix	VERB
cana-730	205	5	𝜆=2	𝜆=2	PUNCT
cana-730	205	6	,	,	PUNCT
cana-730	205	7	𝛼	𝛼	NOUN
cana-730	205	8	=	=	NOUN
cana-730	205	9	0.02	0.02	NUM
cana-730	205	10	,	,	PUNCT
cana-730	205	11	𝛾	𝛾	NOUN
cana-730	205	12	=	=	SYM
cana-730	205	13	1	1	NUM
cana-730	205	14	,	,	PUNCT
cana-730	205	15	g’(1)=0.4	g’(1)=0.4	NOUN
cana-730	205	16	,	,	PUNCT
cana-730	205	17	g’’(1)=0.03	g’’(1)=0.03	NOUN
cana-730	205	18	varying	vary	VERB
cana-730	205	19	𝜇	𝜇	ADP
cana-730	205	20	from	from	ADP
cana-730	205	21	4	4	NUM
cana-730	205	22	to	to	ADP
cana-730	205	23	14	14	NUM
cana-730	205	24	,	,	PUNCT
cana-730	205	25	and	and	CCONJ
cana-730	205	26	choosing	choose	VERB
cana-730	205	27	different	different	ADJ
cana-730	205	28	values	value	NOUN
cana-730	205	29	of	of	ADP
cana-730	205	30	𝜇𝑏	𝜇𝑏	NOUN
cana-730	205	31	,	,	PUNCT
cana-730	205	32	the	the	DET
cana-730	205	33	minimum	minimum	ADJ
cana-730	205	34	expected	expect	VERB
cana-730	205	35	cost	cost	NOUN
cana-730	205	36	f(𝜇	f(𝜇	PROPN
cana-730	205	37	,	,	PUNCT
cana-730	205	38	𝜇𝑏	𝜇𝑏	NOUN
cana-730	205	39	)	)	PUNCT
cana-730	205	40	are	be	AUX
cana-730	205	41	shown	show	VERB
cana-730	205	42	in	in	ADP
cana-730	205	43	table	table	NOUN
cana-730	205	44	1	1	NUM
cana-730	205	45	and	and	CCONJ
cana-730	205	46	figure	figure	VERB
cana-730	205	47	15	15	NUM
cana-730	205	48	for	for	SCONJ
cana-730	205	49	communications	communication	NOUN
cana-730	205	50	on	on	ADP
cana-730	205	51	applied	apply	VERB
cana-730	205	52	nonlinear	nonlinear	ADJ
cana-730	205	53	analysis	analysis	NOUN
cana-730	205	54	issn	issn	NOUN
cana-730	205	55	:	:	PUNCT
cana-730	205	56	1074	1074	NUM
cana-730	205	57	-	-	PUNCT
cana-730	205	58	133x	133x	NUM
cana-730	205	59	vol	vol	NOUN
cana-730	205	60	31	31	NUM
cana-730	205	61	no	no	NOUN
cana-730	205	62	.	.	PUNCT
cana-730	206	1	3s	3s	NUM
cana-730	206	2	(	(	PUNCT
cana-730	206	3	2024	2024	NUM
cana-730	206	4	)	)	PUNCT
cana-730	206	5	57	57	NUM
cana-730	206	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-730	206	7	𝜇𝑏=2.5,3,3.5	𝜇𝑏=2.5,3,3.5	PROPN
cana-730	206	8	the	the	DET
cana-730	206	9	minimum	minimum	ADJ
cana-730	206	10	expected	expect	VERB
cana-730	206	11	cost	cost	NOUN
cana-730	206	12	rs.222.3553	rs.222.3553	PROPN
cana-730	206	13	is	be	AUX
cana-730	206	14	achieved	achieve	VERB
cana-730	206	15	at	at	ADP
cana-730	206	16	𝜇	𝜇	ADP
cana-730	206	17	=	=	NOUN
cana-730	206	18	5	5	NUM
cana-730	206	19	for	for	ADP
cana-730	206	20	𝜇𝑏=2.5	𝜇𝑏=2.5	ADJ
cana-730	206	21	,	,	PUNCT
cana-730	206	22	rs	rs	NOUN
cana-730	206	23	.	.	PUNCT
cana-730	207	1	227.1716	227.1716	NUM
cana-730	207	2	is	be	AUX
cana-730	207	3	achieved	achieve	VERB
cana-730	207	4	at	at	ADP
cana-730	207	5	𝜇	𝜇	ADP
cana-730	207	6	=	=	NOUN
cana-730	207	7	5	5	NUM
cana-730	207	8	for	for	ADP
cana-730	207	9	𝜇𝑏=3	𝜇𝑏=3	NOUN
cana-730	207	10	and	and	CCONJ
cana-730	207	11	rs	rs	NOUN
cana-730	207	12	.	.	PUNCT
cana-730	208	1	rs.232.0458	rs.232.0458	ADJ
cana-730	208	2	is	be	AUX
cana-730	208	3	achieved	achieve	VERB
cana-730	208	4	at	at	ADP
cana-730	208	5	𝜇	𝜇	ADP
cana-730	208	6	=	=	NOUN
cana-730	208	7	5	5	NUM
cana-730	208	8	for	for	ADP
cana-730	208	9	𝜇𝑏=3.5	𝜇𝑏=3.5	NOUN
cana-730	208	10	.	.	PUNCT
cana-730	209	1	it	it	PRON
cana-730	209	2	is	be	AUX
cana-730	209	3	seen	see	VERB
cana-730	209	4	that	that	SCONJ
cana-730	209	5	initially	initially	ADV
cana-730	209	6	the	the	DET
cana-730	209	7	total	total	ADJ
cana-730	209	8	cost	cost	NOUN
cana-730	209	9	decreases	decrease	NOUN
cana-730	209	10	and	and	CCONJ
cana-730	209	11	starts	start	VERB
cana-730	209	12	increasing	increase	VERB
cana-730	209	13	with	with	ADP
cana-730	209	14	the	the	DET
cana-730	209	15	grant	grant	NOUN
cana-730	209	16	of	of	ADP
cana-730	209	17	𝜇	𝜇	ADP
cana-730	209	18	for	for	ADP
cana-730	209	19	fixed	fix	VERB
cana-730	209	20	values	value	NOUN
cana-730	209	21	of	of	ADP
cana-730	209	22	𝜇𝑏.	𝜇𝑏.	PROPN
cana-730	209	23	the	the	DET
cana-730	209	24	convex	convex	ADJ
cana-730	209	25	nature	nature	NOUN
cana-730	209	26	of	of	ADP
cana-730	209	27	the	the	DET
cana-730	209	28	cost	cost	NOUN
cana-730	209	29	function	function	NOUN
cana-730	209	30	with	with	ADP
cana-730	209	31	respect	respect	NOUN
cana-730	209	32	to	to	ADP
cana-730	209	33	𝜇	𝜇	ADP
cana-730	209	34	show	show	VERB
cana-730	209	35	the	the	DET
cana-730	209	36	trend	trend	NOUN
cana-730	209	37	for	for	ADP
cana-730	209	38	the	the	DET
cana-730	209	39	optimum	optimum	ADJ
cana-730	209	40	cost	cost	NOUN
cana-730	209	41	by	by	ADP
cana-730	209	42	increasing	increase	VERB
cana-730	209	43	the	the	DET
cana-730	209	44	normal	normal	ADJ
cana-730	209	45	service	service	NOUN
cana-730	209	46	domain	domain	NOUN
cana-730	209	47	of	of	ADP
cana-730	209	48	the	the	DET
cana-730	209	49	customers	customer	NOUN
cana-730	209	50	.	.	PUNCT
cana-730	210	1	from	from	ADP
cana-730	210	2	table2	table2	PROPN
cana-730	210	3	,	,	PUNCT
cana-730	210	4	we	we	PRON
cana-730	210	5	concluded	conclude	VERB
cana-730	210	6	that	that	SCONJ
cana-730	210	7	the	the	DET
cana-730	210	8	minimum	minimum	ADJ
cana-730	210	9	expected	expect	VERB
cana-730	210	10	cost	cost	NOUN
cana-730	210	11	rs.204.1258	rs.204.1258	PROPN
cana-730	210	12	is	be	AUX
cana-730	210	13	attained	attain	VERB
cana-730	210	14	at	at	ADP
cana-730	210	15	𝜇	𝜇	ADP
cana-730	210	16	=	=	NOUN
cana-730	210	17	5	5	NUM
cana-730	210	18	for	for	ADP
cana-730	210	19	𝜆	𝜆	DET
cana-730	210	20	=	=	NOUN
cana-730	210	21	1.5	1.5	NUM
cana-730	210	22	,	,	PUNCT
cana-730	210	23	rs.232.0458	rs.232.0458	ADJ
cana-730	210	24	is	be	AUX
cana-730	210	25	attained	attain	VERB
cana-730	210	26	at	at	ADP
cana-730	210	27	𝜇	𝜇	ADP
cana-730	210	28	=	=	NOUN
cana-730	210	29	5	5	NUM
cana-730	210	30	,	,	PUNCT
cana-730	210	31	for	for	ADP
cana-730	210	32	𝜆	𝜆	DET
cana-730	210	33	=	=	SYM
cana-730	210	34	2	2	NUM
cana-730	210	35	and	and	CCONJ
cana-730	210	36	rs.2517.3021	rs.2517.3021	NOUN
cana-730	210	37	is	be	AUX
cana-730	210	38	attained	attain	VERB
cana-730	210	39	at	at	ADP
cana-730	210	40	𝜇	𝜇	ADP
cana-730	210	41	=	=	NOUN
cana-730	210	42	6	6	NUM
cana-730	210	43	for	for	ADP
cana-730	210	44	𝜆	𝜆	DET
cana-730	210	45	=	=	NOUN
cana-730	210	46	4.2	4.2	NUM
cana-730	210	47	for	for	ADP
cana-730	210	48	fixed	fix	VERB
cana-730	210	49	𝜆	𝜆	PRON
cana-730	210	50	=	=	NOUN
cana-730	210	51	2.5	2.5	NUM
cana-730	210	52	,	,	PUNCT
cana-730	210	53	𝛼	𝛼	NOUN
cana-730	210	54	=	=	NOUN
cana-730	210	55	0.002	0.002	NUM
cana-730	210	56	,	,	PUNCT
cana-730	210	57	𝜇𝑏=3.5	𝜇𝑏=3.5	X
cana-730	210	58	,	,	PUNCT
cana-730	210	59	𝛾	𝛾	PUNCT
cana-730	210	60	=	=	NOUN
cana-730	210	61	1	1	NUM
cana-730	210	62	,	,	PUNCT
cana-730	210	63	g	g	NOUN
cana-730	210	64	’	'	PUNCT
cana-730	210	65	(	(	PUNCT
cana-730	210	66	1	1	X
cana-730	210	67	)	)	PUNCT
cana-730	211	1	=	=	NOUN
cana-730	211	2	0.4	0.4	NUM
cana-730	211	3	,	,	PUNCT
cana-730	211	4	g	g	NOUN
cana-730	211	5	’’	’'	PUNCT
cana-730	211	6	(	(	PUNCT
cana-730	211	7	1	1	X
cana-730	211	8	)	)	PUNCT
cana-730	211	9	=	=	NOUN
cana-730	211	10	0.03	0.03	NUM
cana-730	211	11	.	.	PUNCT
cana-730	212	1	from	from	ADP
cana-730	212	2	figure16	figure16	NOUN
cana-730	212	3	it	it	PRON
cana-730	212	4	is	be	AUX
cana-730	212	5	evident	evident	ADJ
cana-730	212	6	that	that	SCONJ
cana-730	212	7	total	total	ADJ
cana-730	212	8	cost	cost	NOUN
cana-730	212	9	function	function	NOUN
cana-730	212	10	decreases	decrease	VERB
cana-730	212	11	first	first	ADV
cana-730	212	12	and	and	CCONJ
cana-730	212	13	then	then	ADV
cana-730	212	14	increases	increase	VERB
cana-730	212	15	consequently	consequently	ADV
cana-730	212	16	the	the	DET
cana-730	212	17	convex	convex	ADJ
cana-730	212	18	nature	nature	NOUN
cana-730	212	19	arises	arise	VERB
cana-730	212	20	in	in	ADP
cana-730	212	21	the	the	DET
cana-730	212	22	total	total	ADJ
cana-730	212	23	cost	cost	NOUN
cana-730	212	24	function	function	NOUN
cana-730	212	25	.	.	PUNCT
cana-730	213	1	this	this	PRON
cana-730	213	2	confirms	confirm	VERB
cana-730	213	3	the	the	DET
cana-730	213	4	possibility	possibility	NOUN
cana-730	213	5	of	of	ADP
cana-730	213	6	obtaining	obtain	VERB
cana-730	213	7	the	the	DET
cana-730	213	8	optimum	optimum	ADJ
cana-730	213	9	service	service	NOUN
cana-730	213	10	rates	rate	NOUN
cana-730	213	11	.	.	PUNCT
cana-730	214	1	from	from	ADP
cana-730	214	2	table	table	NOUN
cana-730	214	3	3	3	NUM
cana-730	214	4	,	,	PUNCT
cana-730	214	5	we	we	PRON
cana-730	214	6	concluded	conclude	VERB
cana-730	214	7	that	that	SCONJ
cana-730	214	8	the	the	DET
cana-730	214	9	minimum	minimum	ADJ
cana-730	214	10	expected	expect	VERB
cana-730	214	11	cost	cost	NOUN
cana-730	214	12	rs.236.9736	rs.236.9736	PROPN
cana-730	214	13	is	be	AUX
cana-730	214	14	attained	attain	VERB
cana-730	214	15	at	at	ADP
cana-730	214	16	𝜇	𝜇	ADP
cana-730	214	17	=	=	NOUN
cana-730	214	18	5	5	NUM
cana-730	214	19	for	for	ADP
cana-730	214	20	𝛼	𝛼	NOUN
cana-730	214	21	=	=	NOUN
cana-730	214	22	0.1	0.1	NUM
cana-730	214	23	,	,	PUNCT
cana-730	214	24	rs.242.3192	rs.242.3192	PRON
cana-730	214	25	is	be	AUX
cana-730	214	26	attained	attain	VERB
cana-730	214	27	at	at	ADP
cana-730	214	28	𝜇	𝜇	ADP
cana-730	214	29	=	=	NOUN
cana-730	214	30	6	6	NUM
cana-730	214	31	for	for	ADP
cana-730	214	32	𝛼	𝛼	NOUN
cana-730	214	33	=	=	NOUN
cana-730	214	34	0.2	0.2	NUM
cana-730	214	35	and	and	CCONJ
cana-730	214	36	rs.247.2811	rs.247.2811	PROPN
cana-730	214	37	is	be	AUX
cana-730	214	38	attained	attain	VERB
cana-730	214	39	at	at	ADP
cana-730	214	40	𝜇	𝜇	ADP
cana-730	214	41	=	=	NOUN
cana-730	214	42	6	6	NUM
cana-730	214	43	for	for	ADP
cana-730	214	44	𝛼	𝛼	NOUN
cana-730	214	45	=	=	NOUN
cana-730	214	46	0.3	0.3	NUM
cana-730	214	47	for	for	ADP
cana-730	214	48	fixed	fix	VERB
cana-730	214	49	𝜆	𝜆	PRON
cana-730	214	50	=	=	NOUN
cana-730	214	51	2	2	NUM
cana-730	214	52	,	,	PUNCT
cana-730	214	53	𝛾	𝛾	NOUN
cana-730	214	54	=	=	NOUN
cana-730	214	55	1	1	NUM
cana-730	214	56	,	,	PUNCT
cana-730	214	57	𝜇𝑏=3.5	𝜇𝑏=3.5	X
cana-730	214	58	,	,	PUNCT
cana-730	214	59	g	g	NOUN
cana-730	214	60	’	'	PUNCT
cana-730	214	61	(	(	PUNCT
cana-730	214	62	1	1	X
cana-730	214	63	)	)	PUNCT
cana-730	215	1	=	=	NOUN
cana-730	215	2	0.4	0.4	NUM
cana-730	215	3	,	,	PUNCT
cana-730	215	4	g	g	NOUN
cana-730	215	5	’’	’'	PUNCT
cana-730	215	6	(	(	PUNCT
cana-730	215	7	1	1	X
cana-730	215	8	)	)	PUNCT
cana-730	215	9	=	=	NOUN
cana-730	215	10	0.03	0.03	NUM
cana-730	215	11	.	.	PUNCT
cana-730	216	1	as	as	SCONJ
cana-730	216	2	we	we	PRON
cana-730	216	3	hoped	hope	VERB
cana-730	216	4	,	,	PUNCT
cana-730	216	5	the	the	DET
cana-730	216	6	figure	figure	NOUN
cana-730	216	7	17	17	NUM
cana-730	216	8	shows	show	VERB
cana-730	216	9	the	the	DET
cana-730	216	10	convexity	convexity	NOUN
cana-730	216	11	in	in	ADP
cana-730	216	12	the	the	DET
cana-730	216	13	total	total	ADJ
cana-730	216	14	cost	cost	NOUN
cana-730	216	15	function	function	NOUN
cana-730	216	16	.	.	PUNCT
cana-730	217	1	from	from	ADP
cana-730	217	2	table	table	NOUN
cana-730	217	3	4	4	NUM
cana-730	217	4	,	,	PUNCT
cana-730	217	5	we	we	PRON
cana-730	217	6	conclude	conclude	VERB
cana-730	217	7	that	that	SCONJ
cana-730	217	8	the	the	DET
cana-730	217	9	minimum	minimum	ADJ
cana-730	217	10	expected	expect	VERB
cana-730	217	11	cost	cost	NOUN
cana-730	217	12	rs.367.8189	rs.367.8189	PROPN
cana-730	217	13	is	be	AUX
cana-730	217	14	attained	attain	VERB
cana-730	217	15	at	at	ADP
cana-730	217	16	𝜇	𝜇	ADP
cana-730	217	17	=	=	NOUN
cana-730	217	18	9	9	NUM
cana-730	217	19	for	for	ADP
cana-730	217	20	𝛾	𝛾	NOUN
cana-730	217	21	=	=	SYM
cana-730	217	22	0.2	0.2	NUM
cana-730	217	23	rs.275.5773	rs.275.5773	PROPN
cana-730	217	24	is	be	AUX
cana-730	217	25	attained	attain	VERB
cana-730	217	26	at	at	ADP
cana-730	217	27	𝜇	𝜇	ADP
cana-730	217	28	=	=	NOUN
cana-730	217	29	7	7	NUM
cana-730	217	30	for	for	ADP
cana-730	217	31	𝛾	𝛾	NOUN
cana-730	217	32	=	=	NUM
cana-730	217	33	0.45	0.45	NUM
cana-730	217	34	and	and	CCONJ
cana-730	217	35	rs.251.891	rs.251.891	PROPN
cana-730	217	36	is	be	AUX
cana-730	217	37	attained	attain	VERB
cana-730	217	38	at	at	ADP
cana-730	217	39	𝜇	𝜇	ADP
cana-730	217	40	=	=	NOUN
cana-730	217	41	6	6	NUM
cana-730	217	42	for	for	ADP
cana-730	217	43	𝛾	𝛾	NOUN
cana-730	217	44	=	=	SYM
cana-730	217	45	0.6	0.6	NUM
cana-730	217	46	for	for	ADP
cana-730	217	47	fixed	fix	VERB
cana-730	217	48	𝜆	𝜆	PRON
cana-730	217	49	=	=	SYM
cana-730	217	50	2	2	NUM
cana-730	217	51	,	,	PUNCT
cana-730	217	52	𝜇𝑏=3	𝜇𝑏=3	NOUN
cana-730	217	53	,	,	PUNCT
cana-730	217	54	𝛾	𝛾	NOUN
cana-730	217	55	=	=	NOUN
cana-730	217	56	0.6	0.6	NUM
cana-730	217	57	,	,	PUNCT
cana-730	217	58	𝛼	𝛼	NOUN
cana-730	217	59	=	=	NOUN
cana-730	217	60	0.2	0.2	NUM
cana-730	217	61	,	,	PUNCT
cana-730	217	62	g	g	NOUN
cana-730	217	63	’	'	PUNCT
cana-730	217	64	(	(	PUNCT
cana-730	217	65	1	1	X
cana-730	217	66	)	)	PUNCT
cana-730	217	67	=	=	NOUN
cana-730	217	68	0.4	0.4	NUM
cana-730	217	69	,	,	PUNCT
cana-730	217	70	g	g	NOUN
cana-730	217	71	’’	’'	PUNCT
cana-730	217	72	(	(	PUNCT
cana-730	217	73	1	1	X
cana-730	217	74	)	)	PUNCT
cana-730	217	75	=	=	NOUN
cana-730	217	76	0.03	0.03	NUM
cana-730	217	77	.	.	PUNCT
cana-730	218	1	as	as	SCONJ
cana-730	218	2	we	we	PRON
cana-730	218	3	hoped	hope	VERB
cana-730	218	4	,	,	PUNCT
cana-730	218	5	the	the	DET
cana-730	218	6	figure	figure	NOUN
cana-730	218	7	18	18	NUM
cana-730	218	8	shows	show	VERB
cana-730	218	9	the	the	DET
cana-730	218	10	convexity	convexity	NOUN
cana-730	218	11	in	in	ADP
cana-730	218	12	the	the	DET
cana-730	218	13	total	total	ADJ
cana-730	218	14	cost	cost	NOUN
cana-730	218	15	function	function	NOUN
cana-730	218	16	.	.	PUNCT
cana-730	219	1	figure	figure	VERB
cana-730	219	2	15	15	NUM
cana-730	219	3	:	:	PUNCT
cana-730	219	4	the	the	DET
cana-730	219	5	effect	effect	NOUN
cana-730	219	6	of	of	ADP
cana-730	219	7	𝜇	𝜇	X
cana-730	219	8	on	on	ADP
cana-730	219	9	the	the	DET
cana-730	219	10	total	total	ADJ
cana-730	219	11	cost	cost	NOUN
cana-730	219	12	function	function	NOUN
cana-730	219	13	µ	µ	X
cana-730	219	14	𝜇𝑏	𝜇𝑏	NOUN
cana-730	219	15	=	=	SYM
cana-730	219	16	2.5	2.5	NUM
cana-730	219	17	𝜇𝑏	𝜇𝑏	NOUN
cana-730	219	18	=	=	NOUN
cana-730	219	19	3	3	NUM
cana-730	219	20	𝜇𝑏	𝜇𝑏	NOUN
cana-730	219	21	=	=	NOUN
cana-730	219	22	3.5	3.5	NUM
cana-730	219	23	𝑃1,0	𝑃1,0	NUM
cana-730	219	24	cost	cost	VERB
cana-730	219	25	𝑃1,0	𝑃1,0	NUM
cana-730	219	26	cost	cost	NOUN
cana-730	219	27	𝑃1,0	𝑃1,0	NUM
cana-730	219	28	cost	cost	VERB
cana-730	219	29	4	4	NUM
cana-730	219	30	0.7954	0.7954	NUM
cana-730	219	31	232.9611	232.9611	NUM
cana-730	219	32	0.7957	0.7957	NUM
cana-730	219	33	237.7114	237.7114	NUM
cana-730	219	34	0.7959	0.7959	NUM
cana-730	219	35	242.5405	242.5405	NUM
cana-730	219	36	5	5	NUM
cana-730	219	37	0.8362	0.8362	NUM
cana-730	219	38	222.3553	222.3553	NUM
cana-730	219	39	0.8364	0.8364	NUM
cana-730	219	40	227.1716	227.1716	NUM
cana-730	219	41	0.8365	0.8365	NUM
cana-730	220	1	232.0458	232.0458	NUM
cana-730	220	2	6	6	NUM
cana-730	220	3	0.8634	0.8634	NUM
cana-730	220	4	223.5591	223.5591	NUM
cana-730	220	5	0.8636	0.8636	NUM
cana-730	220	6	228.4138	228.4138	NUM
cana-730	220	7	0.8637	0.8637	NUM
cana-730	220	8	233.3144	233.3144	NUM
cana-730	220	9	7	7	NUM
cana-730	220	10	0.8828	0.8828	NUM
cana-730	220	11	230.8441	230.8441	NUM
cana-730	220	12	0.883	0.883	NUM
cana-730	220	13	235.724	235.724	NUM
cana-730	220	14	0.8831	0.8831	NUM
cana-730	220	15	240.6418	240.6418	NUM
cana-730	220	16	8	8	NUM
cana-730	220	17	0.8975	0.8975	NUM
cana-730	220	18	241.6706	241.6706	NUM
cana-730	220	19	0.8976	0.8976	NUM
cana-730	220	20	246.5683	246.5683	NUM
cana-730	220	21	0.8977	0.8977	NUM
cana-730	220	22	251.4983	251.4983	NUM
cana-730	220	23	table	table	NOUN
cana-730	220	24	1	1	NUM
cana-730	220	25	:	:	PUNCT
cana-730	220	26	the	the	DET
cana-730	220	27	effect	effect	NOUN
cana-730	220	28	of	of	ADP
cana-730	220	29	µ	µ	NOUN
cana-730	220	30	on	on	ADP
cana-730	220	31	the	the	DET
cana-730	220	32	cost	cost	NOUN
cana-730	220	33	function	function	NOUN
cana-730	220	34	for	for	ADP
cana-730	220	35	various	various	ADJ
cana-730	220	36	values	value	NOUN
cana-730	220	37	of	of	ADP
cana-730	220	38	𝜇𝑏	𝜇𝑏	NOUN
cana-730	220	39	communications	communication	NOUN
cana-730	220	40	on	on	ADP
cana-730	220	41	applied	apply	VERB
cana-730	220	42	nonlinear	nonlinear	ADJ
cana-730	220	43	analysis	analysis	NOUN
cana-730	220	44	issn	issn	NOUN
cana-730	220	45	:	:	PUNCT
cana-730	220	46	1074	1074	NUM
cana-730	220	47	-	-	PUNCT
cana-730	220	48	133x	133x	NUM
cana-730	220	49	vol	vol	NOUN
cana-730	220	50	31	31	NUM
cana-730	220	51	no	no	NOUN
cana-730	220	52	.	.	PUNCT
cana-730	221	1	3s	3s	NUM
cana-730	221	2	(	(	PUNCT
cana-730	221	3	2024	2024	NUM
cana-730	221	4	)	)	PUNCT
cana-730	221	5	58	58	NUM
cana-730	221	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-730	221	7	figure	figure	NOUN
cana-730	221	8	16	16	NUM
cana-730	221	9	:	:	PUNCT
cana-730	221	10	the	the	DET
cana-730	221	11	effect	effect	NOUN
cana-730	221	12	of	of	ADP
cana-730	221	13	𝜇	𝜇	X
cana-730	221	14	on	on	ADP
cana-730	221	15	the	the	DET
cana-730	221	16	total	total	ADJ
cana-730	221	17	cost	cost	NOUN
cana-730	221	18	function	function	NOUN
cana-730	221	19	µ	µ	NOUN
cana-730	221	20	𝜆	𝜆	NOUN
cana-730	221	21	=	=	SYM
cana-730	221	22	1.5	1.5	NUM
cana-730	221	23	𝜆	𝜆	NOUN
cana-730	221	24	=	=	SYM
cana-730	221	25	2	2	NUM
cana-730	221	26	𝜆	𝜆	NOUN
cana-730	221	27	=	=	SYM
cana-730	221	28	2.5	2.5	NUM
cana-730	221	29	𝑃1,0	𝑃1,0	NUM
cana-730	221	30	cost	cost	VERB
cana-730	221	31	𝑃1,0	𝑃1,0	NUM
cana-730	221	32	cost	cost	NOUN
cana-730	221	33	𝑃1,0	𝑃1,0	NUM
cana-730	221	34	cost	cost	VERB
cana-730	221	35	4	4	NUM
cana-730	221	36	0.8469	0.8469	NUM
cana-730	221	37	204.5071	204.5071	NUM
cana-730	221	38	0.7959	0.7959	NUM
cana-730	221	39	242.5405	242.5405	NUM
cana-730	221	40	0.7448	0.7448	NUM
cana-730	221	41	286.1305	286.1305	NUM
cana-730	221	42	5	5	NUM
cana-730	221	43	0.8774	0.8774	NUM
cana-730	221	44	204.1258	204.1258	NUM
cana-730	221	45	0.8365	0.8365	NUM
cana-730	221	46	232.0458	232.0458	NUM
cana-730	221	47	0.7957	0.7957	NUM
cana-730	221	48	263.0633	263.0633	NUM
cana-730	221	49	6	6	NUM
cana-730	221	50	0.8978	0.8978	NUM
cana-730	221	51	211.303	211.303	NUM
cana-730	221	52	0.8637	0.8637	NUM
cana-730	221	53	233.3144	233.3144	NUM
cana-730	221	54	0.8296	0.8296	NUM
cana-730	221	55	257.3021	257.3021	NUM
cana-730	221	56	7	7	NUM
cana-730	221	57	0.9123	0.9123	NUM
cana-730	221	58	222.4923	222.4923	NUM
cana-730	221	59	0.8831	0.8831	NUM
cana-730	221	60	240.6418	240.6418	NUM
cana-730	221	61	0.8539	0.8539	NUM
cana-730	221	62	20.1645	20.1645	NUM
cana-730	221	63	8	8	NUM
cana-730	221	64	0.9233	0.9233	NUM
cana-730	221	65	236.0656	236.0656	NUM
cana-730	221	66	0.8977	0.8977	NUM
cana-730	221	67	251.4983	251.4983	NUM
cana-730	221	68	0.8721	0.8721	NUM
cana-730	221	69	267.9425	267.9425	NUM
cana-730	221	70	table	table	NOUN
cana-730	221	71	2	2	NUM
cana-730	221	72	:	:	PUNCT
cana-730	221	73	the	the	DET
cana-730	221	74	effect	effect	NOUN
cana-730	221	75	of	of	ADP
cana-730	221	76	µ	µ	NOUN
cana-730	221	77	on	on	ADP
cana-730	221	78	the	the	DET
cana-730	221	79	cost	cost	NOUN
cana-730	221	80	function	function	NOUN
cana-730	221	81	for	for	ADP
cana-730	221	82	various	various	ADJ
cana-730	221	83	values	value	NOUN
cana-730	221	84	of	of	ADP
cana-730	221	85	𝜆	𝜆	DET
cana-730	221	86	figure	figure	NOUN
cana-730	221	87	17	17	NUM
cana-730	221	88	:	:	PUNCT
cana-730	221	89	the	the	DET
cana-730	221	90	effect	effect	NOUN
cana-730	221	91	of	of	ADP
cana-730	221	92	𝜇	𝜇	X
cana-730	221	93	on	on	ADP
cana-730	221	94	the	the	DET
cana-730	221	95	total	total	ADJ
cana-730	221	96	cost	cost	NOUN
cana-730	221	97	function	function	NOUN
cana-730	221	98	µ	µ	X
cana-730	221	99	𝛼	𝛼	X
cana-730	221	100	=	=	SYM
cana-730	221	101	0.1	0.1	NUM
cana-730	221	102	𝛼	𝛼	NOUN
cana-730	221	103	=	=	NOUN
cana-730	221	104	0.2	0.2	NUM
cana-730	221	105	𝛼	𝛼	NOUN
cana-730	221	106	=	=	NOUN
cana-730	221	107	0.3	0.3	NUM
cana-730	221	108	𝑃1,0	𝑃1,0	NUM
cana-730	221	109	cost	cost	VERB
cana-730	221	110	𝑃1,0	𝑃1,0	NUM
cana-730	221	111	cost	cost	NOUN
cana-730	221	112	𝑃1,0	𝑃1,0	NUM
cana-730	221	113	cost	cost	VERB
cana-730	221	114	4	4	NUM
cana-730	221	115	0.7798	0.7798	NUM
cana-730	221	116	248.9268	248.9268	NUM
cana-730	221	117	0.7605	0.7605	NUM
cana-730	221	118	256.8546	256.8546	NUM
cana-730	221	119	0.7422	0.7422	NUM
cana-730	221	120	264.7262	264.7262	NUM
cana-730	221	121	5	5	NUM
cana-730	221	122	0.823	0.823	NUM
cana-730	221	123	236.9736	236.9736	NUM
cana-730	221	124	0.8066	0.8066	NUM
cana-730	221	125	243.0957	243.0957	NUM
cana-730	221	126	0.7908	0.7908	NUM
cana-730	221	127	249.1787	249.1787	NUM
cana-730	221	128	6	6	NUM
cana-730	221	129	0.852	0.852	NUM
cana-730	221	130	237.3286	237.3286	NUM
cana-730	221	131	0.8378	0.8378	NUM
cana-730	221	132	242.3192	242.3192	NUM
cana-730	221	133	0.824	0.824	NUM
cana-730	221	134	247.2811	247.2811	NUM
cana-730	221	135	7	7	NUM
cana-730	221	136	0.8728	0.8728	NUM
cana-730	221	137	244.0292	244.0292	NUM
cana-730	221	138	0.8603	0.8603	NUM
cana-730	221	139	248.243	248.243	NUM
cana-730	221	140	0.8481	0.8481	NUM
cana-730	221	141	252.435	252.435	NUM
cana-730	221	142	8	8	NUM
cana-730	221	143	0.8885	0.8885	NUM
cana-730	221	144	254.4287	254.4287	NUM
cana-730	221	145	0.8774	0.8774	NUM
cana-730	221	146	258.0757	258.0757	NUM
cana-730	221	147	0.8664	0.8664	NUM
cana-730	221	148	261.7056	261.7056	NUM
cana-730	221	149	9	9	NUM
cana-730	221	150	0.9008	0.9008	NUM
cana-730	221	151	267.1723	267.1723	NUM
cana-730	221	152	0.8907	0.8907	NUM
cana-730	222	1	270.3873	270.3873	NUM
cana-730	222	2	0.8808	0.8808	NUM
cana-730	222	3	273.5886	273.5886	NUM
cana-730	222	4	table	table	NOUN
cana-730	222	5	3	3	NUM
cana-730	222	6	:	:	PUNCT
cana-730	222	7	the	the	DET
cana-730	222	8	effect	effect	NOUN
cana-730	222	9	of	of	ADP
cana-730	222	10	µ	µ	NOUN
cana-730	222	11	on	on	ADP
cana-730	222	12	the	the	DET
cana-730	222	13	cost	cost	NOUN
cana-730	222	14	function	function	NOUN
cana-730	222	15	for	for	ADP
cana-730	222	16	various	various	ADJ
cana-730	222	17	values	value	NOUN
cana-730	222	18	of	of	ADP
cana-730	222	19	𝛼	𝛼	NOUN
cana-730	222	20	communications	communication	NOUN
cana-730	222	21	on	on	ADP
cana-730	222	22	applied	apply	VERB
cana-730	222	23	nonlinear	nonlinear	ADJ
cana-730	222	24	analysis	analysis	NOUN
cana-730	222	25	issn	issn	NOUN
cana-730	222	26	:	:	PUNCT
cana-730	222	27	1074	1074	NUM
cana-730	222	28	-	-	PUNCT
cana-730	222	29	133x	133x	NUM
cana-730	222	30	vol	vol	NOUN
cana-730	222	31	31	31	NUM
cana-730	222	32	no	no	NOUN
cana-730	222	33	.	.	PUNCT
cana-730	223	1	3s	3s	NUM
cana-730	223	2	(	(	PUNCT
cana-730	223	3	2024	2024	NUM
cana-730	223	4	)	)	PUNCT
cana-730	223	5	59	59	NUM
cana-730	223	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-730	223	7	figure	figure	NOUN
cana-730	223	8	18	18	NUM
cana-730	223	9	:	:	PUNCT
cana-730	223	10	the	the	DET
cana-730	223	11	effect	effect	NOUN
cana-730	223	12	of	of	ADP
cana-730	223	13	𝜇	𝜇	X
cana-730	223	14	on	on	ADP
cana-730	223	15	the	the	DET
cana-730	223	16	total	total	ADJ
cana-730	223	17	cost	cost	NOUN
cana-730	223	18	function	function	NOUN
cana-730	223	19	µ	µ	PRON
cana-730	223	20	𝛾	𝛾	NOUN
cana-730	223	21	=	=	SYM
cana-730	223	22	0.2	0.2	NUM
cana-730	223	23	𝛾	𝛾	NOUN
cana-730	223	24	=	=	NUM
cana-730	223	25	0.45	0.45	NUM
cana-730	223	26	𝛾	𝛾	X
cana-730	223	27	=	=	SYM
cana-730	223	28	0.6	0.6	NUM
cana-730	223	29	𝑃1,0	𝑃1,0	NUM
cana-730	223	30	cost	cost	VERB
cana-730	223	31	𝑃1,0	𝑃1,0	NUM
cana-730	223	32	cost	cost	NOUN
cana-730	223	33	𝑃1,0	𝑃1,0	NUM
cana-730	223	34	cost	cost	VERB
cana-730	223	35	4	4	NUM
cana-730	223	36	0.6063	0.6063	NUM
cana-730	223	37	608.7468	608.7468	NUM
cana-730	223	38	0.7016	0.7016	NUM
cana-730	223	39	326.7336	326.7336	NUM
cana-730	223	40	0.7333	0.7333	NUM
cana-730	223	41	278.7352	278.7352	NUM
cana-730	223	42	5	5	NUM
cana-730	223	43	0.6821	0.6821	NUM
cana-730	223	44	480.2275	480.2275	NUM
cana-730	223	45	0.759	0.759	NUM
cana-730	223	46	290.554	290.554	NUM
cana-730	223	47	0.7846	0.7846	NUM
cana-730	223	48	257.072	257.072	NUM
cana-730	223	49	6	6	NUM
cana-730	223	50	0.7333	0.7333	NUM
cana-730	223	51	419.026	419.026	NUM
cana-730	223	52	0.7978	0.7978	NUM
cana-730	223	53	277.4138	277.4138	NUM
cana-730	223	54	0.8194	0.8194	NUM
cana-730	223	55	251.891	251.891	NUM
cana-730	223	56	7	7	NUM
cana-730	223	57	0.7704	0.7704	NUM
cana-730	223	58	388.0538	388.0538	NUM
cana-730	223	59	0.8259	0.8259	NUM
cana-730	223	60	275.5773	275.5773	NUM
cana-730	223	61	0.8444	0.8444	NUM
cana-730	223	62	255.0319	255.0319	NUM
cana-730	223	63	8	8	NUM
cana-730	223	64	0.7984	0.7984	NUM
cana-730	223	65	373.1639	373.1639	NUM
cana-730	223	66	0.8472	0.8472	NUM
cana-730	223	67	280.1133	280.1133	NUM
cana-730	223	68	0.8634	0.8634	NUM
cana-730	223	69	262.9564	262.9564	NUM
cana-730	223	70	9	9	NUM
cana-730	223	71	0.8203	0.8203	NUM
cana-730	223	72	367.8189	367.8189	NUM
cana-730	223	73	0.8638	0.8638	NUM
cana-730	223	74	288.5918	288.5918	NUM
cana-730	223	75	0.8783	0.8783	NUM
cana-730	223	76	273.8824	273.8824	NUM
cana-730	223	77	table	table	NOUN
cana-730	223	78	4	4	NUM
cana-730	223	79	:	:	PUNCT
cana-730	223	80	the	the	DET
cana-730	223	81	effect	effect	NOUN
cana-730	223	82	of	of	ADP
cana-730	223	83	µ	µ	NOUN
cana-730	223	84	on	on	ADP
cana-730	223	85	the	the	DET
cana-730	223	86	cost	cost	NOUN
cana-730	223	87	function	function	NOUN
cana-730	223	88	for	for	ADP
cana-730	223	89	various	various	ADJ
cana-730	223	90	values	value	NOUN
cana-730	223	91	of	of	ADP
cana-730	223	92	𝛾	𝛾	NOUN
cana-730	223	93	conclusion	conclusion	NOUN
cana-730	223	94	we	we	PRON
cana-730	223	95	have	have	AUX
cana-730	223	96	studied	study	VERB
cana-730	223	97	the	the	DET
cana-730	223	98	steady	steady	ADJ
cana-730	223	99	-	-	PUNCT
cana-730	223	100	state	state	NOUN
cana-730	223	101	analysis	analysis	NOUN
cana-730	223	102	of	of	ADP
cana-730	223	103	single	single	ADJ
cana-730	223	104	-	-	PUNCT
cana-730	223	105	server	server	NOUN
cana-730	223	106	markovian	markovian	ADJ
cana-730	223	107	bulk	bulk	NOUN
cana-730	223	108	arrival	arrival	NOUN
cana-730	223	109	queueing	queue	VERB
cana-730	223	110	systems	system	NOUN
cana-730	223	111	with	with	ADP
cana-730	223	112	working	work	VERB
cana-730	223	113	breakdowns	breakdown	NOUN
cana-730	223	114	and	and	CCONJ
cana-730	223	115	interruptions	interruption	NOUN
cana-730	223	116	.	.	PUNCT
cana-730	224	1	for	for	ADP
cana-730	224	2	this	this	DET
cana-730	224	3	model	model	NOUN
cana-730	224	4	,	,	PUNCT
cana-730	224	5	the	the	DET
cana-730	224	6	probability	probability	NOUN
cana-730	224	7	-	-	PUNCT
cana-730	224	8	generating	generate	VERB
cana-730	224	9	functions	function	NOUN
cana-730	224	10	of	of	ADP
cana-730	224	11	the	the	DET
cana-730	224	12	system	system	NOUN
cana-730	224	13	size	size	NOUN
cana-730	224	14	distributions	distribution	NOUN
cana-730	224	15	in	in	ADP
cana-730	224	16	steady	steady	ADJ
cana-730	224	17	state	state	NOUN
cana-730	224	18	are	be	AUX
cana-730	224	19	obtained	obtain	VERB
cana-730	224	20	.	.	PUNCT
cana-730	225	1	various	various	ADJ
cana-730	225	2	important	important	ADJ
cana-730	225	3	characteristics	characteristic	NOUN
cana-730	225	4	of	of	ADP
cana-730	225	5	the	the	DET
cana-730	225	6	model	model	NOUN
cana-730	225	7	,	,	PUNCT
cana-730	225	8	like	like	ADP
cana-730	225	9	the	the	DET
cana-730	225	10	expected	expect	VERB
cana-730	225	11	number	number	NOUN
cana-730	225	12	of	of	ADP
cana-730	225	13	customers	customer	NOUN
cana-730	225	14	in	in	ADP
cana-730	225	15	the	the	DET
cana-730	225	16	system	system	NOUN
cana-730	225	17	,	,	PUNCT
cana-730	225	18	the	the	DET
cana-730	225	19	expected	expect	VERB
cana-730	225	20	waiting	waiting	NOUN
cana-730	225	21	time	time	NOUN
cana-730	225	22	of	of	ADP
cana-730	225	23	a	a	DET
cana-730	225	24	customer	customer	NOUN
cana-730	225	25	in	in	ADP
cana-730	225	26	the	the	DET
cana-730	225	27	system	system	NOUN
cana-730	225	28	,	,	PUNCT
cana-730	225	29	etc	etc	X
cana-730	225	30	.	.	X
cana-730	225	31	,	,	PUNCT
cana-730	225	32	are	be	AUX
cana-730	225	33	derived	derive	VERB
cana-730	225	34	.	.	PUNCT
cana-730	226	1	numerical	numerical	ADJ
cana-730	226	2	examples	example	NOUN
cana-730	226	3	are	be	AUX
cana-730	226	4	presented	present	VERB
cana-730	226	5	to	to	PART
cana-730	226	6	study	study	VERB
cana-730	226	7	the	the	DET
cana-730	226	8	parameters	parameter	NOUN
cana-730	226	9	and	and	CCONJ
cana-730	226	10	their	their	PRON
cana-730	226	11	effects	effect	NOUN
cana-730	226	12	on	on	ADP
cana-730	226	13	the	the	DET
cana-730	226	14	model	model	NOUN
cana-730	226	15	.	.	PUNCT
cana-730	227	1	optimizing	optimize	VERB
cana-730	227	2	the	the	DET
cana-730	227	3	cost	cost	NOUN
cana-730	227	4	function	function	NOUN
cana-730	227	5	is	be	AUX
cana-730	227	6	analyzed	analyze	VERB
cana-730	227	7	using	use	VERB
cana-730	227	8	matlab	matlab	PROPN
cana-730	227	9	.	.	PUNCT
cana-730	228	1	mathematica	mathematica	PROPN
cana-730	228	2	is	be	AUX
cana-730	228	3	used	use	VERB
cana-730	228	4	for	for	ADP
cana-730	228	5	presenting	present	VERB
cana-730	228	6	three	three	NUM
cana-730	228	7	-	-	PUNCT
cana-730	228	8	dimensional	dimensional	ADJ
cana-730	228	9	figures	figure	NOUN
cana-730	228	10	.	.	PUNCT
cana-730	229	1	references	reference	NOUN
cana-730	229	2	[	[	X
cana-730	229	3	1	1	NUM
cana-730	229	4	]	]	PUNCT
cana-730	229	5	v.jacob	v.jacob	NOUN
cana-730	229	6	,	,	PUNCT
cana-730	229	7	s.r.chakravarthy	s.r.chakravarthy	ADJ
cana-730	229	8	,	,	PUNCT
cana-730	229	9	a.krishnamoorthy	a.krishnamoorthy	ADJ
cana-730	229	10	,	,	PUNCT
cana-730	229	11	(	(	PUNCT
cana-730	229	12	2012	2012	NUM
cana-730	229	13	)	)	PUNCT
cana-730	229	14	.	.	PUNCT
cana-730	230	1	on	on	ADP
cana-730	230	2	a	a	DET
cana-730	230	3	customer	customer	NOUN
cana-730	230	4	-	-	PUNCT
cana-730	230	5	induced	induce	VERB
cana-730	230	6	interruption	interruption	NOUN
cana-730	230	7	in	in	ADP
cana-730	230	8	a	a	DET
cana-730	230	9	service	service	NOUN
cana-730	230	10	system.stochastic	system.stochastic	ADJ
cana-730	230	11	analysis	analysis	NOUN
cana-730	230	12	and	and	CCONJ
cana-730	230	13	applications	application	NOUN
cana-730	230	14	30(6),949	30(6),949	NUM
cana-730	230	15	-	-	SYM
cana-730	230	16	962	962	NUM
cana-730	230	17	.	.	PUNCT
cana-730	231	1	[	[	X
cana-730	231	2	2	2	NUM
cana-730	231	3	]	]	PUNCT
cana-730	231	4	v.jacob	v.jacob	NOUN
cana-730	231	5	,	,	PUNCT
cana-730	231	6	a.krishnamoorthy	a.krishnamoorthy	ADJ
cana-730	231	7	,	,	PUNCT
cana-730	231	8	(	(	PUNCT
cana-730	231	9	2015	2015	NUM
cana-730	231	10	)	)	PUNCT
cana-730	231	11	.	.	PUNCT
cana-730	232	1	analysis	analysis	NOUN
cana-730	232	2	of	of	ADP
cana-730	232	3	customer	customer	NOUN
cana-730	232	4	-	-	PUNCT
cana-730	232	5	induced	induce	VERB
cana-730	232	6	interruption	interruption	NOUN
cana-730	232	7	and	and	CCONJ
cana-730	232	8	retrial	retrial	NOUN
cana-730	232	9	of	of	ADP
cana-730	232	10	interrupted	interrupted	ADJ
cana-730	232	11	customers.american	customers.american	ADJ
cana-730	232	12	journal	journal	NOUN
cana-730	232	13	of	of	ADP
cana-730	232	14	mathematical	mathematical	ADJ
cana-730	232	15	and	and	CCONJ
cana-730	232	16	management	management	NOUN
cana-730	232	17	sciences	science	NOUN
cana-730	232	18	34(4),34-	34(4),34-	VERB
cana-730	232	19	.	.	PUNCT
cana-730	233	1	[	[	X
cana-730	233	2	3	3	NUM
cana-730	233	3	]	]	X
cana-730	233	4	jaiswal	jaiswal	PROPN
cana-730	233	5	,	,	PUNCT
cana-730	233	6	n.k	n.k	PROPN
cana-730	233	7	.	.	PROPN
cana-730	233	8	(	(	PUNCT
cana-730	233	9	1961	1961	NUM
cana-730	233	10	)	)	PUNCT
cana-730	233	11	.	.	PUNCT
cana-730	234	1	preemptive	preemptive	ADJ
cana-730	234	2	resume	resume	NOUN
cana-730	234	3	priority	priority	NOUN
cana-730	234	4	queue	queue	NOUN
cana-730	234	5	.	.	PUNCT
cana-730	235	1	operations	operation	NOUN
cana-730	235	2	research	research	NOUN
cana-730	235	3	,	,	PUNCT
cana-730	235	4	732	732	NUM
cana-730	235	5	-	-	SYM
cana-730	235	6	770	770	NUM
cana-730	235	7	.	.	PUNCT
cana-730	236	1	[	[	X
cana-730	236	2	4	4	NUM
cana-730	236	3	]	]	X
cana-730	236	4	jau	jau	PROPN
cana-730	236	5	-	-	PROPN
cana-730	236	6	chuan	chuan	PROPN
cana-730	236	7	ke	ke	PROPN
cana-730	236	8	,	,	PUNCT
cana-730	236	9	(	(	PUNCT
cana-730	236	10	2007	2007	NUM
cana-730	236	11	)	)	PUNCT
cana-730	236	12	batch	batch	NOUN
cana-730	236	13	arrival	arrival	NOUN
cana-730	236	14	queues	queue	NOUN
cana-730	236	15	under	under	ADP
cana-730	236	16	vacation	vacation	NOUN
cana-730	236	17	policies	policy	NOUN
cana-730	236	18	with	with	ADP
cana-730	236	19	server	server	NOUN
cana-730	236	20	breakdown	breakdown	NOUN
cana-730	236	21	and	and	CCONJ
cana-730	236	22	startup	startup	NOUN
cana-730	236	23	/	/	SYM
cana-730	236	24	closedown	closedown	PROPN
cana-730	236	25	times	time	NOUN
cana-730	236	26	,	,	PUNCT
cana-730	236	27	applied	apply	VERB
cana-730	236	28	mathematical	mathematical	ADJ
cana-730	236	29	modeling	modeling	NOUN
cana-730	236	30	,	,	PUNCT
cana-730	236	31	vol.31	vol.31	PROPN
cana-730	236	32	,	,	PUNCT
cana-730	236	33	1282	1282	NUM
cana-730	236	34	-	-	SYM
cana-730	236	35	1292	1292	NUM
cana-730	236	36	.	.	PUNCT
cana-730	237	1	[	[	X
cana-730	237	2	5	5	X
cana-730	237	3	]	]	X
cana-730	237	4	kim	kim	PROPN
cana-730	237	5	bk	bk	PROPN
cana-730	237	6	.	.	PUNCT
cana-730	237	7	lee	lee	PROPN
cana-730	237	8	dh	dh	PROPN
cana-730	237	9	.	.	PUNCT
cana-730	238	1	(	(	PUNCT
cana-730	238	2	2014	2014	NUM
cana-730	238	3	)	)	PUNCT
cana-730	238	4	the	the	DET
cana-730	238	5	m	m	NOUN
cana-730	238	6	/	/	SYM
cana-730	238	7	g/1	g/1	NOUN
cana-730	238	8	queue	queue	NOUN
cana-730	238	9	with	with	ADP
cana-730	238	10	disasters	disaster	NOUN
cana-730	238	11	and	and	CCONJ
cana-730	238	12	working	work	VERB
cana-730	238	13	breakdowns	breakdown	NOUN
cana-730	238	14	,	,	PUNCT
cana-730	238	15	applied	apply	VERB
cana-730	238	16	mathematical	mathematical	ADJ
cana-730	238	17	modelling	model	VERB
cana-730	238	18	38	38	NUM
cana-730	238	19	,	,	PUNCT
cana-730	238	20	1788	1788	NUM
cana-730	238	21	-	-	SYM
cana-730	238	22	1798	1798	NUM
cana-730	238	23	.	.	PUNCT
cana-730	239	1	[	[	X
cana-730	239	2	6	6	NUM
cana-730	239	3	]	]	PUNCT
cana-730	239	4	b.krishna	b.krishna	NOUN
cana-730	239	5	kumar	kumar	PROPN
cana-730	239	6	.	.	PROPN
cana-730	239	7	,d.arivuadainambi	,d.arivuadainambi	PUNCT
cana-730	239	8	and	and	CCONJ
cana-730	239	9	a.vijayakumar,(2002	a.vijayakumar,(2002	NOUN
cana-730	239	10	)	)	PUNCT
cana-730	239	11	.	.	PUNCT
cana-730	240	1	an	an	DET
cana-730	240	2	m	m	PROPN
cana-730	240	3	/	/	SYM
cana-730	240	4	g/1/1	g/1/1	PROPN
cana-730	240	5	queue	queue	NOUN
cana-730	240	6	with	with	ADP
cana-730	240	7	unreliable	unreliable	ADJ
cana-730	240	8	server	server	NOUN
cana-730	240	9	and	and	CCONJ
cana-730	240	10	no	no	DET
cana-730	240	11	waiting	waiting	NOUN
cana-730	240	12	capacity	capacity	NOUN
cana-730	240	13	,	,	PUNCT
cana-730	240	14	information	information	NOUN
cana-730	240	15	and	and	CCONJ
cana-730	240	16	management	management	NOUN
cana-730	240	17	science	science	NOUN
cana-730	240	18	,	,	PUNCT
cana-730	240	19	13(2	13(2	NOUN
cana-730	240	20	)	)	PUNCT
cana-730	240	21	35	35	NUM
cana-730	240	22	-	-	SYM
cana-730	240	23	50	50	NUM
cana-730	240	24	.	.	PUNCT
cana-730	241	1	[	[	X
cana-730	241	2	7	7	X
cana-730	241	3	]	]	X
cana-730	241	4	krishnamoorthy	krishnamoorthy	ADJ
cana-730	241	5	a	a	X
cana-730	241	6	,	,	PUNCT
cana-730	241	7	pramod	pramod	PROPN
cana-730	241	8	pk	pk	PROPN
cana-730	241	9	,	,	PUNCT
cana-730	241	10	chakravarthy	chakravarthy	ADJ
cana-730	241	11	sr.9(2014	sr.9(2014	NUM
cana-730	241	12	)	)	PUNCT
cana-730	241	13	queues	queue	NOUN
cana-730	241	14	with	with	ADP
cana-730	241	15	interruptions	interruption	NOUN
cana-730	241	16	:	:	PUNCT
cana-730	241	17	a	a	DET
cana-730	241	18	survey	survey	NOUN
cana-730	241	19	.	.	PUNCT
cana-730	242	1	top,22:290	top,22:290	X
cana-730	242	2	-	-	SYM
cana-730	242	3	320	320	NUM
cana-730	242	4	.	.	PUNCT
cana-730	243	1	[	[	X
cana-730	243	2	8	8	NUM
cana-730	243	3	]	]	X
cana-730	243	4	keilson	keilson	NOUN
cana-730	243	5	,	,	PUNCT
cana-730	243	6	j.	j.	PROPN
cana-730	243	7	,	,	PUNCT
cana-730	243	8	and	and	CCONJ
cana-730	243	9	servi	servi	ADJ
cana-730	243	10	,	,	PUNCT
cana-730	243	11	l.d	l.d	PROPN
cana-730	243	12	.	.	PROPN
cana-730	243	13	(	(	PUNCT
cana-730	243	14	1988	1988	NUM
cana-730	243	15	):	):	PUNCT
cana-730	243	16	a	a	DET
cana-730	243	17	distributional	distributional	ADJ
cana-730	243	18	form	form	NOUN
cana-730	243	19	of	of	ADP
cana-730	243	20	little	little	ADJ
cana-730	243	21	’s	’s	PART
cana-730	243	22	law	law	NOUN
cana-730	243	23	.	.	PUNCT
cana-730	244	1	m.f	m.f	PROPN
cana-730	244	2	.	.	PUNCT
cana-730	244	3	(	(	PUNCT
cana-730	244	4	1994	1994	NUM
cana-730	244	5	):	):	PUNCT
cana-730	244	6	matrix	matrix	NOUN
cana-730	244	7	-	-	PUNCT
cana-730	244	8	geometric	geometric	ADJ
cana-730	244	9	solutions	solution	NOUN
cana-730	244	10	in	in	ADP
cana-730	244	11	stochastic	stochastic	ADJ
cana-730	244	12	models	model	NOUN
cana-730	244	13	an	an	DET
cana-730	244	14	algorithmic	algorithmic	ADJ
cana-730	244	15	approach	approach	NOUN
cana-730	244	16	,	,	PUNCT
cana-730	244	17	2nd	2nd	ADJ
cana-730	244	18	ed	ed	NOUN
cana-730	244	19	.	.	PROPN
cana-730	244	20	,	,	PUNCT
cana-730	244	21	dover	dover	PROPN
cana-730	244	22	publications	publications	PROPN
cana-730	244	23	,	,	PUNCT
cana-730	244	24	inc	inc	PROPN
cana-730	244	25	.	.	PROPN
cana-730	244	26	,	,	PUNCT
cana-730	244	27	newyork	newyork	PROPN
cana-730	244	28	.	.	PUNCT
cana-730	245	1	communications	communication	NOUN
cana-730	245	2	on	on	ADP
cana-730	245	3	applied	apply	VERB
cana-730	245	4	nonlinear	nonlinear	ADJ
cana-730	245	5	analysis	analysis	NOUN
cana-730	245	6	issn	issn	NOUN
cana-730	245	7	:	:	PUNCT
cana-730	245	8	1074	1074	NUM
cana-730	245	9	-	-	PUNCT
cana-730	245	10	133x	133x	NUM
cana-730	245	11	vol	vol	NOUN
cana-730	245	12	31	31	NUM
cana-730	245	13	no	no	NOUN
cana-730	245	14	.	.	PUNCT
cana-730	246	1	3s	3s	NUM
cana-730	246	2	(	(	PUNCT
cana-730	246	3	2024	2024	NUM
cana-730	246	4	)	)	PUNCT
cana-730	246	5	60	60	NUM
cana-730	246	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-730	247	1	[	[	X
cana-730	247	2	9	9	NUM
cana-730	247	3	]	]	X
cana-730	247	4	khalaf	khalaf	PROPN
cana-730	247	5	r.	r.	PROPN
cana-730	247	6	f.	f.	PROPN
cana-730	247	7	,	,	PUNCT
cana-730	247	8	madan	madan	PROPN
cana-730	247	9	k.	k.	PROPN
cana-730	247	10	c.	c.	PROPN
cana-730	247	11	and	and	CCONJ
cana-730	247	12	lukas	lukas	PROPN
cana-730	247	13	c.	c.	PROPN
cana-730	247	14	a.	a.	PROPN
cana-730	247	15	(	(	PUNCT
cana-730	247	16	2011	2011	NUM
cana-730	247	17	)	)	PUNCT
cana-730	247	18	.	.	PUNCT
cana-730	248	1	an	an	DET
cana-730	248	2	𝑀𝑥/𝐺/1	𝑀𝑥/𝐺/1	ADJ
cana-730	248	3	queue	queue	NOUN
cana-730	248	4	with	with	ADP
cana-730	248	5	bernoulli	bernoulli	PROPN
cana-730	248	6	schedule	schedule	NOUN
cana-730	248	7	general	general	ADJ
cana-730	248	8	vacation	vacation	PROPN
cana-730	248	9	times	time	NOUN
cana-730	248	10	,	,	PUNCT
cana-730	248	11	general	general	ADJ
cana-730	248	12	extended	extend	VERB
cana-730	248	13	vacations	vacation	NOUN
cana-730	248	14	,	,	PUNCT
cana-730	248	15	random	random	ADJ
cana-730	248	16	breakdowns	breakdown	NOUN
cana-730	248	17	,	,	PUNCT
cana-730	248	18	general	general	ADJ
cana-730	248	19	delay	delay	NOUN
cana-730	248	20	times	time	NOUN
cana-730	248	21	for	for	SCONJ
cana-730	248	22	repairs	repair	NOUN
cana-730	248	23	to	to	PART
cana-730	248	24	start	start	VERB
cana-730	248	25	and	and	CCONJ
cana-730	248	26	general	general	ADJ
cana-730	248	27	repair	repair	NOUN
cana-730	248	28	times.journal	times.journal	ADJ
cana-730	248	29	of	of	ADP
cana-730	248	30	mathematics	mathematics	PROPN
cana-730	248	31	research	research	NOUN
cana-730	248	32	,	,	PUNCT
cana-730	248	33	3	3	NUM
cana-730	248	34	,	,	PUNCT
cana-730	248	35	8	8	NUM
cana-730	248	36	-20	-20	NUM
cana-730	248	37	.	.	PUNCT
cana-730	249	1	[	[	X
cana-730	249	2	10	10	NUM
cana-730	249	3	]	]	X
cana-730	249	4	chen	chen	PROPN
cana-730	249	5	,	,	PUNCT
cana-730	249	6	j.-y	j.-y	PROPN
cana-730	249	7	.	.	PROPN
cana-730	249	8	,	,	PUNCT
cana-730	249	9	yen	yen	NOUN
cana-730	249	10	,	,	PUNCT
cana-730	249	11	t.-c	t.-c	PROPN
cana-730	249	12	.	.	PROPN
cana-730	249	13	,	,	PUNCT
cana-730	249	14	and	and	CCONJ
cana-730	249	15	wang	wang	PROPN
cana-730	249	16	,	,	PUNCT
cana-730	249	17	k.-h	k.-h	PROPN
cana-730	249	18	.	.	PUNCT
cana-730	249	19	,	,	PUNCT
cana-730	249	20	(	(	PUNCT
cana-730	249	21	2016	2016	NUM
cana-730	249	22	)	)	PUNCT
cana-730	249	23	.	.	PUNCT
cana-730	250	1	“	"	PUNCT
cana-730	250	2	cost	cost	VERB
cana-730	250	3	optimization	optimization	NOUN
cana-730	250	4	of	of	ADP
cana-730	250	5	a	a	DET
cana-730	250	6	singleserver	singleserver	NOUN
cana-730	250	7	queue	queue	NOUN
cana-730	250	8	with	with	ADP
cana-730	250	9	working	work	VERB
cana-730	250	10	breakdowns	breakdown	NOUN
cana-730	250	11	under	under	ADP
cana-730	250	12	the	the	DET
cana-730	250	13	n	n	PRON
cana-730	250	14	policy	policy	NOUN
cana-730	250	15	,	,	PUNCT
cana-730	250	16	”	"	PUNCT
cana-730	250	17	journal	journal	NOUN
cana-730	250	18	of	of	ADP
cana-730	250	19	testing	testing	NOUN
cana-730	250	20	and	and	CCONJ
cana-730	250	21	evaluation	evaluation	NOUN
cana-730	250	22	,	,	PUNCT
cana-730	250	23	vol	vol	NOUN
cana-730	250	24	44	44	NUM
cana-730	250	25	,	,	PUNCT
cana-730	250	26	no.5	no.5	PROPN
cana-730	250	27	,	,	PUNCT
cana-730	250	28	2059	2059	NUM
cana-730	250	29	-	-	SYM
cana-730	250	30	2067	2067	NUM
cana-730	250	31	.	.	PUNCT
cana-730	251	1	[	[	X
cana-730	251	2	11	11	NUM
cana-730	251	3	]	]	PUNCT
cana-730	251	4	neuts	neut	NOUN
cana-730	251	5	,	,	PUNCT
cana-730	251	6	m.	m.	NOUN
cana-730	251	7	(	(	PUNCT
cana-730	251	8	1981).matrix	1981).matrix	NUM
cana-730	251	9	geometric	geometric	ADJ
cana-730	251	10	solutions	solution	NOUN
cana-730	251	11	in	in	ADP
cana-730	251	12	stochastic	stochastic	ADJ
cana-730	251	13	models	model	NOUN
cana-730	251	14	,	,	PUNCT
cana-730	251	15	baltimore	baltimore	PROPN
cana-730	251	16	:	:	PUNCT
cana-730	251	17	john	john	PROPN
cana-730	251	18	hopkins	hopkins	PROPN
cana-730	251	19	university	university	PROPN
cana-730	251	20	press	press	NOUN
cana-730	251	21	.	.	PUNCT