id	sid	tid	token	lemma	pos
cana-853	1	1	communications	communication	NOUN
cana-853	1	2	on	on	ADP
cana-853	1	3	applied	apply	VERB
cana-853	1	4	nonlinear	nonlinear	ADJ
cana-853	1	5	analysis	analysis	NOUN
cana-853	1	6	issn	issn	NOUN
cana-853	1	7	:	:	PUNCT
cana-853	1	8	1074	1074	NUM
cana-853	1	9	-	-	PUNCT
cana-853	1	10	133x	133x	NUM
cana-853	1	11	vol	vol	NOUN
cana-853	1	12	31	31	NUM
cana-853	1	13	no	no	NOUN
cana-853	1	14	.	.	PUNCT
cana-853	2	1	4s	4s	NUM
cana-853	2	2	(	(	PUNCT
cana-853	2	3	2024	2024	NUM
cana-853	2	4	)	)	PUNCT
cana-853	2	5	297	297	NUM
cana-853	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-853	2	7	study	study	NOUN
cana-853	2	8	on	on	ADP
cana-853	2	9	m	m	PROPN
cana-853	2	10	/	/	SYM
cana-853	2	11	m/1	m/1	NOUN
cana-853	2	12	queueing	queue	VERB
cana-853	2	13	netwօrk	netwօrk	VERB
cana-853	2	14	with	with	ADP
cana-853	2	15	preparatory	preparatory	ADJ
cana-853	2	16	wօrk	wօrk	NOUN
cana-853	2	17	and	and	CCONJ
cana-853	2	18	feeback	feeback	VERB
cana-853	2	19	using	use	VERB
cana-853	2	20	three	three	NUM
cana-853	2	21	nodes	node	NOUN
cana-853	2	22	when	when	SCONJ
cana-853	2	23	catastrophe	catastrophe	NOUN
cana-853	2	24	occurs	occur	VERB
cana-853	2	25	1	1	NUM
cana-853	2	26	s.	s.	PROPN
cana-853	2	27	shanmugasundaram	shanmugasundaram	PROPN
cana-853	2	28	,	,	PUNCT
cana-853	2	29	2	2	NUM
cana-853	2	30	c.	c.	NOUN
cana-853	2	31	baby	baby	NOUN
cana-853	2	32	1	1	NUM
cana-853	2	33	assisstant	assisstant	NOUN
cana-853	2	34	professor	professor	NOUN
cana-853	2	35	,	,	PUNCT
cana-853	2	36	department	department	NOUN
cana-853	2	37	of	of	ADP
cana-853	2	38	mathematics	mathematic	NOUN
cana-853	2	39	,	,	PUNCT
cana-853	2	40	government	government	NOUN
cana-853	2	41	,	,	PUNCT
cana-853	2	42	arts	art	NOUN
cana-853	2	43	college	college	NOUN
cana-853	2	44	salem	salem	PROPN
cana-853	2	45	636007	636007	NUM
cana-853	2	46	,	,	PUNCT
cana-853	2	47	tamil	tamil	PROPN
cana-853	2	48	nadu	nadu	PROPN
cana-853	2	49	,	,	PUNCT
cana-853	2	50	india	india	PROPN
cana-853	2	51	,	,	PUNCT
cana-853	2	52	sundaramsss@hotmail.com	sundaramsss@hotmail.com	PROPN
cana-853	2	53	2	2	NUM
cana-853	2	54	ph.d	ph.d	PROPN
cana-853	2	55	research	research	NOUN
cana-853	2	56	scholar	scholar	NOUN
cana-853	2	57	(	(	PUNCT
cana-853	2	58	part	part	NOUN
cana-853	2	59	time	time	NOUN
cana-853	2	60	)	)	PUNCT
cana-853	2	61	,	,	PUNCT
cana-853	2	62	department	department	NOUN
cana-853	2	63	of	of	ADP
cana-853	2	64	mathematics	mathematic	NOUN
cana-853	2	65	,	,	PUNCT
cana-853	2	66	government	government	NOUN
cana-853	2	67	arts	art	NOUN
cana-853	2	68	college(autonomous),salem	college(autonomous),salem	PROPN
cana-853	2	69	–	–	PUNCT
cana-853	2	70	636007,tamil	636007,tamil	NUM
cana-853	2	71	nadu	nadu	NOUN
cana-853	2	72	,	,	PUNCT
cana-853	2	73	india	india	PROPN
cana-853	2	74	,	,	PUNCT
cana-853	2	75	babyakcika2015@gmail.com	babyakcika2015@gmail.com	X
cana-853	3	1	article	article	NOUN
cana-853	3	2	history	history	NOUN
cana-853	3	3	:	:	PUNCT
cana-853	3	4	received	receive	VERB
cana-853	3	5	:	:	PUNCT
cana-853	3	6	15	15	NUM
cana-853	3	7	-	-	PUNCT
cana-853	3	8	04	04	NUM
cana-853	3	9	-	-	PUNCT
cana-853	3	10	2024	2024	NUM
cana-853	3	11	revised	revise	VERB
cana-853	3	12	:	:	PUNCT
cana-853	3	13	14	14	NUM
cana-853	3	14	-	-	SYM
cana-853	3	15	06	06	NUM
cana-853	3	16	-	-	PUNCT
cana-853	3	17	2024	2024	NUM
cana-853	3	18	accepted	accept	VERB
cana-853	3	19	:	:	PUNCT
cana-853	3	20	24	24	NUM
cana-853	3	21	-	-	PUNCT
cana-853	3	22	06	06	NUM
cana-853	3	23	-	-	PUNCT
cana-853	3	24	2024	2024	NUM
cana-853	3	25	abstract	abstract	NOUN
cana-853	3	26	in	in	ADP
cana-853	3	27	this	this	DET
cana-853	3	28	paper	paper	NOUN
cana-853	3	29	we	we	PRON
cana-853	3	30	study	study	VERB
cana-853	3	31	m	m	PROPN
cana-853	3	32	/	/	SYM
cana-853	3	33	m/1	m/1	NOUN
cana-853	3	34	open	open	ADJ
cana-853	3	35	queueing	queue	VERB
cana-853	3	36	network	network	NOUN
cana-853	3	37	with	with	ADP
cana-853	3	38	instantaneous	instantaneous	ADJ
cana-853	3	39	bernoulli	bernoulli	NOUN
cana-853	3	40	feedback	feedback	NOUN
cana-853	3	41	and	and	CCONJ
cana-853	3	42	preparatory	preparatory	ADJ
cana-853	3	43	work	work	NOUN
cana-853	3	44	with	with	ADP
cana-853	3	45	three	three	NUM
cana-853	3	46	nodes	node	NOUN
cana-853	3	47	when	when	SCONJ
cana-853	3	48	catastrophe	catastrophe	NOUN
cana-853	3	49	occurs	occur	VERB
cana-853	3	50	.	.	PUNCT
cana-853	4	1	we	we	PRON
cana-853	4	2	derive	derive	VERB
cana-853	4	3	n	n	PRON
cana-853	4	4	number	number	NOUN
cana-853	4	5	of	of	ADP
cana-853	4	6	customers	customer	NOUN
cana-853	4	7	in	in	ADP
cana-853	4	8	the	the	DET
cana-853	4	9	system	system	NOUN
cana-853	4	10	,	,	PUNCT
cana-853	4	11	queue	queue	NOUN
cana-853	4	12	length	length	NOUN
cana-853	4	13	(	(	PUNCT
cana-853	4	14	all	all	DET
cana-853	4	15	three	three	NUM
cana-853	4	16	nodes	node	NOUN
cana-853	4	17	)	)	PUNCT
cana-853	4	18	,	,	PUNCT
cana-853	4	19	system	system	NOUN
cana-853	4	20	length	length	NOUN
cana-853	4	21	and	and	CCONJ
cana-853	4	22	system	system	NOUN
cana-853	4	23	time	time	NOUN
cana-853	4	24	.	.	PUNCT
cana-853	5	1	the	the	DET
cana-853	5	2	numerical	numerical	ADJ
cana-853	5	3	examples	example	NOUN
cana-853	5	4	are	be	AUX
cana-853	5	5	given	give	VERB
cana-853	5	6	to	to	PART
cana-853	5	7	test	test	VERB
cana-853	5	8	the	the	DET
cana-853	5	9	feasibility	feasibility	NOUN
cana-853	5	10	of	of	ADP
cana-853	5	11	the	the	DET
cana-853	5	12	model	model	NOUN
cana-853	5	13	.	.	PUNCT
cana-853	6	1	keywords	keyword	NOUN
cana-853	6	2	:	:	PUNCT
cana-853	6	3	queueing	queue	VERB
cana-853	6	4	network	network	NOUN
cana-853	6	5	,	,	PUNCT
cana-853	6	6	feedback	feedback	NOUN
cana-853	6	7	,	,	PUNCT
cana-853	6	8	preparatory	preparatory	ADJ
cana-853	6	9	work	work	NOUN
cana-853	6	10	,	,	PUNCT
cana-853	6	11	catastrophes	catastrophe	VERB
cana-853	6	12	1	1	NUM
cana-853	6	13	.	.	PUNCT
cana-853	6	14	introduction	introduction	NOUN
cana-853	6	15	the	the	DET
cana-853	6	16	appearance	appearance	NOUN
cana-853	6	17	cycle	cycle	NOUN
cana-853	6	18	,	,	PUNCT
cana-853	6	19	the	the	DET
cana-853	6	20	assistance	assistance	NOUN
cana-853	6	21	interaction	interaction	NOUN
cana-853	6	22	,	,	PUNCT
cana-853	6	23	the	the	DET
cana-853	6	24	size	size	NOUN
cana-853	6	25	of	of	ADP
cana-853	6	26	servers	server	NOUN
cana-853	6	27	,	,	PUNCT
cana-853	6	28	how	how	SCONJ
cana-853	6	29	much	much	ADJ
cana-853	6	30	framework	framework	NOUN
cana-853	6	31	spaces	space	NOUN
cana-853	6	32	,	,	PUNCT
cana-853	6	33	and	and	CCONJ
cana-853	6	34	the	the	DET
cana-853	6	35	quantity	quantity	NOUN
cana-853	6	36	of	of	ADP
cana-853	6	37	clients	client	NOUN
cana-853	6	38	—	—	PUNCT
cana-853	6	39	who	who	PRON
cana-853	6	40	may	may	AUX
cana-853	6	41	be	be	AUX
cana-853	6	42	individuals	individual	NOUN
cana-853	6	43	as	as	ADP
cana-853	6	44	a	a	DET
cana-853	6	45	rule	rule	NOUN
cana-853	6	46	,	,	PUNCT
cana-853	6	47	information	information	NOUN
cana-853	6	48	bundles	bundle	NOUN
cana-853	6	49	,	,	PUNCT
cana-853	6	50	vehicles	vehicle	NOUN
cana-853	6	51	,	,	PUNCT
cana-853	6	52	or	or	CCONJ
cana-853	6	53	whatever	whatever	PRON
cana-853	6	54	else	else	ADV
cana-853	6	55	—	—	PUNCT
cana-853	6	56	are	be	AUX
cana-853	6	57	totally	totally	ADV
cana-853	6	58	inspected	inspect	VERB
cana-853	6	59	by	by	ADP
cana-853	6	60	lining	line	VERB
cana-853	6	61	hypothesis	hypothesis	NOUN
cana-853	6	62	.	.	PUNCT
cana-853	7	1	this	this	DET
cana-853	7	2	present	present	ADJ
cana-853	7	3	reality	reality	NOUN
cana-853	7	4	utilizations	utilization	NOUN
cana-853	7	5	of	of	ADP
cana-853	7	6	hypothesis	hypothesis	NOUN
cana-853	7	7	of	of	ADP
cana-853	7	8	lines	line	NOUN
cana-853	7	9	range	range	VERB
cana-853	7	10	various	various	ADJ
cana-853	7	11	areas	area	NOUN
cana-853	7	12	.	.	PUNCT
cana-853	8	1	agner	agner	PROPN
cana-853	8	2	kraruperlang	kraruperlang	PROPN
cana-853	9	1	[	[	X
cana-853	9	2	3	3	NUM
cana-853	9	3	]	]	PUNCT
cana-853	9	4	,	,	PUNCT
cana-853	9	5	a	a	DET
cana-853	9	6	danish	danish	ADJ
cana-853	9	7	mathematician	mathematician	NOUN
cana-853	9	8	and	and	CCONJ
cana-853	9	9	engineer	engineer	NOUN
cana-853	9	10	,	,	PUNCT
cana-853	9	11	pioneered	pioneer	VERB
cana-853	9	12	queuing	queue	VERB
cana-853	9	13	theory	theory	NOUN
cana-853	9	14	with	with	ADP
cana-853	9	15	his	his	PRON
cana-853	9	16	first	first	ADJ
cana-853	9	17	paper	paper	NOUN
cana-853	9	18	published	publish	VERB
cana-853	9	19	in	in	ADP
cana-853	9	20	1909	1909	NUM
cana-853	9	21	,	,	PUNCT
cana-853	9	22	which	which	PRON
cana-853	9	23	was	be	AUX
cana-853	9	24	the	the	DET
cana-853	9	25	basis	basis	NOUN
cana-853	9	26	for	for	ADP
cana-853	9	27	applied	applied	ADJ
cana-853	9	28	queuing	queuing	NOUN
cana-853	9	29	theory	theory	NOUN
cana-853	9	30	.	.	PUNCT
cana-853	10	1	telecommunications	telecommunication	NOUN
cana-853	10	2	,	,	PUNCT
cana-853	10	3	transportation	transportation	NOUN
cana-853	10	4	,	,	PUNCT
cana-853	10	5	logistics	logistic	NOUN
cana-853	10	6	,	,	PUNCT
cana-853	10	7	finance	finance	NOUN
cana-853	10	8	,	,	PUNCT
cana-853	10	9	and	and	CCONJ
cana-853	10	10	other	other	ADJ
cana-853	10	11	fields	field	NOUN
cana-853	10	12	use	use	VERB
cana-853	10	13	queueing	queue	VERB
cana-853	10	14	theory	theory	NOUN
cana-853	10	15	.	.	PUNCT
cana-853	11	1	james	james	PROPN
cana-853	11	2	r.	r.	PROPN
cana-853	11	3	jackson	jackson	PROPN
cana-853	11	4	pioneered	pioneer	VERB
cana-853	11	5	the	the	DET
cana-853	11	6	use	use	NOUN
cana-853	11	7	of	of	ADP
cana-853	11	8	queueing	queue	VERB
cana-853	11	9	netwօrks	netwօrk	NOUN
cana-853	11	10	in	in	ADP
cana-853	11	11	1957	1957	NUM
cana-853	11	12	.	.	PUNCT
cana-853	12	1	jackson	jackson	PROPN
cana-853	13	1	[	[	X
cana-853	13	2	5	5	NUM
cana-853	13	3	]	]	PUNCT
cana-853	13	4	discovered	discover	VERB
cana-853	13	5	an	an	DET
cana-853	13	6	earlier	early	ADJ
cana-853	13	7	product	product	NOUN
cana-853	13	8	-	-	PUNCT
cana-853	13	9	form	form	NOUN
cana-853	13	10	solution	solution	NOUN
cana-853	13	11	for	for	ADP
cana-853	13	12	tandem	tandem	NOUN
cana-853	13	13	queues	queue	NOUN
cana-853	13	14	.	.	PUNCT
cana-853	14	1	the	the	DET
cana-853	14	2	queueing	queueing	NOUN
cana-853	14	3	netwօrk	netwօrk	NOUN
cana-853	14	4	's	's	PART
cana-853	14	5	most	most	ADV
cana-853	14	6	crucial	crucial	ADJ
cana-853	14	7	element	element	NOUN
cana-853	14	8	is	be	AUX
cana-853	14	9	jackson	jackson	PROPN
cana-853	14	10	’s	’s	PART
cana-853	14	11	netwօrk	netwօrk	PROPN
cana-853	14	12	.	.	PUNCT
cana-853	15	1	there	there	PRON
cana-853	15	2	are	be	VERB
cana-853	15	3	three	three	NUM
cana-853	15	4	types	type	NOUN
cana-853	15	5	of	of	ADP
cana-853	15	6	queuing	queue	VERB
cana-853	15	7	netwօrks	netwօrk	NOUN
cana-853	15	8	:	:	PUNCT
cana-853	15	9	open	open	ADJ
cana-853	15	10	,	,	PUNCT
cana-853	15	11	closed	closed	ADJ
cana-853	15	12	,	,	PUNCT
cana-853	15	13	and	and	CCONJ
cana-853	15	14	mixed	mixed	ADJ
cana-853	15	15	.	.	PUNCT
cana-853	16	1	buyers	buyer	NOUN
cana-853	16	2	access	access	VERB
cana-853	16	3	an	an	DET
cana-853	16	4	open	open	ADJ
cana-853	16	5	netwօrk	netwօrk	NOUN
cana-853	16	6	from	from	ADP
cana-853	16	7	the	the	DET
cana-853	16	8	outside	outside	NOUN
cana-853	16	9	,	,	PUNCT
cana-853	16	10	use	use	VERB
cana-853	16	11	the	the	DET
cana-853	16	12	systems	system	NOUN
cana-853	16	13	to	to	PART
cana-853	16	14	offer	offer	VERB
cana-853	16	15	them	they	PRON
cana-853	16	16	with	with	ADP
cana-853	16	17	services	service	NOUN
cana-853	16	18	,	,	PUNCT
cana-853	16	19	and	and	CCONJ
cana-853	16	20	then	then	ADV
cana-853	16	21	leave	leave	VERB
cana-853	16	22	the	the	DET
cana-853	16	23	netwօrk	netwօrk	NOUN
cana-853	16	24	.	.	PUNCT
cana-853	17	1	a	a	DET
cana-853	17	2	closed	close	VERB
cana-853	17	3	netwօrk	netwօrk	NOUN
cana-853	17	4	prevents	prevent	VERB
cana-853	17	5	both	both	DET
cana-853	17	6	new	new	ADJ
cana-853	17	7	users	user	NOUN
cana-853	17	8	from	from	ADP
cana-853	17	9	joining	join	VERB
cana-853	17	10	and	and	CCONJ
cana-853	17	11	current	current	ADJ
cana-853	17	12	ones	one	NOUN
cana-853	17	13	from	from	ADP
cana-853	17	14	leaving	leave	VERB
cana-853	17	15	.	.	PUNCT
cana-853	18	1	in	in	ADP
cana-853	18	2	a	a	DET
cana-853	18	3	mixed	mixed	ADJ
cana-853	18	4	netwօrk	netwօrk	NOUN
cana-853	18	5	,	,	PUNCT
cana-853	18	6	some	some	DET
cana-853	18	7	classes	class	NOUN
cana-853	18	8	of	of	ADP
cana-853	18	9	customers	customer	NOUN
cana-853	18	10	may	may	AUX
cana-853	18	11	have	have	VERB
cana-853	18	12	access	access	NOUN
cana-853	18	13	to	to	ADP
cana-853	18	14	the	the	DET
cana-853	18	15	netwօrk	netwօrk	NOUN
cana-853	18	16	while	while	SCONJ
cana-853	18	17	others	other	NOUN
cana-853	18	18	do	do	VERB
cana-853	18	19	not	not	PART
cana-853	18	20	.	.	PUNCT
cana-853	19	1	when	when	SCONJ
cana-853	19	2	the	the	DET
cana-853	19	3	functioning	functioning	NOUN
cana-853	19	4	of	of	ADP
cana-853	19	5	a	a	DET
cana-853	19	6	system	system	NOUN
cana-853	19	7	of	of	ADP
cana-853	19	8	queue	queue	NOUN
cana-853	19	9	is	be	AUX
cana-853	19	10	time	time	NOUN
cana-853	19	11	-	-	PUNCT
cana-853	19	12	varying	vary	VERB
cana-853	19	13	,	,	PUNCT
cana-853	19	14	the	the	DET
cana-853	19	15	system	system	NOUN
cana-853	19	16	is	be	AUX
cana-853	19	17	said	say	VERB
cana-853	19	18	to	to	PART
cana-853	19	19	be	be	AUX
cana-853	19	20	in	in	ADP
cana-853	19	21	transient	transient	NOUN
cana-853	19	22	.	.	PUNCT
cana-853	20	1	a	a	DET
cana-853	20	2	queueing	queueing	NOUN
cana-853	20	3	netwօrk	netwօrk	NOUN
cana-853	20	4	is	be	AUX
cana-853	20	5	thought	think	VERB
cana-853	20	6	of	of	ADP
cana-853	20	7	to	to	PART
cana-853	20	8	be	be	AUX
cana-853	20	9	in	in	ADP
cana-853	20	10	steady	steady	ADJ
cana-853	20	11	state	state	NOUN
cana-853	20	12	when	when	SCONJ
cana-853	20	13	its	its	PRON
cana-853	20	14	functional	functional	ADJ
cana-853	20	15	characteristics	characteristic	NOUN
cana-853	20	16	are	be	AUX
cana-853	20	17	independent	independent	ADJ
cana-853	20	18	of	of	ADP
cana-853	20	19	time.parthasarathy	time.parthasarathy	PROPN
cana-853	20	20	[	[	X
cana-853	20	21	7	7	NUM
cana-853	20	22	]	]	PUNCT
cana-853	20	23	and	and	CCONJ
cana-853	20	24	parthasarathy	parthasarathy	ADJ
cana-853	20	25	,	,	PUNCT
cana-853	20	26	sharafali	sharafali	ADJ
cana-853	20	27	[	[	X
cana-853	20	28	8	8	NUM
cana-853	20	29	]	]	PUNCT
cana-853	20	30	have	have	AUX
cana-853	20	31	described	describe	VERB
cana-853	20	32	an	an	DET
cana-853	20	33	efficient	efficient	ADJ
cana-853	20	34	solution	solution	NOUN
cana-853	20	35	for	for	ADP
cana-853	20	36	an	an	DET
cana-853	20	37	𝑀/𝑀/1	𝑀/𝑀/1	NOUN
cana-853	20	38	queue	queue	NOUN
cana-853	20	39	using	use	VERB
cana-853	20	40	an	an	DET
cana-853	20	41	easy	easy	ADJ
cana-853	20	42	strategy	strategy	NOUN
cana-853	20	43	and	and	CCONJ
cana-853	20	44	a	a	DET
cana-853	20	45	multi	multi	ADJ
cana-853	20	46	-	-	ADJ
cana-853	20	47	server	server	ADJ
cana-853	20	48	poisson	poisson	NOUN
cana-853	20	49	queue	queue	NOUN
cana-853	20	50	.	.	PUNCT
cana-853	21	1	in	in	ADP
cana-853	21	2	actual	actual	ADJ
cana-853	21	3	service	service	NOUN
cana-853	21	4	systems	system	NOUN
cana-853	21	5	,	,	PUNCT
cana-853	21	6	where	where	SCONJ
cana-853	21	7	jobs	job	NOUN
cana-853	21	8	may	may	AUX
cana-853	21	9	necessitate	necessitate	VERB
cana-853	21	10	multiple	multiple	ADJ
cana-853	21	11	services	service	NOUN
cana-853	21	12	,	,	PUNCT
cana-853	21	13	the	the	DET
cana-853	21	14	feedback	feedback	NOUN
cana-853	21	15	queue	queue	NOUN
cana-853	21	16	is	be	AUX
cana-853	21	17	essential	essential	ADJ
cana-853	21	18	.	.	PUNCT
cana-853	22	1	queueing	queue	VERB
cana-853	22	2	systems	system	NOUN
cana-853	22	3	with	with	ADP
cana-853	22	4	feedback	feedback	NOUN
cana-853	22	5	are	be	AUX
cana-853	22	6	those	those	PRON
cana-853	22	7	that	that	PRON
cana-853	22	8	allows	allow	VERB
cana-853	22	9	a	a	DET
cana-853	22	10	customer	customer	NOUN
cana-853	22	11	to	to	PART
cana-853	22	12	return	return	VERB
cana-853	22	13	in	in	ADP
cana-853	22	14	the	the	DET
cana-853	22	15	event	event	NOUN
cana-853	22	16	that	that	PRON
cana-853	22	17	they	they	PRON
cana-853	22	18	have	have	AUX
cana-853	22	19	not	not	PART
cana-853	22	20	been	be	AUX
cana-853	22	21	satisfied	satisfied	ADJ
cana-853	22	22	or	or	CCONJ
cana-853	22	23	want	want	VERB
cana-853	22	24	more	more	ADJ
cana-853	22	25	assistance	assistance	NOUN
cana-853	22	26	.	.	PUNCT
cana-853	23	1	feedback	feedback	NOUN
cana-853	23	2	may	may	AUX
cana-853	23	3	be	be	AUX
cana-853	23	4	observed	observe	VERB
cana-853	23	5	in	in	ADP
cana-853	23	6	a	a	DET
cana-853	23	7	variety	variety	NOUN
cana-853	23	8	of	of	ADP
cana-853	23	9	real	real	ADJ
cana-853	23	10	-	-	PUNCT
cana-853	23	11	world	world	NOUN
cana-853	23	12	settings	setting	NOUN
cana-853	23	13	,	,	PUNCT
cana-853	23	14	including	include	VERB
cana-853	23	15	supermarkets	supermarket	NOUN
cana-853	23	16	,	,	PUNCT
cana-853	23	17	communication	communication	NOUN
cana-853	23	18	netwօrks	netwօrk	NOUN
cana-853	23	19	,	,	PUNCT
cana-853	23	20	and	and	CCONJ
cana-853	23	21	changes	change	NOUN
cana-853	23	22	made	make	VERB
cana-853	23	23	to	to	ADP
cana-853	23	24	industrial	industrial	ADJ
cana-853	23	25	systems	system	NOUN
cana-853	23	26	.	.	PUNCT
cana-853	24	1	takacs	takac	NOUN
cana-853	25	1	[	[	X
cana-853	25	2	12	12	NUM
cana-853	25	3	]	]	PUNCT
cana-853	25	4	communications	communication	NOUN
cana-853	25	5	on	on	ADP
cana-853	25	6	applied	apply	VERB
cana-853	25	7	nonlinear	nonlinear	ADJ
cana-853	25	8	analysis	analysis	NOUN
cana-853	25	9	issn	issn	NOUN
cana-853	25	10	:	:	PUNCT
cana-853	25	11	1074	1074	NUM
cana-853	25	12	-	-	PUNCT
cana-853	25	13	133x	133x	NUM
cana-853	25	14	vol	vol	NOUN
cana-853	25	15	31	31	NUM
cana-853	25	16	no	no	NOUN
cana-853	25	17	.	.	PUNCT
cana-853	26	1	4s	4s	NUM
cana-853	26	2	(	(	PUNCT
cana-853	26	3	2024	2024	NUM
cana-853	26	4	)	)	PUNCT
cana-853	26	5	298	298	NUM
cana-853	26	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-853	26	7	pioneered	pioneer	VERB
cana-853	26	8	the	the	DET
cana-853	26	9	use	use	NOUN
cana-853	26	10	of	of	ADP
cana-853	26	11	queues	queue	NOUN
cana-853	26	12	with	with	ADP
cana-853	26	13	feedback	feedback	NOUN
cana-853	26	14	mechanisms	mechanism	NOUN
cana-853	26	15	in	in	ADP
cana-853	26	16	1963	1963	NUM
cana-853	26	17	.	.	PUNCT
cana-853	27	1	thangaraj	thangaraj	PROPN
cana-853	27	2	and	and	CCONJ
cana-853	27	3	vanitha	vanitha	ADJ
cana-853	28	1	[	[	X
cana-853	28	2	13	13	NUM
cana-853	28	3	]	]	PUNCT
cana-853	28	4	reviewed	review	VERB
cana-853	28	5	the	the	DET
cana-853	28	6	continued	continue	VERB
cana-853	28	7	fraction	fraction	NOUN
cana-853	28	8	method	method	NOUN
cana-853	28	9	for	for	ADP
cana-853	28	10	the	the	DET
cana-853	28	11	m	m	PROPN
cana-853	28	12	/	/	SYM
cana-853	28	13	m/1	m/1	NOUN
cana-853	28	14	queue	queue	NOUN
cana-853	28	15	with	with	ADP
cana-853	28	16	comments	comment	NOUN
cana-853	28	17	.	.	PUNCT
cana-853	29	1	unpredictable	unpredictable	ADJ
cana-853	29	2	instances	instance	NOUN
cana-853	29	3	that	that	PRON
cana-853	29	4	take	take	VERB
cana-853	29	5	place	place	NOUN
cana-853	29	6	at	at	ADP
cana-853	29	7	a	a	DET
cana-853	29	8	service	service	NOUN
cana-853	29	9	system	system	NOUN
cana-853	29	10	are	be	AUX
cana-853	29	11	called	call	VERB
cana-853	29	12	catastrophes.gelenbe	catastrophes.gelenbe	NOUN
cana-853	29	13	[	[	X
cana-853	29	14	4	4	NUM
cana-853	29	15	]	]	PUNCT
cana-853	29	16	suggested	suggest	VERB
cana-853	29	17	the	the	DET
cana-853	29	18	concept	concept	NOUN
cana-853	29	19	of	of	ADP
cana-853	29	20	disasters	disaster	NOUN
cana-853	29	21	,	,	PUNCT
cana-853	29	22	which	which	PRON
cana-853	29	23	has	have	AUX
cana-853	29	24	drawn	draw	VERB
cana-853	29	25	a	a	DET
cana-853	29	26	lot	lot	NOUN
cana-853	29	27	of	of	ADP
cana-853	29	28	research	research	NOUN
cana-853	29	29	passion	passion	NOUN
cana-853	29	30	currently	currently	ADV
cana-853	29	31	due	due	ADJ
cana-853	29	32	to	to	ADP
cana-853	29	33	its	its	PRON
cana-853	29	34	extensive	extensive	ADJ
cana-853	29	35	deployment	deployment	NOUN
cana-853	29	36	in	in	ADP
cana-853	29	37	industrial	industrial	ADJ
cana-853	29	38	,	,	PUNCT
cana-853	29	39	computing	computing	NOUN
cana-853	29	40	,	,	PUNCT
cana-853	29	41	and	and	CCONJ
cana-853	29	42	service	service	NOUN
cana-853	29	43	systems	system	NOUN
cana-853	29	44	.	.	PUNCT
cana-853	30	1	science	science	NOUN
cana-853	30	2	and	and	CCONJ
cana-853	30	3	technology	technology	NOUN
cana-853	30	4	have	have	AUX
cana-853	30	5	benefited	benefit	VERB
cana-853	30	6	from	from	ADP
cana-853	30	7	the	the	DET
cana-853	30	8	notion	notion	NOUN
cana-853	30	9	of	of	ADP
cana-853	30	10	calamity	calamity	NOUN
cana-853	30	11	.	.	PUNCT
cana-853	31	1	in	in	ADP
cana-853	31	2	the	the	DET
cana-853	31	3	majority	majority	NOUN
cana-853	31	4	of	of	ADP
cana-853	31	5	situations	situation	NOUN
cana-853	31	6	in	in	ADP
cana-853	31	7	life	life	NOUN
cana-853	31	8	,	,	PUNCT
cana-853	31	9	it	it	PRON
cana-853	31	10	occurs	occur	VERB
cana-853	31	11	at	at	ADP
cana-853	31	12	random	random	ADJ
cana-853	31	13	,	,	PUNCT
cana-853	31	14	causing	cause	VERB
cana-853	31	15	all	all	DET
cana-853	31	16	units	unit	NOUN
cana-853	31	17	for	for	ADP
cana-853	31	18	extinguishing	extinguishing	NOUN
cana-853	31	19	and	and	CCONJ
cana-853	31	20	the	the	DET
cana-853	31	21	servicing	servicing	NOUN
cana-853	31	22	facility	facility	NOUN
cana-853	31	23	to	to	PART
cana-853	31	24	activate	activate	VERB
cana-853	31	25	until	until	ADP
cana-853	31	26	a	a	DET
cana-853	31	27	fresh	fresh	ADJ
cana-853	31	28	arrival	arrival	NOUN
cana-853	31	29	.	.	PUNCT
cana-853	32	1	a	a	DET
cana-853	32	2	system	system	NOUN
cana-853	32	3	failure	failure	NOUN
cana-853	32	4	results	result	VERB
cana-853	32	5	in	in	ADP
cana-853	32	6	the	the	DET
cana-853	32	7	instantaneous	instantaneous	ADJ
cana-853	32	8	destruction	destruction	NOUN
cana-853	32	9	of	of	ADP
cana-853	32	10	all	all	DET
cana-853	32	11	clients	client	NOUN
cana-853	32	12	and	and	CCONJ
cana-853	32	13	the	the	DET
cana-853	32	14	deactivation	deactivation	NOUN
cana-853	32	15	of	of	ADP
cana-853	32	16	the	the	DET
cana-853	32	17	server	server	NOUN
cana-853	32	18	.	.	PUNCT
cana-853	33	1	when	when	SCONJ
cana-853	33	2	someone	someone	PRON
cana-853	33	3	fresh	fresh	ADJ
cana-853	33	4	shows	show	VERB
cana-853	33	5	up	up	ADP
cana-853	33	6	,	,	PUNCT
cana-853	33	7	the	the	DET
cana-853	33	8	server	server	NOUN
cana-853	33	9	is	be	AUX
cana-853	33	10	prepared	prepare	VERB
cana-853	33	11	to	to	PART
cana-853	33	12	serve	serve	VERB
cana-853	33	13	.	.	PUNCT
cana-853	34	1	chandrasekaran	chandrasekaran	VERB
cana-853	34	2	,	,	PUNCT
cana-853	34	3	saravanarajan	saravanarajan	ADJ
cana-853	34	4	[	[	X
cana-853	34	5	1	1	NUM
cana-853	34	6	]	]	PUNCT
cana-853	34	7	discussed	discuss	VERB
cana-853	34	8	the	the	DET
cana-853	34	9	m	m	NOUN
cana-853	34	10	/	/	SYM
cana-853	34	11	m/1	m/1	NOUN
cana-853	34	12	feedback	feedback	NOUN
cana-853	34	13	queue	queue	NOUN
cana-853	34	14	's	's	PART
cana-853	34	15	transient	transient	ADJ
cana-853	34	16	and	and	CCONJ
cana-853	34	17	reliability	reliability	NOUN
cana-853	34	18	study	study	NOUN
cana-853	34	19	in	in	ADP
cana-853	34	20	the	the	DET
cana-853	34	21	event	event	NOUN
cana-853	34	22	of	of	ADP
cana-853	34	23	disasters	disaster	NOUN
cana-853	34	24	,	,	PUNCT
cana-853	34	25	server	server	NOUN
cana-853	34	26	troubles	trouble	NOUN
cana-853	34	27	,	,	PUNCT
cana-853	34	28	and	and	CCONJ
cana-853	34	29	servicing	servicing	NOUN
cana-853	34	30	.	.	PUNCT
cana-853	35	1	[	[	X
cana-853	35	2	2].krishnakumar	2].krishnakumar	NUM
cana-853	35	3	and	and	CCONJ
cana-853	35	4	arivudainambi	arivudainambi	NOUN
cana-853	36	1	[	[	X
cana-853	36	2	6	6	NUM
cana-853	36	3	]	]	PUNCT
cana-853	36	4	investigated	investigate	VERB
cana-853	36	5	the	the	DET
cana-853	36	6	transient	transient	ADJ
cana-853	36	7	solution	solution	NOUN
cana-853	36	8	of	of	ADP
cana-853	36	9	an	an	DET
cana-853	36	10	𝑀/𝑀/1	𝑀/𝑀/1	NOUN
cana-853	36	11	queue	queue	NOUN
cana-853	36	12	with	with	ADP
cana-853	36	13	disasters.shanmugasundaram	disasters.shanmugasundaram	PROPN
cana-853	36	14	and	and	CCONJ
cana-853	36	15	vanitha	vanitha	NOUN
cana-853	37	1	[	[	X
cana-853	37	2	11	11	NUM
cana-853	37	3	]	]	PUNCT
cana-853	37	4	proposed	propose	VERB
cana-853	37	5	analysis	analysis	NOUN
cana-853	37	6	of	of	ADP
cana-853	37	7	𝑀/𝑀/1	𝑀/𝑀/1	NOUN
cana-853	37	8	retrial	retrial	NOUN
cana-853	37	9	queueing	queueing	NOUN
cana-853	37	10	netwօrk	netwօrk	NOUN
cana-853	37	11	in	in	ADP
cana-853	37	12	steady	steady	ADJ
cana-853	37	13	-	-	PUNCT
cana-853	37	14	state	state	NOUN
cana-853	37	15	with	with	ADP
cana-853	37	16	catastrophes	catastrophe	NOUN
cana-853	37	17	.	.	PUNCT
cana-853	38	1	thangaraj	thangaraj	NOUN
cana-853	38	2	and	and	CCONJ
cana-853	38	3	vanitha	vanitha	ADJ
cana-853	39	1	[	[	X
cana-853	39	2	14	14	NUM
cana-853	39	3	]	]	PUNCT
cana-853	39	4	have	have	AUX
cana-853	39	5	evaluated	evaluate	VERB
cana-853	39	6	using	use	VERB
cana-853	39	7	continued	continue	VERB
cana-853	39	8	fractions	fraction	NOUN
cana-853	39	9	to	to	PART
cana-853	39	10	analyse	analyse	VERB
cana-853	39	11	.to	.to	PUNCT
cana-853	39	12	avoid	avoid	VERB
cana-853	39	13	a	a	DET
cana-853	39	14	too	too	ADV
cana-853	39	15	-	-	PUNCT
cana-853	39	16	long	long	ADJ
cana-853	39	17	queue	queue	NOUN
cana-853	39	18	,	,	PUNCT
cana-853	39	19	every	every	DET
cana-853	39	20	server	server	NOUN
cana-853	39	21	request	request	NOUN
cana-853	39	22	and	and	CCONJ
cana-853	39	23	customer	customer	NOUN
cana-853	39	24	that	that	PRON
cana-853	39	25	needs	need	VERB
cana-853	39	26	setup	setup	NOUN
cana-853	39	27	time	time	NOUN
cana-853	39	28	(	(	PUNCT
cana-853	39	29	preparatory	preparatory	ADJ
cana-853	39	30	wօrk	wօrk	NOUN
cana-853	39	31	time	time	NOUN
cana-853	39	32	)	)	PUNCT
cana-853	39	33	before	before	ADP
cana-853	39	34	getting	get	VERB
cana-853	39	35	service	service	NOUN
cana-853	39	36	should	should	AUX
cana-853	39	37	be	be	AUX
cana-853	39	38	accommodated	accommodate	VERB
cana-853	39	39	to	to	PART
cana-853	39	40	prevent	prevent	VERB
cana-853	39	41	an	an	DET
cana-853	39	42	excessively	excessively	ADV
cana-853	39	43	lengthy	lengthy	ADJ
cana-853	39	44	line	line	NOUN
cana-853	39	45	.	.	PUNCT
cana-853	40	1	examined	examine	VERB
cana-853	40	2	was	be	AUX
cana-853	40	3	the	the	DET
cana-853	40	4	preparatory	preparatory	ADJ
cana-853	40	5	wօrk	wօrk	NOUN
cana-853	40	6	done	do	VERB
cana-853	40	7	for	for	ADP
cana-853	40	8	arriving	arrive	VERB
cana-853	40	9	clients	client	NOUN
cana-853	40	10	who	who	PRON
cana-853	40	11	only	only	ADV
cana-853	40	12	had	have	VERB
cana-853	40	13	one	one	NUM
cana-853	40	14	server	server	NOUN
cana-853	40	15	feedback	feedback	NOUN
cana-853	40	16	queueby	queueby	ADV
cana-853	40	17	santhakumaran	santhakumaran	VERB
cana-853	40	18	and	and	CCONJ
cana-853	40	19	shanmugasundaram	shanmugasundaram	VERB
cana-853	41	1	[	[	X
cana-853	41	2	9].when	9].when	NOUN
cana-853	41	3	a	a	DET
cana-853	41	4	disaster	disaster	NOUN
cana-853	41	5	occurs	occur	VERB
cana-853	41	6	,	,	PUNCT
cana-853	41	7	shanmugasundaram	shanmugasundaram	PROPN
cana-853	41	8	and	and	CCONJ
cana-853	41	9	chitra	chitra	NOUN
cana-853	42	1	[	[	X
cana-853	42	2	10	10	NUM
cana-853	42	3	]	]	PUNCT
cana-853	42	4	discussed	discuss	VERB
cana-853	42	5	the	the	DET
cana-853	42	6	time	time	NOUN
cana-853	42	7	dependent	dependent	ADJ
cana-853	42	8	solution	solution	NOUN
cana-853	42	9	of	of	ADP
cana-853	42	10	a	a	DET
cana-853	42	11	single	single	ADJ
cana-853	42	12	server	server	NOUN
cana-853	42	13	feedback	feedback	NOUN
cana-853	42	14	queue	queue	NOUN
cana-853	42	15	customer	customer	NOUN
cana-853	42	16	having	have	VERB
cana-853	42	17	a	a	DET
cana-853	42	18	service	service	NOUN
cana-853	42	19	with	with	ADP
cana-853	42	20	and	and	CCONJ
cana-853	42	21	without	without	ADP
cana-853	42	22	preparatory	preparatory	ADJ
cana-853	42	23	wօrk	wօrk	NOUN
cana-853	42	24	2	2	NUM
cana-853	42	25	.	.	PUNCT
cana-853	42	26	description	description	NOUN
cana-853	42	27	of	of	ADP
cana-853	42	28	the	the	DET
cana-853	42	29	model	model	NOUN
cana-853	42	30	in	in	ADP
cana-853	42	31	this	this	DET
cana-853	42	32	paper	paper	NOUN
cana-853	42	33	we	we	PRON
cana-853	42	34	see	see	VERB
cana-853	42	35	𝑀/𝑀/1queueing	𝑀/𝑀/1queueing	NOUN
cana-853	42	36	netwօrk	netwօrk	NOUN
cana-853	42	37	with	with	ADP
cana-853	42	38	instantaneous	instantaneous	ADJ
cana-853	42	39	bernoulli	bernoulli	NOUN
cana-853	42	40	feedback	feedback	NOUN
cana-853	42	41	and	and	CCONJ
cana-853	42	42	preparatory	preparatory	ADJ
cana-853	42	43	wօrk	wօrk	NOUN
cana-853	42	44	for	for	ADP
cana-853	42	45	three	three	NUM
cana-853	42	46	node	node	ADJ
cana-853	42	47	open	open	ADJ
cana-853	42	48	queue	queue	NOUN
cana-853	42	49	.	.	PUNCT
cana-853	43	1	the	the	DET
cana-853	43	2	arrival	arrival	NOUN
cana-853	43	3	rate	rate	NOUN
cana-853	43	4	of	of	ADP
cana-853	43	5	the	the	DET
cana-853	43	6	customer	customer	NOUN
cana-853	43	7	entering	enter	VERB
cana-853	43	8	the	the	DET
cana-853	43	9	queue	queue	NOUN
cana-853	43	10	is	be	AUX
cana-853	43	11	a	a	DET
cana-853	43	12	poisson	poisson	NOUN
cana-853	43	13	process	process	NOUN
cana-853	43	14	with	with	ADP
cana-853	43	15	rate	rate	NOUN
cana-853	43	16	λ	λ	PROPN
cana-853	43	17	.	.	PUNCT
cana-853	43	18	before	before	SCONJ
cana-853	43	19	getting	get	VERB
cana-853	43	20	service	service	NOUN
cana-853	43	21	the	the	DET
cana-853	43	22	customers	customer	NOUN
cana-853	43	23	either	either	CCONJ
cana-853	43	24	directly	directly	ADV
cana-853	43	25	goes	go	VERB
cana-853	43	26	with	with	ADP
cana-853	43	27	preparatory	preparatory	ADJ
cana-853	43	28	wօrk	wօrk	NOUN
cana-853	43	29	or	or	CCONJ
cana-853	43	30	without	without	ADP
cana-853	43	31	preparatory	preparatory	ADJ
cana-853	43	32	wօrk	wօrk	NOUN
cana-853	43	33	.here	.here	ADP
cana-853	43	34	the	the	DET
cana-853	43	35	customers	customer	NOUN
cana-853	43	36	with	with	ADP
cana-853	43	37	preparatory	preparatory	ADJ
cana-853	43	38	wօrk	wօrk	NOUN
cana-853	43	39	does	do	AUX
cana-853	43	40	not	not	PART
cana-853	43	41	get	get	VERB
cana-853	43	42	feedback	feedback	NOUN
cana-853	43	43	,	,	PUNCT
cana-853	43	44	but	but	CCONJ
cana-853	43	45	the	the	DET
cana-853	43	46	customers	customer	NOUN
cana-853	43	47	without	without	ADP
cana-853	43	48	preparatory	preparatory	ADJ
cana-853	43	49	wօrk	wօrk	NOUN
cana-853	43	50	are	be	AUX
cana-853	43	51	allowed	allow	VERB
cana-853	43	52	for	for	ADP
cana-853	43	53	feedback	feedback	NOUN
cana-853	43	54	.	.	PUNCT
cana-853	44	1	after	after	ADP
cana-853	44	2	getting	get	VERB
cana-853	44	3	service	service	NOUN
cana-853	44	4	,	,	PUNCT
cana-853	44	5	the	the	DET
cana-853	44	6	customers	customer	NOUN
cana-853	44	7	with	with	ADP
cana-853	44	8	preparatory	preparatory	ADJ
cana-853	44	9	wօrk	wօrk	NOUN
cana-853	44	10	join	join	VERB
cana-853	44	11	the	the	DET
cana-853	44	12	node	node	NOUN
cana-853	44	13	one	one	NUM
cana-853	44	14	with	with	ADP
cana-853	44	15	probability	probability	NOUN
cana-853	44	16	�	�	NOUN
cana-853	44	17	̅	̅	NOUN
cana-853	44	18	�	�	NOUN
cana-853	44	19	,	,	PUNCT
cana-853	44	20	after	after	ADP
cana-853	44	21	getting	get	VERB
cana-853	44	22	service	service	NOUN
cana-853	44	23	from	from	ADP
cana-853	44	24	node	node	PROPN
cana-853	44	25	one	one	NUM
cana-853	44	26	,	,	PUNCT
cana-853	44	27	they	they	PRON
cana-853	44	28	move	move	VERB
cana-853	44	29	to	to	PART
cana-853	44	30	node	node	VERB
cana-853	44	31	two	two	NUM
cana-853	44	32	with	with	ADP
cana-853	44	33	probability	probability	NOUN
cana-853	44	34	q	q	NOUN
cana-853	44	35	or	or	CCONJ
cana-853	44	36	to	to	ADP
cana-853	44	37	the	the	DET
cana-853	44	38	node	node	NOUN
cana-853	44	39	three	three	NUM
cana-853	44	40	with	with	ADP
cana-853	44	41	probability	probability	NOUN
cana-853	44	42	1-	1-	PROPN
cana-853	44	43	�	�	PROPN
cana-853	44	44	̅	̅	NOUN
cana-853	44	45	�	�	NOUN
cana-853	44	46	,from	,from	PUNCT
cana-853	44	47	node	node	VERB
cana-853	44	48	two	two	NUM
cana-853	44	49	the	the	DET
cana-853	44	50	customers	customer	NOUN
cana-853	44	51	leaves	leave	VERB
cana-853	44	52	the	the	DET
cana-853	44	53	system	system	NOUN
cana-853	44	54	after	after	ADP
cana-853	44	55	completing	complete	VERB
cana-853	44	56	the	the	DET
cana-853	44	57	service	service	NOUN
cana-853	44	58	with	with	ADP
cana-853	44	59	the	the	DET
cana-853	44	60	probability	probability	NOUN
cana-853	44	61	r	r	NOUN
cana-853	44	62	,	,	PUNCT
cana-853	44	63	or	or	CCONJ
cana-853	44	64	moves	move	NOUN
cana-853	44	65	to	to	ADP
cana-853	44	66	the	the	DET
cana-853	44	67	node	node	NOUN
cana-853	44	68	three	three	NUM
cana-853	44	69	with	with	ADP
cana-853	44	70	probability	probability	NOUN
cana-853	44	71	1	1	NUM
cana-853	44	72	-	-	PUNCT
cana-853	44	73	r	r	NOUN
cana-853	44	74	,	,	PUNCT
cana-853	44	75	after	after	ADP
cana-853	44	76	getting	get	VERB
cana-853	44	77	service	service	NOUN
cana-853	44	78	in	in	ADP
cana-853	44	79	node	node	PROPN
cana-853	44	80	three	three	NUM
cana-853	44	81	the	the	DET
cana-853	44	82	customers	customer	NOUN
cana-853	44	83	leaves	leave	VERB
cana-853	44	84	the	the	DET
cana-853	44	85	system	system	NOUN
cana-853	44	86	.	.	PUNCT
cana-853	45	1	the	the	DET
cana-853	45	2	customer	customer	NOUN
cana-853	45	3	without	without	ADP
cana-853	45	4	preparatory	preparatory	ADJ
cana-853	45	5	wօrk	wօrk	NOUN
cana-853	45	6	decides	decide	VERB
cana-853	45	7	whether	whether	SCONJ
cana-853	45	8	to	to	PART
cana-853	45	9	go	go	VERB
cana-853	45	10	for	for	ADP
cana-853	45	11	feedback	feedback	NOUN
cana-853	45	12	or	or	CCONJ
cana-853	45	13	not	not	PART
cana-853	45	14	.	.	PUNCT
cana-853	46	1	if	if	SCONJ
cana-853	46	2	the	the	DET
cana-853	46	3	customer	customer	NOUN
cana-853	46	4	makes	make	VERB
cana-853	46	5	the	the	DET
cana-853	46	6	decision	decision	NOUN
cana-853	46	7	for	for	ADP
cana-853	46	8	feedback	feedback	NOUN
cana-853	46	9	,	,	PUNCT
cana-853	46	10	then	then	ADV
cana-853	46	11	he	he	PRON
cana-853	46	12	joins	join	VERB
cana-853	46	13	the	the	DET
cana-853	46	14	feedback	feedback	NOUN
cana-853	46	15	with	with	ADP
cana-853	46	16	probability	probability	NOUN
cana-853	46	17	1-	1-	PROPN
cana-853	46	18	�	�	PROPN
cana-853	46	19	̅	̅	NOUN
cana-853	46	20	�	�	NOUN
cana-853	46	21	,	,	PUNCT
cana-853	46	22	if	if	SCONJ
cana-853	46	23	not	not	PART
cana-853	46	24	the	the	DET
cana-853	46	25	customer	customer	NOUN
cana-853	46	26	joins	join	VERB
cana-853	46	27	the	the	DET
cana-853	46	28	preparatory	preparatory	ADJ
cana-853	46	29	wօrk	wօrk	NOUN
cana-853	46	30	and	and	CCONJ
cana-853	46	31	get	get	VERB
cana-853	46	32	the	the	DET
cana-853	46	33	service	service	NOUN
cana-853	46	34	.	.	PUNCT
cana-853	47	1	here	here	ADV
cana-853	47	2	the	the	DET
cana-853	47	3	service	service	NOUN
cana-853	47	4	times	time	NOUN
cana-853	47	5	are	be	AUX
cana-853	47	6	independent	independent	ADJ
cana-853	47	7	but	but	CCONJ
cana-853	47	8	not	not	PART
cana-853	47	9	identically	identically	ADV
cana-853	47	10	distributed	distribute	VERB
cana-853	47	11	.	.	PUNCT
cana-853	48	1	service	service	NOUN
cana-853	48	2	rates	rate	NOUN
cana-853	48	3	are	be	AUX
cana-853	48	4	exponentially	exponentially	ADV
cana-853	48	5	distributed	distribute	VERB
cana-853	48	6	with	with	ADP
cana-853	48	7	rate𝜇1	rate𝜇1	PROPN
cana-853	48	8	,	,	PUNCT
cana-853	48	9	𝜇2	𝜇2	PROPN
cana-853	48	10	,	,	PUNCT
cana-853	48	11	where	where	SCONJ
cana-853	48	12	𝜇1	𝜇1	PROPN
cana-853	48	13	is	be	AUX
cana-853	48	14	the	the	DET
cana-853	48	15	service	service	NOUN
cana-853	48	16	rate	rate	NOUN
cana-853	48	17	for	for	ADP
cana-853	48	18	the	the	DET
cana-853	48	19	customer	customer	NOUN
cana-853	48	20	with	with	ADP
cana-853	48	21	preparatory	preparatory	ADJ
cana-853	48	22	wօrk	wօrk	NOUN
cana-853	48	23	and	and	CCONJ
cana-853	48	24	𝜇2	𝜇2	NOUN
cana-853	48	25	is	be	AUX
cana-853	48	26	the	the	DET
cana-853	48	27	service	service	NOUN
cana-853	48	28	rate	rate	NOUN
cana-853	48	29	for	for	ADP
cana-853	48	30	the	the	DET
cana-853	48	31	customer	customer	NOUN
cana-853	48	32	without	without	ADP
cana-853	48	33	preparatory	preparatory	ADJ
cana-853	48	34	wօrk	wօrk	NOUN
cana-853	48	35	.	.	PUNCT
cana-853	49	1	service	service	NOUN
cana-853	49	2	rate	rate	NOUN
cana-853	49	3	for	for	ADP
cana-853	49	4	node	node	NOUN
cana-853	49	5	one	one	NUM
cana-853	49	6	,	,	PUNCT
cana-853	49	7	node	node	NOUN
cana-853	49	8	two	two	NUM
cana-853	49	9	and	and	CCONJ
cana-853	49	10	node	node	VERB
cana-853	49	11	three	three	NUM
cana-853	49	12	are𝜇3	are𝜇3	PROPN
cana-853	49	13	,	,	PUNCT
cana-853	49	14	𝜇4	𝜇4	NOUN
cana-853	49	15	and	and	CCONJ
cana-853	49	16	𝜇5.the	𝜇5.the	DET
cana-853	49	17	capacity	capacity	NOUN
cana-853	49	18	of	of	ADP
cana-853	49	19	the	the	DET
cana-853	49	20	queue	queue	NOUN
cana-853	49	21	is	be	AUX
cana-853	49	22	infinite	infinite	ADJ
cana-853	49	23	and	and	CCONJ
cana-853	49	24	the	the	DET
cana-853	49	25	discipline	discipline	NOUN
cana-853	49	26	is	be	AUX
cana-853	49	27	fifo	fifo	ADJ
cana-853	49	28	.	.	PUNCT
cana-853	50	1	catastrophes	catastrophe	NOUN
cana-853	50	2	occurs	occur	VERB
cana-853	50	3	as	as	ADP
cana-853	50	4	a	a	DET
cana-853	50	5	result	result	NOUN
cana-853	50	6	from	from	ADP
cana-853	50	7	arrival	arrival	NOUN
cana-853	50	8	and	and	CCONJ
cana-853	50	9	service	service	NOUN
cana-853	50	10	prօcesses	prօcesse	NOUN
cana-853	50	11	,	,	PUNCT
cana-853	50	12	here	here	ADV
cana-853	50	13	service	service	NOUN
cana-853	50	14	prօcess	prօcess	PROPN
cana-853	50	15	follows	follow	VERB
cana-853	50	16	pօisson	pօisson	NOUN
cana-853	50	17	process	process	NOUN
cana-853	50	18	with	with	ADP
cana-853	50	19	rate	rate	NOUN
cana-853	50	20	𝛾.	𝛾.	ADV
cana-853	50	21	the	the	DET
cana-853	50	22	system	system	NOUN
cana-853	50	23	is	be	AUX
cana-853	50	24	shown	show	VERB
cana-853	50	25	in	in	ADP
cana-853	50	26	fig.1	fig.1	PROPN
cana-853	50	27	.	.	PUNCT
cana-853	51	1	communications	communication	NOUN
cana-853	51	2	on	on	ADP
cana-853	51	3	applied	apply	VERB
cana-853	51	4	nonlinear	nonlinear	ADJ
cana-853	51	5	analysis	analysis	NOUN
cana-853	51	6	issn	issn	NOUN
cana-853	51	7	:	:	PUNCT
cana-853	51	8	1074	1074	NUM
cana-853	51	9	-	-	PUNCT
cana-853	51	10	133x	133x	NUM
cana-853	51	11	vol	vol	NOUN
cana-853	51	12	31	31	NUM
cana-853	51	13	no	no	NOUN
cana-853	51	14	.	.	PUNCT
cana-853	52	1	4s	4s	NUM
cana-853	52	2	(	(	PUNCT
cana-853	52	3	2024	2024	NUM
cana-853	52	4	)	)	PUNCT
cana-853	52	5	299	299	NUM
cana-853	52	6	https://internationalpubls.com	https://internationalpubls.com	NUM
cana-853	52	7	fig	fig	NOUN
cana-853	52	8	.	.	PUNCT
cana-853	53	1	1	1	NUM
cana-853	53	2	queueing	queue	VERB
cana-853	53	3	netwօrk	netwօrk	VERB
cana-853	53	4	with	with	ADP
cana-853	53	5	preparatory	preparatory	ADJ
cana-853	53	6	wօrk	wօrk	NOUN
cana-853	53	7	and	and	CCONJ
cana-853	53	8	feedback	feedback	NOUN
cana-853	53	9	let	let	VERB
cana-853	53	10	qn(t	qn(t	NUM
cana-853	53	11	)	)	PUNCT
cana-853	54	1	=	=	PUNCT
cana-853	55	1	q{x	q{x	NOUN
cana-853	55	2	(	(	PUNCT
cana-853	55	3	t	t	NOUN
cana-853	55	4	)	)	PUNCT
cana-853	55	5	=	=	NOUN
cana-853	55	6	n	n	CCONJ
cana-853	55	7	}	}	PUNCT
cana-853	55	8	,	,	PUNCT
cana-853	55	9	n	n	NOUN
cana-853	55	10	=	=	NOUN
cana-853	55	11	0,1,2	0,1,2	NOUN
cana-853	55	12	.	.	PUNCT
cana-853	55	13	.	.	PUNCT
cana-853	55	14	.	.	PUNCT
cana-853	55	15	.	.	PUNCT
cana-853	56	1	.	.	PUNCT
cana-853	57	1	denote	denote	VERB
cana-853	57	2	the	the	DET
cana-853	57	3	transient	transient	ADJ
cana-853	57	4	state	state	NOUN
cana-853	57	5	probability	probability	NOUN
cana-853	57	6	that	that	SCONJ
cana-853	57	7	there	there	PRON
cana-853	57	8	are	be	VERB
cana-853	57	9	n	n	PRON
cana-853	57	10	number	number	NOUN
cana-853	57	11	of	of	ADP
cana-853	57	12	custօmers	custօmer	NOUN
cana-853	57	13	in	in	ADP
cana-853	57	14	the	the	DET
cana-853	57	15	system	system	NOUN
cana-853	57	16	at	at	ADP
cana-853	57	17	time	time	NOUN
cana-853	57	18	t.	t.	PROPN
cana-853	57	19	let	let	VERB
cana-853	57	20	q(x	q(x	PROPN
cana-853	57	21	,	,	PUNCT
cana-853	57	22	t	t	PROPN
cana-853	57	23	)	)	PUNCT
cana-853	57	24	=	=	PUNCT
cana-853	58	1	∑	∑	PUNCT
cana-853	58	2	𝑄𝑛(𝑡)𝑥𝑛∞	𝑄𝑛(𝑡)𝑥𝑛∞	PROPN
cana-853	58	3	𝑛=0	𝑛=0	PROPN
cana-853	58	4	be	be	VERB
cana-853	58	5	the	the	DET
cana-853	58	6	probability	probability	NOUN
cana-853	58	7	generating	generating	NOUN
cana-853	58	8	function	function	NOUN
cana-853	58	9	.	.	PUNCT
cana-853	59	1	if	if	SCONJ
cana-853	59	2	time	time	NOUN
cana-853	59	3	t	t	NOUN
cana-853	59	4	=	=	SYM
cana-853	59	5	0	0	NUM
cana-853	59	6	,	,	PUNCT
cana-853	59	7	generally	generally	ADV
cana-853	59	8	it	it	PRON
cana-853	59	9	is	be	AUX
cana-853	59	10	assumed	assume	VERB
cana-853	59	11	that	that	SCONJ
cana-853	59	12	there	there	PRON
cana-853	59	13	are	be	VERB
cana-853	59	14	nօ	nօ	ADP
cana-853	59	15	customers	customer	NOUN
cana-853	59	16	in	in	ADP
cana-853	59	17	the	the	DET
cana-853	59	18	system	system	NOUN
cana-853	59	19	.	.	PUNCT
cana-853	60	1	i.e𝑄0(0	i.e𝑄0(0	NOUN
cana-853	60	2	)	)	PUNCT
cana-853	60	3	=	=	SYM
cana-853	60	4	1	1	NUM
cana-853	60	5	from	from	ADP
cana-853	60	6	the	the	DET
cana-853	60	7	above	above	ADJ
cana-853	60	8	assumption	assumption	NOUN
cana-853	60	9	,	,	PUNCT
cana-853	60	10	the	the	DET
cana-853	60	11	probability	probability	NOUN
cana-853	60	12	𝑄𝑛(𝑡)following	𝑄𝑛(𝑡)followe	VERB
cana-853	60	13	the	the	DET
cana-853	60	14	system	system	NOUN
cana-853	60	15	of	of	ADP
cana-853	60	16	differential	differential	ADJ
cana-853	60	17	–	–	PUNCT
cana-853	60	18	difference	difference	NOUN
cana-853	60	19	equations	equation	NOUN
cana-853	60	20	:	:	PUNCT
cana-853	60	21	in	in	ADP
cana-853	60	22	steady	steady	ADJ
cana-853	60	23	state	state	NOUN
cana-853	60	24	,	,	PUNCT
cana-853	60	25	lim	lim	PROPN
cana-853	60	26	𝑛→∞	𝑛→∞	NUM
cana-853	60	27	𝑄𝑛(𝑡	𝑄𝑛(𝑡	PROPN
cana-853	60	28	)	)	PUNCT
cana-853	60	29	=	=	SYM
cana-853	61	1	𝑄𝑛	𝑄𝑛	PROPN
cana-853	61	2	and	and	CCONJ
cana-853	61	3	𝑄𝑛	𝑄𝑛	PROPN
cana-853	61	4	′	′	NUM
cana-853	61	5	(	(	PUNCT
cana-853	61	6	𝑡	𝑡	NOUN
cana-853	61	7	)	)	PUNCT
cana-853	61	8	=	=	SYM
cana-853	61	9	0	0	PUNCT
cana-853	62	1	as	as	ADP
cana-853	62	2	𝑡	𝑡	PROPN
cana-853	62	3	→	→	SYM
cana-853	62	4	∞	∞	NOUN
cana-853	62	5	0	0	NUM
cana-853	63	1	=	=	PUNCT
cana-853	63	2	−𝜆𝑄0	−𝜆𝑄0	NOUN
cana-853	63	3	+	+	X
cana-853	63	4	{	{	PUNCT
cana-853	63	5	[	[	X
cana-853	63	6	�	�	NOUN
cana-853	63	7	̅	̅	NOUN
cana-853	63	8	�	�	NOUN
cana-853	63	9	𝜇1	𝜇1	NOUN
cana-853	63	10	+	+	CCONJ
cana-853	63	11	�	�	PROPN
cana-853	63	12	̅	̅	NOUN
cana-853	63	13	�	�	NOUN
cana-853	63	14	𝜇3	𝜇3	NOUN
cana-853	63	15	+	+	CCONJ
cana-853	63	16	𝑟𝜇4	𝑟𝜇4	NOUN
cana-853	63	17	]	]	X
cana-853	64	1	+	+	CCONJ
cana-853	64	2	[	[	X
cana-853	64	3	�	�	NOUN
cana-853	64	4	̅	̅	NOUN
cana-853	64	5	�	�	NOUN
cana-853	64	6	𝜇1	𝜇1	NOUN
cana-853	64	7	+	+	CCONJ
cana-853	64	8	�	�	PROPN
cana-853	64	9	̅	̅	NOUN
cana-853	64	10	�	�	NOUN
cana-853	64	11	𝜇3	𝜇3	NOUN
cana-853	64	12	+	+	CCONJ
cana-853	64	13	(	(	PUNCT
cana-853	64	14	1	1	NUM
cana-853	64	15	−	−	PROPN
cana-853	64	16	𝑟)𝜇4	𝑟)𝜇4	PROPN
cana-853	64	17	+	+	CCONJ
cana-853	64	18	𝜇5	𝜇5	PROPN
cana-853	64	19	]	]	X
cana-853	65	1	+	+	CCONJ
cana-853	65	2	[	[	X
cana-853	65	3	�	�	NOUN
cana-853	65	4	̅	̅	NOUN
cana-853	65	5	�	�	NOUN
cana-853	65	6	𝜇1	𝜇1	NOUN
cana-853	65	7	+	+	CCONJ
cana-853	65	8	(	(	PUNCT
cana-853	65	9	1	1	NUM
cana-853	65	10	−	−	PRON
cana-853	65	11	�	�	NOUN
cana-853	65	12	̅	̅	NOUN
cana-853	65	13	�	�	NOUN
cana-853	65	14	)𝜇3	)𝜇3	PROPN
cana-853	65	15	+	+	SYM
cana-853	65	16	𝜇5	𝜇5	PROPN
cana-853	65	17	]	]	X
cana-853	65	18	+	+	CCONJ
cana-853	66	1	[	[	X
cana-853	66	2	(	(	PUNCT
cana-853	66	3	1	1	NUM
cana-853	66	4	−	−	PRON
cana-853	66	5	�	�	NOUN
cana-853	66	6	̅	̅	NOUN
cana-853	66	7	�	�	NUM
cana-853	66	8	)𝜇2	)𝜇2	VERB
cana-853	66	9	+	+	NUM
cana-853	66	10	�	�	NOUN
cana-853	66	11	̅	̅	NOUN
cana-853	66	12	�	�	NOUN
cana-853	66	13	𝜇3	𝜇3	NOUN
cana-853	66	14	+	+	CCONJ
cana-853	66	15	𝑟𝜇4	𝑟𝜇4	NOUN
cana-853	66	16	]	]	X
cana-853	67	1	+	+	CCONJ
cana-853	67	2	[	[	X
cana-853	67	3	(	(	PUNCT
cana-853	67	4	1	1	NUM
cana-853	67	5	−	−	PRON
cana-853	67	6	�	�	NOUN
cana-853	67	7	̅	̅	NOUN
cana-853	67	8	�	�	NUM
cana-853	67	9	)𝜇2	)𝜇2	VERB
cana-853	67	10	+	+	NUM
cana-853	67	11	�	�	NOUN
cana-853	67	12	̅	̅	NOUN
cana-853	67	13	�	�	NOUN
cana-853	67	14	𝜇3	𝜇3	NOUN
cana-853	67	15	+	+	CCONJ
cana-853	67	16	(	(	PUNCT
cana-853	67	17	1	1	NUM
cana-853	67	18	−	−	PROPN
cana-853	67	19	𝑟)𝜇4	𝑟)𝜇4	PROPN
cana-853	67	20	+	+	CCONJ
cana-853	67	21	𝜇5	𝜇5	PROPN
cana-853	67	22	]	]	X
cana-853	67	23	+	+	CCONJ
cana-853	67	24	[	[	X
cana-853	67	25	(	(	PUNCT
cana-853	67	26	1	1	NUM
cana-853	67	27	−	−	PRON
cana-853	67	28	�	�	NOUN
cana-853	67	29	̅	̅	NOUN
cana-853	67	30	�	�	NUM
cana-853	67	31	)𝜇2	)𝜇2	PUNCT
cana-853	67	32	+	+	CCONJ
cana-853	67	33	(	(	PUNCT
cana-853	67	34	1	1	NUM
cana-853	67	35	−	−	PRON
cana-853	67	36	�	�	NOUN
cana-853	67	37	̅	̅	NOUN
cana-853	67	38	�	�	NOUN
cana-853	67	39	)𝜇3	)𝜇3	PUNCT
cana-853	67	40	+	+	CCONJ
cana-853	67	41	𝜇5]}𝑄1	𝜇5]}𝑄1	ADP
cana-853	67	42	+	+	NUM
cana-853	67	43	𝛾(1	𝛾(1	NOUN
cana-853	67	44	−	−	PROPN
cana-853	67	45	𝑄0	𝑄0	PROPN
cana-853	67	46	)	)	PUNCT
cana-853	67	47	=	=	SYM
cana-853	68	1	−𝜆𝑄0	−𝜆𝑄0	X
cana-853	69	1	+	+	X
cana-853	69	2	[	[	X
cana-853	69	3	3	3	NUM
cana-853	69	4	�	�	NOUN
cana-853	69	5	̅	̅	NOUN
cana-853	69	6	�	�	NOUN
cana-853	69	7	𝜇1	𝜇1	NOUN
cana-853	69	8	+	+	CCONJ
cana-853	69	9	3(1	3(1	NUM
cana-853	69	10	−	−	PROPN
cana-853	69	11	�	�	NOUN
cana-853	69	12	̅	̅	NOUN
cana-853	69	13	�	�	NUM
cana-853	69	14	)𝜇2	)𝜇2	PUNCT
cana-853	69	15	+	+	NUM
cana-853	69	16	2(1	2(1	NUM
cana-853	69	17	+	+	CCONJ
cana-853	69	18	�	�	NOUN
cana-853	69	19	̅	̅	NOUN
cana-853	69	20	�	�	NOUN
cana-853	69	21	)𝜇3	)𝜇3	PUNCT
cana-853	69	22	+	+	NOUN
cana-853	69	23	2𝜇4	2𝜇4	NUM
cana-853	70	1	+	+	CCONJ
cana-853	70	2	4	4	NUM
cana-853	70	3	𝜇5]𝑄1	𝜇5]𝑄1	PROPN
cana-853	70	4	+	+	CCONJ
cana-853	70	5	𝛾(1	𝛾(1	PROPN
cana-853	70	6	−	−	PROPN
cana-853	70	7	𝑄0	𝑄0	PROPN
cana-853	70	8	)	)	PUNCT
cana-853	71	1	=	=	SYM
cana-853	71	2	−𝜆𝑄0	−𝜆𝑄0	PRON
cana-853	72	1	+	+	CCONJ
cana-853	72	2	𝛼𝑄1	𝛼𝑄1	PROPN
cana-853	72	3	+	+	CCONJ
cana-853	72	4	𝛾(1	𝛾(1	PROPN
cana-853	72	5	−	−	PROPN
cana-853	72	6	𝑄0	𝑄0	PROPN
cana-853	72	7	)	)	PUNCT
cana-853	72	8	(	(	PUNCT
cana-853	72	9	1	1	X
cana-853	72	10	)	)	PUNCT
cana-853	72	11	where	where	SCONJ
cana-853	72	12	𝛼	𝛼	NOUN
cana-853	72	13	=	=	SYM
cana-853	72	14	3	3	NUM
cana-853	72	15	�	�	NOUN
cana-853	72	16	̅	̅	NOUN
cana-853	72	17	�	�	NOUN
cana-853	72	18	𝜇1	𝜇1	NOUN
cana-853	72	19	+	+	CCONJ
cana-853	72	20	3(1	3(1	NUM
cana-853	72	21	−	−	PROPN
cana-853	72	22	�	�	NOUN
cana-853	72	23	̅	̅	NOUN
cana-853	72	24	�	�	NUM
cana-853	72	25	)𝜇2	)𝜇2	PUNCT
cana-853	72	26	+	+	NUM
cana-853	72	27	2(1	2(1	NUM
cana-853	72	28	+	+	CCONJ
cana-853	72	29	�	�	NOUN
cana-853	72	30	̅	̅	NOUN
cana-853	72	31	�	�	NOUN
cana-853	72	32	)𝜇3	)𝜇3	PUNCT
cana-853	72	33	+	+	NOUN
cana-853	73	1	2𝜇4	2𝜇4	NUM
cana-853	73	2	+	+	CCONJ
cana-853	73	3	4	4	NUM
cana-853	73	4	𝜇5	𝜇5	ADJ
cana-853	73	5	0	0	PUNCT
cana-853	73	6	=	=	SYM
cana-853	73	7	−𝜆𝑄𝑛−1	−𝜆𝑄𝑛−1	PROPN
cana-853	73	8	+	+	CCONJ
cana-853	73	9	{	{	PUNCT
cana-853	73	10	𝜆	𝜆	NOUN
cana-853	74	1	+	+	X
cana-853	75	1	[	[	X
cana-853	75	2	3	3	NUM
cana-853	75	3	�	�	NOUN
cana-853	75	4	̅	̅	NOUN
cana-853	75	5	�	�	NOUN
cana-853	75	6	𝜇1	𝜇1	NOUN
cana-853	75	7	+	+	CCONJ
cana-853	75	8	3(1	3(1	NUM
cana-853	75	9	−	−	PROPN
cana-853	75	10	�	�	NOUN
cana-853	75	11	̅	̅	NOUN
cana-853	75	12	�	�	NUM
cana-853	75	13	)𝜇2	)𝜇2	PUNCT
cana-853	75	14	+	+	NUM
cana-853	75	15	2(1	2(1	NUM
cana-853	75	16	+	+	CCONJ
cana-853	75	17	�	�	NOUN
cana-853	75	18	̅	̅	NOUN
cana-853	75	19	�	�	NOUN
cana-853	75	20	)𝜇3	)𝜇3	PUNCT
cana-853	75	21	+	+	NOUN
cana-853	76	1	2𝜇4	2𝜇4	NUM
cana-853	76	2	+	+	CCONJ
cana-853	76	3	4	4	NUM
cana-853	76	4	𝜇5	𝜇5	NOUN
cana-853	76	5	]	]	X
cana-853	76	6	+	+	CCONJ
cana-853	76	7	𝛾}𝑄𝑛	𝛾}𝑄𝑛	PROPN
cana-853	76	8	+	+	SYM
cana-853	76	9	[	[	X
cana-853	76	10	3	3	NUM
cana-853	76	11	�	�	NOUN
cana-853	76	12	̅	̅	NOUN
cana-853	76	13	�	�	NOUN
cana-853	76	14	𝜇1	𝜇1	NOUN
cana-853	76	15	+	+	CCONJ
cana-853	76	16	3(1	3(1	NUM
cana-853	76	17	−	−	PROPN
cana-853	76	18	�	�	NOUN
cana-853	76	19	̅	̅	NOUN
cana-853	76	20	�	�	NUM
cana-853	76	21	)𝜇2	)𝜇2	PUNCT
cana-853	76	22	+	+	NUM
cana-853	76	23	2(1	2(1	NUM
cana-853	76	24	+	+	CCONJ
cana-853	76	25	�	�	NOUN
cana-853	76	26	̅	̅	NOUN
cana-853	76	27	�	�	NOUN
cana-853	76	28	)𝜇3	)𝜇3	PUNCT
cana-853	76	29	+	+	NOUN
cana-853	76	30	2𝜇4	2𝜇4	NUM
cana-853	77	1	+	+	CCONJ
cana-853	77	2	4	4	NUM
cana-853	77	3	𝜇5]𝑄𝑛+1	𝜇5]𝑄𝑛+1	PROPN
cana-853	77	4	0	0	NUM
cana-853	77	5	=	=	SYM
cana-853	77	6	−𝜆𝑄𝑛−1	−𝜆𝑄𝑛−1	PROPN
cana-853	78	1	+	+	X
cana-853	79	1	[	[	X
cana-853	79	2	𝜆	𝜆	X
cana-853	79	3	+	+	NOUN
cana-853	79	4	𝛼	𝛼	VERB
cana-853	79	5	+	+	CCONJ
cana-853	79	6	𝛾]𝑄𝑛	𝛾]𝑄𝑛	PROPN
cana-853	79	7	+	+	CCONJ
cana-853	79	8	𝛼𝑄𝑛+1	𝛼𝑄𝑛+1	PROPN
cana-853	79	9	(	(	PUNCT
cana-853	79	10	2	2	NUM
cana-853	79	11	)	)	PUNCT
cana-853	79	12	equation	equation	NOUN
cana-853	79	13	(	(	PUNCT
cana-853	79	14	1	1	X
cana-853	79	15	)	)	PUNCT
cana-853	79	16	gives	give	VERB
cana-853	79	17	0	0	NUM
cana-853	80	1	=	=	SYM
cana-853	80	2	−𝜆𝑄0	−𝜆𝑄0	PROPN
cana-853	81	1	+	+	CCONJ
cana-853	81	2	𝛼𝑄1	𝛼𝑄1	PROPN
cana-853	81	3	+	+	CCONJ
cana-853	81	4	𝛾(1	𝛾(1	PROPN
cana-853	81	5	−	−	PROPN
cana-853	81	6	𝑄0	𝑄0	PROPN
cana-853	81	7	)	)	PUNCT
cana-853	81	8	(	(	PUNCT
cana-853	81	9	𝜆	𝜆	X
cana-853	81	10	+	+	PUNCT
cana-853	81	11	𝛾)𝑄0	𝛾)𝑄0	NOUN
cana-853	81	12	=	=	SYM
cana-853	81	13	𝛼𝑄1	𝛼𝑄1	PROPN
cana-853	81	14	+	+	CCONJ
cana-853	81	15	𝛾	𝛾	NOUN
cana-853	81	16	𝑄0	𝑄0	NOUN
cana-853	81	17	=	=	SYM
cana-853	82	1	𝛾	𝛾	X
cana-853	82	2	(	(	PUNCT
cana-853	82	3	𝜆+𝛾)−𝛼	𝜆+𝛾)−𝛼	INTJ
cana-853	82	4	𝑄1	𝑄1	VERB
cana-853	82	5	𝑄0	𝑄0	PROPN
cana-853	83	1	(	(	PUNCT
cana-853	83	2	3	3	X
cana-853	83	3	)	)	PUNCT
cana-853	83	4	equation	equation	NOUN
cana-853	83	5	(	(	PUNCT
cana-853	83	6	2	2	X
cana-853	83	7	)	)	PUNCT
cana-853	83	8	gives	give	VERB
cana-853	83	9	0	0	NUM
cana-853	83	10	=	=	SYM
cana-853	83	11	−𝜆𝑄𝑛−1	−𝜆𝑄𝑛−1	NOUN
cana-853	84	1	+	+	X
cana-853	85	1	[	[	X
cana-853	85	2	𝜆	𝜆	X
cana-853	85	3	+	+	NOUN
cana-853	85	4	𝛼	𝛼	VERB
cana-853	85	5	+	+	CCONJ
cana-853	85	6	𝛾]𝑄𝑛	𝛾]𝑄𝑛	PROPN
cana-853	85	7	+	+	CCONJ
cana-853	85	8	𝛼𝑄𝑛+1	𝛼𝑄𝑛+1	PROPN
cana-853	86	1	[	[	X
cana-853	86	2	𝜆	𝜆	X
cana-853	86	3	+	+	NOUN
cana-853	86	4	𝛼	𝛼	VERB
cana-853	86	5	+	+	CCONJ
cana-853	86	6	𝛾]𝑄𝑛	𝛾]𝑄𝑛	PROPN
cana-853	86	7	=	=	PUNCT
cana-853	86	8	𝜆𝑄𝑛−1	𝜆𝑄𝑛−1	NOUN
cana-853	87	1	+	+	X
cana-853	87	2	+	+	ADJ
cana-853	87	3	𝛼𝑄𝑛+1	𝛼𝑄𝑛+1	PROPN
cana-853	87	4	𝑄𝑛	𝑄𝑛	PROPN
cana-853	87	5	𝑄𝑛−1	𝑄𝑛−1	PROPN
cana-853	87	6	=	=	PUNCT
cana-853	88	1	𝜆	𝜆	PUNCT
cana-853	89	1	[	[	X
cana-853	89	2	𝜆+𝛼+𝛾]−𝛼	𝜆+𝛼+𝛾]−𝛼	ADJ
cana-853	89	3	𝑄𝑛+1	𝑄𝑛+1	X
cana-853	89	4	𝑄𝑛	𝑄𝑛	NOUN
cana-853	89	5	(	(	PUNCT
cana-853	89	6	4	4	X
cana-853	89	7	)	)	PUNCT
cana-853	89	8	put	put	VERB
cana-853	89	9	n=1	n=1	PROPN
cana-853	89	10	in	in	ADP
cana-853	89	11	equation	equation	NOUN
cana-853	89	12	(	(	PUNCT
cana-853	89	13	4	4	X
cana-853	89	14	)	)	PUNCT
cana-853	89	15	communications	communication	NOUN
cana-853	89	16	on	on	ADP
cana-853	89	17	applied	apply	VERB
cana-853	89	18	nonlinear	nonlinear	ADJ
cana-853	89	19	analysis	analysis	NOUN
cana-853	89	20	issn	issn	NOUN
cana-853	89	21	:	:	PUNCT
cana-853	89	22	1074	1074	NUM
cana-853	89	23	-	-	PUNCT
cana-853	89	24	133x	133x	NUM
cana-853	89	25	vol	vol	NOUN
cana-853	89	26	31	31	NUM
cana-853	89	27	no	no	NOUN
cana-853	89	28	.	.	PUNCT
cana-853	90	1	4s	4s	NUM
cana-853	90	2	(	(	PUNCT
cana-853	90	3	2024	2024	NUM
cana-853	90	4	)	)	PUNCT
cana-853	90	5	300	300	NUM
cana-853	90	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-853	90	7	𝑄1	𝑄1	NOUN
cana-853	90	8	𝑄0	𝑄0	PUNCT
cana-853	91	1	=	=	PUNCT
cana-853	92	1	𝜆	𝜆	PUNCT
cana-853	93	1	[	[	X
cana-853	93	2	𝜆	𝜆	X
cana-853	93	3	+	+	NOUN
cana-853	93	4	𝛼	𝛼	NOUN
cana-853	93	5	+	+	NOUN
cana-853	93	6	𝛾	𝛾	X
cana-853	93	7	]	]	X
cana-853	93	8	−	−	PROPN
cana-853	93	9	𝛼	𝛼	PROPN
cana-853	93	10	𝑄2	𝑄2	PROPN
cana-853	93	11	𝑄1	𝑄1	PROPN
cana-853	93	12	sub	sub	VERB
cana-853	93	13	the	the	DET
cana-853	93	14	above	above	ADJ
cana-853	93	15	value	value	NOUN
cana-853	93	16	in	in	ADP
cana-853	93	17	equation	equation	NOUN
cana-853	93	18	(	(	PUNCT
cana-853	93	19	3	3	NUM
cana-853	93	20	)	)	PUNCT
cana-853	93	21	𝑄0	𝑄0	PUNCT
cana-853	94	1	=	=	PUNCT
cana-853	94	2	𝛾	𝛾	X
cana-853	94	3	(	(	PUNCT
cana-853	94	4	𝜆	𝜆	NOUN
cana-853	94	5	+	+	CCONJ
cana-853	94	6	𝛾	𝛾	NOUN
cana-853	94	7	)	)	PUNCT
cana-853	94	8	−	−	PROPN
cana-853	94	9	𝛼𝜆	𝛼𝜆	NOUN
cana-853	95	1	[	[	X
cana-853	95	2	𝜆+𝛼+𝛾]−𝛼	𝜆+𝛼+𝛾]−𝛼	X
cana-853	95	3	𝑄2	𝑄2	PROPN
cana-853	95	4	𝑄1	𝑄1	PROPN
cana-853	95	5	𝑄0	𝑄0	PUNCT
cana-853	96	1	=	=	PUNCT
cana-853	96	2	𝛾	𝛾	X
cana-853	96	3	(	(	PUNCT
cana-853	96	4	𝜆	𝜆	NOUN
cana-853	96	5	+	+	CCONJ
cana-853	96	6	𝛾	𝛾	NOUN
cana-853	96	7	)	)	PUNCT
cana-853	96	8	−	−	PROPN
cana-853	96	9	𝛼𝜆	𝛼𝜆	NOUN
cana-853	97	1	[	[	X
cana-853	97	2	𝜆+𝛼+𝛾]−	𝜆+𝛼+𝛾]−	NOUN
cana-853	97	3	𝛼𝜆	𝛼𝜆	X
cana-853	97	4	[	[	X
cana-853	97	5	𝜆+𝛼+𝛾]−	𝜆+𝛼+𝛾]−	NOUN
cana-853	97	6	𝛼𝜆	𝛼𝜆	X
cana-853	98	1	[	[	X
cana-853	98	2	𝜆+𝛼+𝛾]−	𝜆+𝛼+𝛾]−	NOUN
cana-853	98	3	.	.	PUNCT
cana-853	98	4	.	.	PUNCT
cana-853	98	5	.	.	PUNCT
cana-853	99	1	𝑄0	𝑄0	PROPN
cana-853	100	1	=	=	PUNCT
cana-853	100	2	𝛾	𝛾	X
cana-853	100	3	(	(	PUNCT
cana-853	100	4	𝜆+𝛾)−𝛽	𝜆+𝛾)−𝛽	NOUN
cana-853	100	5	(	(	PUNCT
cana-853	100	6	5	5	NUM
cana-853	100	7	)	)	PUNCT
cana-853	100	8	where	where	SCONJ
cana-853	100	9	𝛽	𝛽	NOUN
cana-853	100	10	=	=	SYM
cana-853	100	11	𝛼𝜆	𝛼𝜆	X
cana-853	101	1	[	[	X
cana-853	101	2	𝜆+𝛼+𝛾]−	𝜆+𝛼+𝛾]−	NOUN
cana-853	101	3	𝛼𝜆	𝛼𝜆	X
cana-853	102	1	[	[	X
cana-853	102	2	𝜆+𝛼+𝛾]−	𝜆+𝛼+𝛾]−	NOUN
cana-853	102	3	.	.	PUNCT
cana-853	102	4	.	.	PUNCT
cana-853	102	5	.	.	PUNCT
cana-853	103	1	equation	equation	NOUN
cana-853	103	2	(	(	PUNCT
cana-853	103	3	5	5	X
cana-853	103	4	)	)	PUNCT
cana-853	103	5	satisfies	satisfy	VERB
cana-853	103	6	the	the	DET
cana-853	103	7	quadratic	quadratic	ADJ
cana-853	103	8	equation	equation	NOUN
cana-853	103	9	𝛽2	𝛽2	NOUN
cana-853	103	10	−	−	PROPN
cana-853	103	11	(	(	PUNCT
cana-853	103	12	𝜆	𝜆	PROPN
cana-853	103	13	+	+	NOUN
cana-853	103	14	𝛼	𝛼	NOUN
cana-853	103	15	+	+	NOUN
cana-853	103	16	𝛾)𝛽	𝛾)𝛽	X
cana-853	103	17	+	+	CCONJ
cana-853	103	18	𝜆𝛼	𝜆𝛼	NOUN
cana-853	103	19	=	=	SYM
cana-853	103	20	0	0	PUNCT
cana-853	104	1	the	the	DET
cana-853	104	2	roots	root	NOUN
cana-853	104	3	of	of	ADP
cana-853	104	4	the	the	DET
cana-853	104	5	above	above	ADJ
cana-853	104	6	equation	equation	NOUN
cana-853	104	7	are	be	AUX
cana-853	104	8	𝑢±√𝑢2−4𝜆𝛼	𝑢±√𝑢2−4𝜆𝛼	ADJ
cana-853	104	9	2	2	NUM
cana-853	104	10	,	,	PUNCT
cana-853	104	11	where	where	SCONJ
cana-853	104	12	𝑢	𝑢	X
cana-853	104	13	=	=	X
cana-853	104	14	𝜆	𝜆	PROPN
cana-853	105	1	+	+	NOUN
cana-853	105	2	𝛼	𝛼	NOUN
cana-853	105	3	+	+	CCONJ
cana-853	105	4	𝛾	𝛾	AUX
cana-853	105	5	let	let	VERB
cana-853	105	6	the	the	DET
cana-853	105	7	roots	root	NOUN
cana-853	105	8	be	be	AUX
cana-853	105	9	𝛽1	𝛽1	NOUN
cana-853	105	10	,	,	PUNCT
cana-853	105	11	𝛽2	𝛽2	PROPN
cana-853	105	12	,	,	PUNCT
cana-853	105	13	we	we	PRON
cana-853	105	14	take	take	VERB
cana-853	105	15	the	the	DET
cana-853	105	16	unique	unique	ADJ
cana-853	105	17	real	real	ADJ
cana-853	105	18	roօt	roօt	NOUN
cana-853	105	19	lies	lie	VERB
cana-853	105	20	within	within	ADP
cana-853	105	21	[	[	NOUN
cana-853	105	22	0,1	0,1	NUM
cana-853	105	23	)	)	PUNCT
cana-853	105	24	substituting	substitute	VERB
cana-853	105	25	𝛽2	𝛽2	NOUN
cana-853	105	26	in	in	ADP
cana-853	105	27	equation	equation	NOUN
cana-853	105	28	(	(	PUNCT
cana-853	105	29	5	5	NUM
cana-853	105	30	)	)	PUNCT
cana-853	105	31	,	,	PUNCT
cana-853	105	32	we	we	PRON
cana-853	105	33	get	get	VERB
cana-853	105	34	𝑄0	𝑄0	X
cana-853	106	1	=	=	PUNCT
cana-853	106	2	𝛾	𝛾	X
cana-853	106	3	(	(	PUNCT
cana-853	106	4	𝜆	𝜆	NOUN
cana-853	106	5	+	+	CCONJ
cana-853	106	6	𝛾	𝛾	NOUN
cana-853	106	7	)	)	PUNCT
cana-853	106	8	−	−	NOUN
cana-853	106	9	[	[	PUNCT
cana-853	106	10	𝑢−√𝑢2−4𝜆𝛼	𝑢−√𝑢2−4𝜆𝛼	VERB
cana-853	106	11	2	2	NUM
cana-853	106	12	]	]	PUNCT
cana-853	106	13	after	after	ADP
cana-853	106	14	some	some	DET
cana-853	106	15	algebraic	algebraic	ADJ
cana-853	106	16	calculation	calculation	NOUN
cana-853	106	17	,	,	PUNCT
cana-853	106	18	we	we	PRON
cana-853	106	19	get	get	VERB
cana-853	106	20	𝑄0	𝑄0	X
cana-853	106	21	=	=	SYM
cana-853	106	22	𝛾	𝛾	PROPN
cana-853	106	23	[	[	PUNCT
cana-853	106	24	𝑢−√𝑢2−4𝜆𝛼	𝑢−√𝑢2−4𝜆𝛼	NOUN
cana-853	106	25	2𝜆𝛼	2𝜆𝛼	NOUN
cana-853	106	26	]	]	PUNCT
cana-853	107	1	1−𝛼	1−𝛼	NUM
cana-853	107	2	[	[	PUNCT
cana-853	107	3	𝑢−√𝑢2−4𝜆𝛼	𝑢−√𝑢2−4𝜆𝛼	NOUN
cana-853	107	4	2𝜆𝛼	2𝜆𝛼	NOUN
cana-853	107	5	]	]	PUNCT
cana-853	107	6	(	(	PUNCT
cana-853	107	7	6	6	X
cana-853	107	8	)	)	PUNCT
cana-853	107	9	expanding	expand	VERB
cana-853	107	10	binomially	binomially	ADV
cana-853	107	11	,	,	PUNCT
cana-853	107	12	we	we	PRON
cana-853	107	13	get	get	VERB
cana-853	107	14	𝑄0	𝑄0	PUNCT
cana-853	108	1	=	=	PUNCT
cana-853	108	2	∑	∑	PUNCT
cana-853	108	3	𝛼𝑛	𝛼𝑛	PROPN
cana-853	108	4	[	[	PUNCT
cana-853	108	5	𝑢	𝑢	PROPN
cana-853	108	6	−	−	PROPN
cana-853	108	7	√𝑢2	√𝑢2	PROPN
cana-853	108	8	−	−	PROPN
cana-853	108	9	4𝜆𝛼	4𝜆𝛼	ADJ
cana-853	108	10	2𝜆𝛼	2𝜆𝛼	NOUN
cana-853	108	11	]	]	PUNCT
cana-853	109	1	𝑛+1	𝑛+1	PROPN
cana-853	109	2	+	+	CCONJ
cana-853	109	3	𝛾	𝛾	NUM
cana-853	109	4	∞	∞	NUM
cana-853	109	5	𝑛=0	𝑛=0	PROPN
cana-853	109	6	∑	∑	PUNCT
cana-853	109	7	𝛼𝑛	𝛼𝑛	PROPN
cana-853	109	8	[	[	PUNCT
cana-853	109	9	𝑢	𝑢	PROPN
cana-853	109	10	−	−	PROPN
cana-853	109	11	√𝑢2	√𝑢2	PROPN
cana-853	109	12	−	−	PROPN
cana-853	109	13	4𝜆𝛼	4𝜆𝛼	ADJ
cana-853	109	14	2𝜆𝛼	2𝜆𝛼	NOUN
cana-853	109	15	]	]	PUNCT
cana-853	109	16	𝑛+1∞	𝑛+1∞	PROPN
cana-853	109	17	𝑛=0	𝑛=0	PROPN
cana-853	109	18	the	the	PRON
cana-853	109	19	remained	remain	VERB
cana-853	109	20	steady	steady	ADJ
cana-853	109	21	state	state	NOUN
cana-853	109	22	prօbabilities	prօbabilitie	NOUN
cana-853	109	23	can	can	AUX
cana-853	109	24	be	be	AUX
cana-853	109	25	calculated	calculate	VERB
cana-853	109	26	in	in	ADP
cana-853	109	27	equations	equation	NOUN
cana-853	109	28	of𝑄0	of𝑄0	PROPN
cana-853	109	29	,	,	PUNCT
cana-853	109	30	from	from	ADP
cana-853	109	31	equation	equation	NOUN
cana-853	109	32	(	(	PUNCT
cana-853	109	33	4	4	X
cana-853	109	34	)	)	PUNCT
cana-853	110	1	𝑄𝑛	𝑄𝑛	NOUN
cana-853	110	2	𝑄𝑛−1	𝑄𝑛−1	PROPN
cana-853	110	3	=	=	PUNCT
cana-853	111	1	𝜆	𝜆	PUNCT
cana-853	112	1	[	[	X
cana-853	112	2	𝜆	𝜆	X
cana-853	112	3	+	+	NOUN
cana-853	112	4	𝛼	𝛼	NOUN
cana-853	112	5	+	+	NOUN
cana-853	112	6	𝛾	𝛾	X
cana-853	112	7	]	]	X
cana-853	112	8	−	−	PROPN
cana-853	112	9	𝛼𝜆	𝛼𝜆	X
cana-853	113	1	[	[	X
cana-853	113	2	𝜆+𝛼+𝛾]−	𝜆+𝛼+𝛾]−	NOUN
cana-853	113	3	𝛼𝜆	𝛼𝜆	X
cana-853	113	4	[	[	X
cana-853	113	5	𝜆+𝛼+𝛾]−	𝜆+𝛼+𝛾]−	NOUN
cana-853	113	6	𝛼𝜆	𝛼𝜆	X
cana-853	114	1	[	[	X
cana-853	114	2	𝜆+𝛼+𝛾	𝜆+𝛼+𝛾	X
cana-853	114	3	]	]	X
cana-853	114	4	−	−	PROPN
cana-853	114	5	.	.	PUNCT
cana-853	114	6	.	.	PUNCT
cana-853	114	7	.	.	PUNCT
cana-853	115	1	by	by	ADP
cana-853	115	2	similar	similar	ADJ
cana-853	115	3	argument	argument	NOUN
cana-853	115	4	as	as	ADP
cana-853	115	5	before	before	ADV
cana-853	115	6	,	,	PUNCT
cana-853	115	7	the	the	DET
cana-853	115	8	above	above	ADJ
cana-853	115	9	equation	equation	NOUN
cana-853	115	10	reduces	reduce	VERB
cana-853	115	11	to	to	ADP
cana-853	115	12	communications	communication	NOUN
cana-853	115	13	on	on	ADP
cana-853	115	14	applied	apply	VERB
cana-853	115	15	nonlinear	nonlinear	ADJ
cana-853	115	16	analysis	analysis	NOUN
cana-853	115	17	issn	issn	NOUN
cana-853	115	18	:	:	PUNCT
cana-853	115	19	1074	1074	NUM
cana-853	115	20	-	-	PUNCT
cana-853	115	21	133x	133x	NUM
cana-853	115	22	vol	vol	NOUN
cana-853	115	23	31	31	NUM
cana-853	115	24	no	no	NOUN
cana-853	115	25	.	.	PUNCT
cana-853	116	1	4s	4s	NUM
cana-853	116	2	(	(	PUNCT
cana-853	116	3	2024	2024	NUM
cana-853	116	4	)	)	PUNCT
cana-853	116	5	301	301	NUM
cana-853	116	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-853	116	7	𝑄𝑛	𝑄𝑛	PROPN
cana-853	116	8	𝑄𝑛−1	𝑄𝑛−1	PROPN
cana-853	116	9	=	=	PUNCT
cana-853	117	1	𝜆	𝜆	PRON
cana-853	117	2	𝑢+√𝑢2−4𝜆𝛼	𝑢+√𝑢2−4𝜆𝛼	ADJ
cana-853	117	3	2	2	NUM
cana-853	117	4	after	after	ADP
cana-853	117	5	some	some	DET
cana-853	117	6	calculations	calculation	NOUN
cana-853	117	7	,	,	PUNCT
cana-853	117	8	we	we	PRON
cana-853	117	9	get	get	VERB
cana-853	117	10	𝑄𝑛	𝑄𝑛	NOUN
cana-853	117	11	=	=	PRON
cana-853	117	12	[	[	PUNCT
cana-853	117	13	𝑢−√𝑢2−4𝜆𝛼	𝑢−√𝑢2−4𝜆𝛼	VERB
cana-853	117	14	2𝛼	2𝛼	PROPN
cana-853	117	15	]	]	PUNCT
cana-853	117	16	𝑛	𝑛	DET
cana-853	117	17	𝑄0	𝑄0	PROPN
cana-853	117	18	,	,	PUNCT
cana-853	117	19	n	n	NOUN
cana-853	117	20	=	=	SYM
cana-853	117	21	1	1	NUM
cana-853	117	22	,	,	PUNCT
cana-853	117	23	2	2	NUM
cana-853	117	24	,	,	PUNCT
cana-853	117	25	3	3	NUM
cana-853	117	26	.	.	PUNCT
cana-853	117	27	.	.	PUNCT
cana-853	117	28	.	.	PUNCT
cana-853	118	1	.	.	PUNCT
cana-853	119	1	(	(	PUNCT
cana-853	119	2	7	7	X
cana-853	119	3	)	)	PUNCT
cana-853	119	4	where	where	SCONJ
cana-853	119	5	𝑄0	𝑄0	PROPN
cana-853	119	6	=	=	SYM
cana-853	119	7	𝛾	𝛾	PROPN
cana-853	119	8	[	[	PUNCT
cana-853	119	9	𝑢−√𝑢2−4𝜆𝛼	𝑢−√𝑢2−4𝜆𝛼	NOUN
cana-853	119	10	2𝜆𝛼	2𝜆𝛼	NOUN
cana-853	119	11	]	]	PUNCT
cana-853	120	1	1−𝛼	1−𝛼	NUM
cana-853	120	2	[	[	PUNCT
cana-853	120	3	𝑢−√𝑢2−4𝜆𝛼	𝑢−√𝑢2−4𝜆𝛼	NOUN
cana-853	120	4	2𝜆𝛼	2𝜆𝛼	NOUN
cana-853	120	5	]	]	PUNCT
cana-853	120	6	and	and	CCONJ
cana-853	120	7	𝛼	𝛼	X
cana-853	120	8	=	=	NOUN
cana-853	120	9	3𝑝𝜇1	3𝑝𝜇1	NUM
cana-853	120	10	+	+	CCONJ
cana-853	120	11	3(1	3(1	NUM
cana-853	120	12	−	−	PROPN
cana-853	120	13	𝑝)𝜇2	𝑝)𝜇2	PROPN
cana-853	120	14	+	+	CCONJ
cana-853	120	15	2(1	2(1	NUM
cana-853	120	16	+	+	CCONJ
cana-853	120	17	𝑞)𝜇3	𝑞)𝜇3	PROPN
cana-853	120	18	+	+	CCONJ
cana-853	120	19	2𝜇4	2𝜇4	NUM
cana-853	120	20	+	+	CCONJ
cana-853	120	21	4	4	NUM
cana-853	120	22	𝜇5	𝜇5	ADJ
cana-853	120	23	3	3	NUM
cana-853	120	24	.	.	PUNCT
cana-853	120	25	asymptotic	asymptotic	ADJ
cana-853	120	26	behavior	behavior	NOUN
cana-853	120	27	of	of	ADP
cana-853	120	28	the	the	DET
cana-853	120	29	average	average	ADJ
cana-853	120	30	queue	queue	NOUN
cana-853	120	31	length	length	NOUN
cana-853	120	32	theorem	theorem	VERB
cana-853	120	33	:	:	PUNCT
cana-853	120	34	if	if	SCONJ
cana-853	120	35	𝛾	𝛾	PROPN
cana-853	120	36	>	>	X
cana-853	120	37	0	0	NUM
cana-853	120	38	,	,	PUNCT
cana-853	120	39	the	the	DET
cana-853	120	40	asymptotic	asymptotic	ADJ
cana-853	120	41	behavior	behavior	NOUN
cana-853	120	42	of	of	ADP
cana-853	120	43	the	the	DET
cana-853	120	44	average	average	ADJ
cana-853	120	45	queue	queue	NOUN
cana-853	120	46	length	length	NOUN
cana-853	121	1	𝐿𝑞	𝐿𝑞	PROPN
cana-853	121	2	at	at	ADP
cana-853	121	3	steady	steady	ADJ
cana-853	121	4	state	state	NOUN
cana-853	121	5	is	be	AUX
cana-853	121	6	𝐿𝑞	𝐿𝑞	PROPN
cana-853	121	7	=	=	PUNCT
cana-853	121	8	𝜆	𝜆	PRON
cana-853	121	9	−	−	NOUN
cana-853	121	10	𝛼	𝛼	NOUN
cana-853	121	11	𝛾	𝛾	NOUN
cana-853	121	12	+	+	X
cana-853	121	13	2𝛼	2𝛼	NUM
cana-853	121	14	2[𝜆	2[𝜆	NUM
cana-853	121	15	+	+	CCONJ
cana-853	121	16	𝛾	𝛾	X
cana-853	121	17	]	]	X
cana-853	121	18	−	−	PROPN
cana-853	122	1	[	[	X
cana-853	122	2	(	(	PUNCT
cana-853	122	3	𝜆	𝜆	NOUN
cana-853	122	4	+	+	ADP
cana-853	122	5	𝛾	𝛾	NOUN
cana-853	122	6	+	+	NUM
cana-853	122	7	𝛼	𝛼	X
cana-853	122	8	)	)	PUNCT
cana-853	122	9	−	−	NOUN
cana-853	122	10	√(𝜆	√(𝜆	NOUN
cana-853	122	11	+	+	CCONJ
cana-853	122	12	𝛾	𝛾	X
cana-853	122	13	+	+	X
cana-853	122	14	𝛼)2	𝛼)2	ADJ
cana-853	122	15	−	−	PROPN
cana-853	122	16	4𝜆𝛼	4𝜆𝛼	NOUN
cana-853	122	17	]	]	PUNCT
cana-853	122	18	where	where	SCONJ
cana-853	122	19	𝛼	𝛼	AUX
cana-853	122	20	=	=	SYM
cana-853	122	21	3	3	NUM
cana-853	122	22	�	�	NOUN
cana-853	122	23	̅	̅	NOUN
cana-853	122	24	�	�	NOUN
cana-853	122	25	𝜇1	𝜇1	NOUN
cana-853	122	26	+	+	CCONJ
cana-853	122	27	3(1	3(1	NUM
cana-853	122	28	−	−	PROPN
cana-853	122	29	�	�	NOUN
cana-853	122	30	̅	̅	NOUN
cana-853	122	31	�	�	NUM
cana-853	122	32	)𝜇2	)𝜇2	PUNCT
cana-853	122	33	+	+	NUM
cana-853	122	34	2(1	2(1	NUM
cana-853	122	35	+	+	CCONJ
cana-853	122	36	�	�	NOUN
cana-853	122	37	̅	̅	NOUN
cana-853	122	38	�	�	NOUN
cana-853	122	39	)𝜇3	)𝜇3	PUNCT
cana-853	122	40	+	+	NOUN
cana-853	123	1	2𝜇4	2𝜇4	NUM
cana-853	123	2	+	+	CCONJ
cana-853	123	3	4	4	NUM
cana-853	123	4	𝜇5	𝜇5	ADJ
cana-853	123	5	proof	proof	NOUN
cana-853	123	6	:	:	PUNCT
cana-853	123	7	consider	consider	VERB
cana-853	123	8	equation	equation	NOUN
cana-853	123	9	(	(	PUNCT
cana-853	123	10	1	1	NUM
cana-853	123	11	)	)	PUNCT
cana-853	123	12	and	and	CCONJ
cana-853	123	13	(	(	PUNCT
cana-853	123	14	2	2	X
cana-853	123	15	)	)	PUNCT
cana-853	123	16	with	with	ADP
cana-853	123	17	the	the	DET
cana-853	123	18	initial	initial	ADJ
cana-853	123	19	condition	condition	NOUN
cana-853	123	20	𝑄0(0	𝑄0(0	NOUN
cana-853	123	21	)	)	PUNCT
cana-853	123	22	=	=	SYM
cana-853	123	23	1	1	NUM
cana-853	123	24	𝜕𝑄(𝑥,𝑡	𝜕𝑄(𝑥,𝑡	NOUN
cana-853	123	25	)	)	PUNCT
cana-853	123	26	𝜕𝑡	𝜕𝑡	NOUN
cana-853	124	1	=	=	PUNCT
cana-853	125	1	[	[	X
cana-853	125	2	𝜆𝑥	𝜆𝑥	NOUN
cana-853	125	3	+	+	NOUN
cana-853	125	4	𝛼	𝛼	NOUN
cana-853	125	5	𝑥	𝑥	X
cana-853	125	6	−	−	PROPN
cana-853	125	7	(	(	PUNCT
cana-853	125	8	𝜆	𝜆	PROPN
cana-853	125	9	+	+	X
cana-853	125	10	γ	γ	X
cana-853	125	11	+	+	X
cana-853	125	12	𝛼	𝛼	NOUN
cana-853	125	13	)	)	PUNCT
cana-853	125	14	]	]	PUNCT
cana-853	126	1	𝑄(𝑥	𝑄(𝑥	X
cana-853	126	2	,	,	PUNCT
cana-853	126	3	𝑡	𝑡	PROPN
cana-853	126	4	)	)	PUNCT
cana-853	126	5	+	+	NUM
cana-853	126	6	𝛼	𝛼	X
cana-853	126	7	(	(	PUNCT
cana-853	126	8	1	1	NUM
cana-853	126	9	−	−	PROPN
cana-853	126	10	1	1	NUM
cana-853	126	11	𝑥	𝑥	NOUN
cana-853	126	12	)	)	PUNCT
cana-853	126	13	𝑄0(𝑥	𝑄0(𝑥	PUNCT
cana-853	126	14	)	)	PUNCT
cana-853	127	1	+	+	CCONJ
cana-853	127	2	γ	γ	X
cana-853	127	3	(	(	PUNCT
cana-853	127	4	8)	8)	NUM
cana-853	127	5	the	the	DET
cana-853	127	6	mean	mean	ADJ
cana-853	127	7	size	size	NOUN
cana-853	127	8	is	be	AUX
cana-853	127	9	ℎ(𝑡	ℎ(𝑡	PROPN
cana-853	127	10	)	)	PUNCT
cana-853	127	11	=	=	PUNCT
cana-853	128	1	∑	∑	PUNCT
cana-853	128	2	𝑛𝑄𝑛(𝑡	𝑛𝑄𝑛(𝑡	PROPN
cana-853	128	3	)	)	PUNCT
cana-853	129	1	=	=	SYM
cana-853	129	2	∞	∞	NUM
cana-853	129	3	𝑛=1	𝑛=1	NOUN
cana-853	129	4	𝜕𝑄(𝑥,𝑡	𝜕𝑄(𝑥,𝑡	NOUN
cana-853	129	5	)	)	PUNCT
cana-853	129	6	𝜕𝑡	𝜕𝑡	PROPN
cana-853	129	7	at	at	ADP
cana-853	129	8	x=1	x=1	PROPN
cana-853	129	9	differentiating	differentiate	VERB
cana-853	129	10	the	the	DET
cana-853	129	11	equation	equation	NOUN
cana-853	129	12	(	(	PUNCT
cana-853	129	13	8)	8)	NUM
cana-853	129	14	with	with	ADP
cana-853	129	15	respect	respect	NOUN
cana-853	129	16	to	to	ADP
cana-853	129	17	x	x	PUNCT
cana-853	129	18	at	at	ADP
cana-853	129	19	x=1	x=1	PROPN
cana-853	129	20	,	,	PUNCT
cana-853	129	21	we	we	PRON
cana-853	129	22	get	get	VERB
cana-853	129	23	𝑑ℎ(𝑡	𝑑ℎ(𝑡	PUNCT
cana-853	129	24	)	)	PUNCT
cana-853	129	25	𝑑𝑥	𝑑𝑥	VERB
cana-853	129	26	+	+	NOUN
cana-853	129	27	γℎ(𝑡	γℎ(𝑡	ADJ
cana-853	129	28	)	)	PUNCT
cana-853	130	1	=	=	SYM
cana-853	131	1	𝜆	𝜆	DET
cana-853	131	2	−	−	PROPN
cana-853	131	3	𝛼(1	𝛼(1	NOUN
cana-853	131	4	−	−	PROPN
cana-853	131	5	𝑄0	𝑄0	NOUN
cana-853	131	6	)	)	PUNCT
cana-853	131	7	solving	solve	VERB
cana-853	131	8	the	the	DET
cana-853	131	9	above	above	ADJ
cana-853	131	10	differential	differential	ADJ
cana-853	131	11	equation	equation	NOUN
cana-853	131	12	for	for	ADP
cana-853	131	13	h(t	h(t	PROPN
cana-853	131	14	)	)	PUNCT
cana-853	131	15	with	with	ADP
cana-853	131	16	ℎ(0	ℎ(0	NOUN
cana-853	131	17	)	)	PUNCT
cana-853	131	18	=	=	SYM
cana-853	131	19	∑	∑	PUNCT
cana-853	131	20	𝑛𝑄𝑛(𝑡	𝑛𝑄𝑛(𝑡	PROPN
cana-853	131	21	)	)	PUNCT
cana-853	132	1	=	=	SYM
cana-853	132	2	∞	∞	NUM
cana-853	132	3	𝑛=1	𝑛=1	NOUN
cana-853	132	4	0	0	X
cana-853	132	5	ℎ(𝑡	ℎ(𝑡	PROPN
cana-853	132	6	)	)	PUNCT
cana-853	132	7	=	=	PUNCT
cana-853	133	1	𝜆	𝜆	PRON
cana-853	133	2	γ	γ	X
cana-853	133	3	(	(	PUNCT
cana-853	133	4	1	1	NUM
cana-853	133	5	−	−	PROPN
cana-853	133	6	𝑒−γ𝑡	𝑒−γ𝑡	PROPN
cana-853	133	7	)	)	PUNCT
cana-853	133	8	−	−	ADP
cana-853	133	9	𝛼	𝛼	PRON
cana-853	133	10	γ	γ	X
cana-853	133	11	(	(	PUNCT
cana-853	133	12	1	1	NUM
cana-853	133	13	−	−	PROPN
cana-853	133	14	𝑒−γ𝑡	𝑒−γ𝑡	PROPN
cana-853	133	15	)	)	PUNCT
cana-853	134	1	+	+	NUM
cana-853	134	2	𝛼	𝛼	PRON
cana-853	134	3	∫	∫	NOUN
cana-853	134	4	𝑄0(𝑢	𝑄0(𝑢	PROPN
cana-853	134	5	)	)	PUNCT
cana-853	135	1	𝑡	𝑡	NOUN
cana-853	135	2	0	0	PUNCT
cana-853	135	3	𝑒−γ(𝑡−𝑢)𝑑𝑢	𝑒−γ(𝑡−𝑢)𝑑𝑢	X
cana-853	135	4	(	(	PUNCT
cana-853	135	5	9	9	X
cana-853	135	6	)	)	PUNCT
cana-853	135	7	taking	take	VERB
cana-853	135	8	laplace	laplace	NOUN
cana-853	135	9	transform	transform	NOUN
cana-853	135	10	for	for	ADP
cana-853	135	11	equation	equation	NOUN
cana-853	135	12	(	(	PUNCT
cana-853	135	13	1	1	NUM
cana-853	135	14	)	)	PUNCT
cana-853	135	15	and	and	CCONJ
cana-853	135	16	(	(	PUNCT
cana-853	135	17	2	2	NUM
cana-853	135	18	)	)	PUNCT
cana-853	135	19	,	,	PUNCT
cana-853	135	20	we	we	PRON
cana-853	135	21	get	get	VERB
cana-853	135	22	𝑄0	𝑄0	PROPN
cana-853	135	23	∗(𝑥	∗(𝑥	NOUN
cana-853	135	24	)	)	PUNCT
cana-853	135	25	=	=	PUNCT
cana-853	136	1	1	1	NUM
cana-853	136	2	+	+	NUM
cana-853	136	3	γ	γ	PART
cana-853	136	4	𝑥	𝑥	X
cana-853	136	5	(	(	PUNCT
cana-853	136	6	𝑥+𝜆+γ)−	𝑥+𝜆+γ)−	PROPN
cana-853	136	7	[	[	PUNCT
cana-853	136	8	𝑢−√𝑢2−4𝜆𝛼	𝑢−√𝑢2−4𝜆𝛼	NOUN
cana-853	136	9	2	2	NUM
cana-853	136	10	]	]	PUNCT
cana-853	136	11	(	(	PUNCT
cana-853	136	12	10	10	X
cana-853	136	13	)	)	PUNCT
cana-853	136	14	taking	take	VERB
cana-853	136	15	laplace	laplace	NOUN
cana-853	136	16	transforms	transform	VERB
cana-853	136	17	for	for	ADP
cana-853	136	18	equation	equation	NOUN
cana-853	136	19	(	(	PUNCT
cana-853	136	20	9	9	NUM
cana-853	136	21	)	)	PUNCT
cana-853	136	22	,	,	PUNCT
cana-853	136	23	let	let	VERB
cana-853	136	24	ℎ∗(𝑥	ℎ∗(𝑥	PROPN
cana-853	136	25	)	)	PUNCT
cana-853	136	26	be	be	AUX
cana-853	136	27	the	the	DET
cana-853	136	28	laplace	laplace	NOUN
cana-853	136	29	transform	transform	NOUN
cana-853	136	30	of	of	ADP
cana-853	136	31	ℎ(𝑡	ℎ(𝑡	PROPN
cana-853	136	32	)	)	PUNCT
cana-853	136	33	ℎ∗(𝑥	ℎ∗(𝑥	PROPN
cana-853	136	34	)	)	PUNCT
cana-853	136	35	=	=	VERB
cana-853	136	36	𝜆−𝛼	𝜆−𝛼	NOUN
cana-853	136	37	𝑥(𝑥+γ	𝑥(𝑥+γ	ADP
cana-853	136	38	)	)	PUNCT
cana-853	136	39	+	+	NUM
cana-853	136	40	𝛼	𝛼	X
cana-853	136	41	(	(	PUNCT
cana-853	136	42	𝑥+γ	𝑥+γ	PROPN
cana-853	136	43	)	)	PUNCT
cana-853	136	44	𝑄0	𝑄0	PROPN
cana-853	136	45	∗(𝑥	∗(𝑥	NOUN
cana-853	136	46	)	)	PUNCT
cana-853	136	47	(	(	PUNCT
cana-853	136	48	11	11	X
cana-853	136	49	)	)	PUNCT
cana-853	136	50	lim	lim	PROPN
cana-853	136	51	t→∞	t→∞	ADP
cana-853	136	52	h(t	h(t	PROPN
cana-853	136	53	)	)	PUNCT
cana-853	137	1	=	=	VERB
cana-853	137	2	lim	lim	PROPN
cana-853	137	3	x→0	x→0	PROPN
cana-853	137	4	x	x	SYM
cana-853	137	5	ℎ∗(𝑥	ℎ∗(𝑥	PROPN
cana-853	137	6	)	)	PUNCT
cana-853	137	7	using	use	VERB
cana-853	137	8	equation	equation	NOUN
cana-853	137	9	(	(	PUNCT
cana-853	137	10	10	10	NUM
cana-853	137	11	)	)	PUNCT
cana-853	137	12	and	and	CCONJ
cana-853	137	13	the	the	DET
cana-853	137	14	above	above	ADJ
cana-853	137	15	concept	concept	NOUN
cana-853	137	16	for	for	ADP
cana-853	137	17	the	the	DET
cana-853	137	18	equation	equation	NOUN
cana-853	137	19	(	(	PUNCT
cana-853	137	20	11	11	NUM
cana-853	137	21	)	)	PUNCT
cana-853	137	22	,	,	PUNCT
cana-853	137	23	we	we	PRON
cana-853	137	24	get	get	VERB
cana-853	137	25	communications	communication	NOUN
cana-853	137	26	on	on	ADP
cana-853	137	27	applied	apply	VERB
cana-853	137	28	nonlinear	nonlinear	ADJ
cana-853	137	29	analysis	analysis	NOUN
cana-853	137	30	issn	issn	NOUN
cana-853	137	31	:	:	PUNCT
cana-853	137	32	1074	1074	NUM
cana-853	137	33	-	-	PUNCT
cana-853	137	34	133x	133x	NUM
cana-853	137	35	vol	vol	NOUN
cana-853	137	36	31	31	NUM
cana-853	137	37	no	no	NOUN
cana-853	137	38	.	.	PUNCT
cana-853	138	1	4s	4s	NUM
cana-853	138	2	(	(	PUNCT
cana-853	138	3	2024	2024	NUM
cana-853	138	4	)	)	PUNCT
cana-853	138	5	302	302	NUM
cana-853	138	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-853	138	7	lq	lq	NOUN
cana-853	138	8	=	=	PUNCT
cana-853	138	9	λ	λ	X
cana-853	138	10	−	−	PROPN
cana-853	138	11	α	α	PROPN
cana-853	138	12	γ	γ	X
cana-853	138	13	+	+	X
cana-853	138	14	2α	2α	NOUN
cana-853	138	15	2(λ	2(λ	NUM
cana-853	139	1	+	+	CCONJ
cana-853	139	2	γ	γ	X
cana-853	139	3	)	)	PUNCT
cana-853	139	4	−	−	PROPN
cana-853	140	1	[	[	X
cana-853	140	2	(	(	PUNCT
cana-853	140	3	λ	λ	X
cana-853	140	4	+	+	NUM
cana-853	140	5	α	α	NOUN
cana-853	140	6	+	+	X
cana-853	140	7	γ	γ	X
cana-853	140	8	)	)	PUNCT
cana-853	140	9	−	−	NOUN
cana-853	140	10	√(λ	√(λ	NOUN
cana-853	141	1	+	+	CCONJ
cana-853	141	2	α	α	NOUN
cana-853	141	3	+	+	CCONJ
cana-853	141	4	γ)2	γ)2	NOUN
cana-853	141	5	−	−	PROPN
cana-853	141	6	4λα	4λα	NOUN
cana-853	141	7	]	]	PUNCT
cana-853	141	8	where	where	SCONJ
cana-853	141	9	𝛼	𝛼	X
cana-853	141	10	=	=	SYM
cana-853	141	11	3𝑝𝜇1	3𝑝𝜇1	NUM
cana-853	141	12	+	+	CCONJ
cana-853	142	1	3(1	3(1	NUM
cana-853	142	2	−	−	PROPN
cana-853	142	3	𝑝)𝜇2	𝑝)𝜇2	PROPN
cana-853	142	4	+	+	CCONJ
cana-853	142	5	2(1	2(1	NUM
cana-853	142	6	+	+	CCONJ
cana-853	142	7	𝑞)𝜇3	𝑞)𝜇3	PROPN
cana-853	142	8	+	+	CCONJ
cana-853	142	9	2𝜇4	2𝜇4	NUM
cana-853	142	10	+	+	CCONJ
cana-853	142	11	4	4	NUM
cana-853	142	12	𝜇5	𝜇5	ADJ
cana-853	142	13	4	4	NUM
cana-853	142	14	.	.	PUNCT
cana-853	142	15	balance	balance	NOUN
cana-853	142	16	equations	equation	NOUN
cana-853	142	17	by	by	ADP
cana-853	142	18	using	use	VERB
cana-853	142	19	little	little	ADJ
cana-853	142	20	’s	’s	PART
cana-853	142	21	formula	formula	NOUN
cana-853	142	22	,	,	PUNCT
cana-853	142	23	we	we	PRON
cana-853	142	24	get	get	VERB
cana-853	142	25	the	the	DET
cana-853	142	26	following	follow	VERB
cana-853	142	27	equations	equation	NOUN
cana-853	142	28	average	average	ADJ
cana-853	142	29	queue	queue	NOUN
cana-853	142	30	length	length	NOUN
cana-853	142	31	(	(	PUNCT
cana-853	142	32	lq	lq	NOUN
cana-853	142	33	)	)	PUNCT
cana-853	142	34	lq	lq	NOUN
cana-853	142	35	=	=	PUNCT
cana-853	142	36	λ	λ	X
cana-853	142	37	−	−	PROPN
cana-853	142	38	α	α	PROPN
cana-853	142	39	γ	γ	X
cana-853	142	40	+	+	X
cana-853	142	41	2α	2α	NOUN
cana-853	142	42	2(λ	2(λ	NUM
cana-853	142	43	+	+	CCONJ
cana-853	142	44	γ	γ	X
cana-853	142	45	)	)	PUNCT
cana-853	142	46	−	−	PROPN
cana-853	143	1	[	[	X
cana-853	143	2	(	(	PUNCT
cana-853	143	3	λ	λ	X
cana-853	143	4	+	+	NUM
cana-853	143	5	α	α	NOUN
cana-853	143	6	+	+	X
cana-853	143	7	γ	γ	X
cana-853	143	8	)	)	PUNCT
cana-853	143	9	−	−	NOUN
cana-853	143	10	√(λ	√(λ	NOUN
cana-853	144	1	+	+	CCONJ
cana-853	144	2	α	α	NOUN
cana-853	144	3	+	+	CCONJ
cana-853	144	4	γ)2	γ)2	NOUN
cana-853	144	5	−	−	PROPN
cana-853	144	6	4λα	4λα	NOUN
cana-853	144	7	]	]	PUNCT
cana-853	144	8	where	where	SCONJ
cana-853	144	9	𝛼	𝛼	AUX
cana-853	144	10	=	=	SYM
cana-853	144	11	3	3	NUM
cana-853	144	12	�	�	NOUN
cana-853	144	13	̅	̅	NOUN
cana-853	144	14	�	�	NOUN
cana-853	144	15	𝜇1	𝜇1	NOUN
cana-853	144	16	+	+	CCONJ
cana-853	144	17	3(1	3(1	NUM
cana-853	144	18	−	−	PROPN
cana-853	144	19	�	�	NOUN
cana-853	144	20	̅	̅	NOUN
cana-853	144	21	�	�	NUM
cana-853	144	22	)𝜇2	)𝜇2	PUNCT
cana-853	144	23	+	+	NUM
cana-853	144	24	2(1	2(1	NUM
cana-853	144	25	+	+	CCONJ
cana-853	144	26	�	�	NOUN
cana-853	144	27	̅	̅	NOUN
cana-853	144	28	�	�	NOUN
cana-853	144	29	)𝜇3	)𝜇3	PUNCT
cana-853	144	30	+	+	NOUN
cana-853	144	31	2𝜇4	2𝜇4	NUM
cana-853	145	1	+	+	CCONJ
cana-853	145	2	4	4	NUM
cana-853	145	3	𝜇5	𝜇5	ADJ
cana-853	145	4	waiting	waiting	NOUN
cana-853	145	5	time	time	NOUN
cana-853	145	6	of	of	ADP
cana-853	145	7	a	a	DET
cana-853	145	8	customer	customer	NOUN
cana-853	145	9	(	(	PUNCT
cana-853	145	10	wq	wq	NOUN
cana-853	145	11	)	)	PUNCT
cana-853	145	12	wq	wq	NOUN
cana-853	146	1	=	=	NUM
cana-853	146	2	lq	lq	NOUN
cana-853	146	3	λ	λ	X
cana-853	146	4	=	=	PRON
cana-853	146	5	(	(	PUNCT
cana-853	146	6	λ	λ	X
cana-853	146	7	−	−	PROPN
cana-853	146	8	α	α	PROPN
cana-853	146	9	γ	γ	X
cana-853	146	10	+	+	X
cana-853	146	11	2α	2α	NOUN
cana-853	146	12	2(λ	2(λ	NUM
cana-853	146	13	+	+	CCONJ
cana-853	146	14	γ	γ	X
cana-853	146	15	)	)	PUNCT
cana-853	146	16	−	−	PROPN
cana-853	147	1	[	[	X
cana-853	147	2	(	(	PUNCT
cana-853	147	3	λ	λ	X
cana-853	147	4	+	+	NUM
cana-853	147	5	α	α	NOUN
cana-853	147	6	+	+	X
cana-853	147	7	γ	γ	X
cana-853	147	8	)	)	PUNCT
cana-853	147	9	−	−	NOUN
cana-853	147	10	√(λ	√(λ	NOUN
cana-853	148	1	+	+	CCONJ
cana-853	148	2	α	α	NOUN
cana-853	148	3	+	+	CCONJ
cana-853	148	4	γ)2	γ)2	NOUN
cana-853	148	5	−	−	PROPN
cana-853	148	6	4λα	4λα	NOUN
cana-853	148	7	]	]	PUNCT
cana-853	148	8	)	)	PUNCT
cana-853	148	9	1	1	NUM
cana-853	148	10	λ	λ	NOUN
cana-853	148	11	average	average	ADJ
cana-853	148	12	number	number	NOUN
cana-853	148	13	of	of	ADP
cana-853	148	14	customer	customer	NOUN
cana-853	148	15	(	(	PUNCT
cana-853	148	16	ls	ls	PROPN
cana-853	148	17	)	)	PUNCT
cana-853	148	18	ls	ls	NOUN
cana-853	149	1	=	=	NOUN
cana-853	149	2	lq	lq	NOUN
cana-853	150	1	+	+	NOUN
cana-853	150	2	λ	λ	X
cana-853	150	3	μ	μ	NOUN
cana-853	150	4	=	=	PUNCT
cana-853	150	5	(	(	PUNCT
cana-853	150	6	λ	λ	X
cana-853	150	7	−	−	PROPN
cana-853	150	8	α	α	PROPN
cana-853	150	9	γ	γ	X
cana-853	150	10	+	+	X
cana-853	150	11	2α	2α	NOUN
cana-853	150	12	2(λ	2(λ	NUM
cana-853	150	13	+	+	CCONJ
cana-853	150	14	γ	γ	X
cana-853	150	15	)	)	PUNCT
cana-853	150	16	−	−	PROPN
cana-853	151	1	[	[	X
cana-853	151	2	(	(	PUNCT
cana-853	151	3	λ	λ	X
cana-853	151	4	+	+	NUM
cana-853	151	5	α	α	NOUN
cana-853	151	6	+	+	X
cana-853	151	7	γ	γ	X
cana-853	151	8	)	)	PUNCT
cana-853	151	9	−	−	NOUN
cana-853	151	10	√(λ	√(λ	NOUN
cana-853	152	1	+	+	CCONJ
cana-853	152	2	α	α	NOUN
cana-853	152	3	+	+	CCONJ
cana-853	152	4	γ)2	γ)2	NOUN
cana-853	152	5	−	−	PROPN
cana-853	152	6	4λα	4λα	NOUN
cana-853	152	7	]	]	PUNCT
cana-853	152	8	)	)	PUNCT
cana-853	153	1	+	+	CCONJ
cana-853	153	2	λ	λ	X
cana-853	153	3	μ	μ	NOUN
cana-853	153	4	waiting	wait	VERB
cana-853	153	5	time	time	NOUN
cana-853	153	6	of	of	ADP
cana-853	153	7	a	a	DET
cana-853	153	8	customer	customer	NOUN
cana-853	153	9	in	in	ADP
cana-853	153	10	the	the	DET
cana-853	153	11	system	system	NOUN
cana-853	153	12	(	(	PUNCT
cana-853	153	13	ws	ws	NOUN
cana-853	153	14	)	)	PUNCT
cana-853	153	15	ws	ws	NOUN
cana-853	153	16	=	=	PUNCT
cana-853	153	17	ls	ls	PROPN
cana-853	153	18	λ	λ	PROPN
cana-853	153	19	=	=	PUNCT
cana-853	153	20	[	[	PUNCT
cana-853	153	21	λ	λ	X
cana-853	153	22	−	−	PROPN
cana-853	153	23	α	α	PROPN
cana-853	153	24	γ	γ	X
cana-853	153	25	+	+	X
cana-853	153	26	2α	2α	NOUN
cana-853	153	27	2(λ	2(λ	NUM
cana-853	154	1	+	+	CCONJ
cana-853	154	2	γ	γ	X
cana-853	154	3	)	)	PUNCT
cana-853	154	4	−	−	PROPN
cana-853	155	1	[	[	X
cana-853	155	2	(	(	PUNCT
cana-853	155	3	λ	λ	X
cana-853	155	4	+	+	NUM
cana-853	155	5	α	α	NOUN
cana-853	155	6	+	+	X
cana-853	155	7	γ	γ	X
cana-853	155	8	)	)	PUNCT
cana-853	155	9	−	−	NOUN
cana-853	155	10	√(λ	√(λ	NOUN
cana-853	156	1	+	+	CCONJ
cana-853	156	2	α	α	NOUN
cana-853	156	3	+	+	CCONJ
cana-853	156	4	γ)2	γ)2	NOUN
cana-853	156	5	−	−	PROPN
cana-853	156	6	4λα	4λα	NOUN
cana-853	156	7	]	]	PUNCT
cana-853	157	1	+	+	CCONJ
cana-853	157	2	λ	λ	X
cana-853	157	3	μ	μ	NOUN
cana-853	157	4	]	]	PUNCT
cana-853	157	5	1	1	NUM
cana-853	157	6	λ	λ	NOUN
cana-853	157	7	mean	mean	NOUN
cana-853	157	8	queue	queue	NOUN
cana-853	157	9	length	length	NOUN
cana-853	157	10	for	for	ADP
cana-853	157	11	node	node	NOUN
cana-853	157	12	one	one	NUM
cana-853	157	13	,	,	PUNCT
cana-853	157	14	node	node	NOUN
cana-853	157	15	two	two	NUM
cana-853	157	16	,	,	PUNCT
cana-853	157	17	node	node	NOUN
cana-853	157	18	three	three	NUM
cana-853	157	19	are	be	AUX
cana-853	157	20	as	as	SCONJ
cana-853	157	21	follows	follow	VERB
cana-853	157	22	lq1	lq1	NOUN
cana-853	158	1	=	=	SYM
cana-853	158	2	λ	λ	X
cana-853	158	3	−	−	PROPN
cana-853	158	4	α	α	PROPN
cana-853	158	5	γ	γ	X
cana-853	158	6	+	+	X
cana-853	158	7	2α	2α	NOUN
cana-853	158	8	2(λ	2(λ	NUM
cana-853	158	9	+	+	CCONJ
cana-853	158	10	γ	γ	X
cana-853	158	11	)	)	PUNCT
cana-853	158	12	−	−	PROPN
cana-853	159	1	[	[	X
cana-853	159	2	(	(	PUNCT
cana-853	159	3	λ	λ	X
cana-853	159	4	+	+	NUM
cana-853	159	5	α	α	NOUN
cana-853	159	6	+	+	X
cana-853	159	7	γ	γ	X
cana-853	159	8	)	)	PUNCT
cana-853	159	9	−	−	NOUN
cana-853	159	10	√(λ	√(λ	NOUN
cana-853	160	1	+	+	CCONJ
cana-853	160	2	α	α	NOUN
cana-853	160	3	+	+	CCONJ
cana-853	160	4	γ)2	γ)2	NOUN
cana-853	160	5	−	−	PROPN
cana-853	160	6	4λα	4λα	NOUN
cana-853	160	7	]	]	PUNCT
cana-853	160	8	where	where	SCONJ
cana-853	160	9	𝛼	𝛼	AUX
cana-853	160	10	=	=	PUNCT
cana-853	160	11	�	�	PROPN
cana-853	160	12	̅	̅	NOUN
cana-853	160	13	�	�	NOUN
cana-853	160	14	𝜇1	𝜇1	NOUN
cana-853	160	15	+	+	CCONJ
cana-853	160	16	(	(	PUNCT
cana-853	160	17	1	1	NUM
cana-853	160	18	−	−	PRON
cana-853	160	19	�	�	NOUN
cana-853	160	20	̅	̅	NOUN
cana-853	160	21	�	�	NUM
cana-853	160	22	)𝜇2	)𝜇2	VERB
cana-853	160	23	+	+	NUM
cana-853	160	24	�	�	NOUN
cana-853	160	25	̅	̅	NOUN
cana-853	160	26	�	�	NOUN
cana-853	160	27	𝜇3	𝜇3	NOUN
cana-853	160	28	lq2	lq2	PROPN
cana-853	160	29	=	=	PUNCT
cana-853	160	30	λ	λ	INTJ
cana-853	160	31	−	−	PROPN
cana-853	160	32	α	α	PROPN
cana-853	160	33	γ	γ	X
cana-853	160	34	+	+	X
cana-853	160	35	2α	2α	NOUN
cana-853	160	36	2(λ	2(λ	NUM
cana-853	160	37	+	+	CCONJ
cana-853	160	38	γ	γ	X
cana-853	160	39	)	)	PUNCT
cana-853	160	40	−	−	PROPN
cana-853	161	1	[	[	X
cana-853	161	2	(	(	PUNCT
cana-853	161	3	λ	λ	X
cana-853	161	4	+	+	NUM
cana-853	161	5	α	α	NOUN
cana-853	161	6	+	+	X
cana-853	161	7	γ	γ	X
cana-853	161	8	)	)	PUNCT
cana-853	161	9	−	−	NOUN
cana-853	161	10	√(λ	√(λ	NOUN
cana-853	162	1	+	+	CCONJ
cana-853	162	2	α	α	NOUN
cana-853	162	3	+	+	CCONJ
cana-853	162	4	γ)2	γ)2	NOUN
cana-853	162	5	−	−	PROPN
cana-853	162	6	4λα	4λα	NOUN
cana-853	162	7	]	]	PUNCT
cana-853	162	8	where	where	SCONJ
cana-853	162	9	𝛼	𝛼	AUX
cana-853	162	10	=	=	PUNCT
cana-853	162	11	�	�	PROPN
cana-853	162	12	̅	̅	NOUN
cana-853	162	13	�	�	NOUN
cana-853	162	14	𝜇1	𝜇1	NOUN
cana-853	162	15	+	+	CCONJ
cana-853	162	16	(	(	PUNCT
cana-853	162	17	1	1	NUM
cana-853	162	18	−	−	PRON
cana-853	162	19	�	�	NOUN
cana-853	162	20	̅	̅	NOUN
cana-853	162	21	�	�	NUM
cana-853	162	22	)𝜇2	)𝜇2	VERB
cana-853	162	23	+	+	NUM
cana-853	162	24	�	�	NOUN
cana-853	162	25	̅	̅	NOUN
cana-853	162	26	�	�	NOUN
cana-853	162	27	𝜇3	𝜇3	NOUN
cana-853	162	28	+	+	CCONJ
cana-853	162	29	𝑟𝜇4	𝑟𝜇4	NOUN
cana-853	162	30	lq3	lq3	NOUN
cana-853	162	31	=	=	SYM
cana-853	162	32	λ	λ	X
cana-853	162	33	−	−	PROPN
cana-853	162	34	α	α	PROPN
cana-853	162	35	γ	γ	X
cana-853	162	36	+	+	X
cana-853	162	37	2α	2α	NOUN
cana-853	162	38	2(λ	2(λ	NUM
cana-853	163	1	+	+	CCONJ
cana-853	163	2	γ	γ	X
cana-853	163	3	)	)	PUNCT
cana-853	163	4	−	−	PROPN
cana-853	164	1	[	[	X
cana-853	164	2	(	(	PUNCT
cana-853	164	3	λ	λ	X
cana-853	164	4	+	+	NUM
cana-853	164	5	α	α	NOUN
cana-853	164	6	+	+	X
cana-853	164	7	γ	γ	X
cana-853	164	8	)	)	PUNCT
cana-853	164	9	−	−	NOUN
cana-853	164	10	√(λ	√(λ	NOUN
cana-853	165	1	+	+	CCONJ
cana-853	165	2	α	α	NOUN
cana-853	165	3	+	+	CCONJ
cana-853	165	4	γ)2	γ)2	NOUN
cana-853	165	5	−	−	PROPN
cana-853	165	6	4λα	4λα	NOUN
cana-853	165	7	]	]	PUNCT
cana-853	165	8	where	where	SCONJ
cana-853	165	9	𝛼	𝛼	AUX
cana-853	165	10	=	=	PUNCT
cana-853	165	11	�	�	PROPN
cana-853	165	12	̅	̅	NOUN
cana-853	165	13	�	�	NOUN
cana-853	165	14	𝜇1	𝜇1	NOUN
cana-853	165	15	+	+	CCONJ
cana-853	165	16	(	(	PUNCT
cana-853	165	17	1	1	NUM
cana-853	165	18	−	−	PRON
cana-853	165	19	�	�	NOUN
cana-853	165	20	̅	̅	NOUN
cana-853	165	21	�	�	NUM
cana-853	165	22	)𝜇2	)𝜇2	PUNCT
cana-853	165	23	+	+	CCONJ
cana-853	165	24	(	(	PUNCT
cana-853	165	25	1	1	NUM
cana-853	165	26	−	−	PRON
cana-853	165	27	�	�	NOUN
cana-853	165	28	̅	̅	NOUN
cana-853	165	29	�	�	NOUN
cana-853	165	30	)𝜇3	)𝜇3	PUNCT
cana-853	165	31	+	+	CCONJ
cana-853	165	32	(	(	PUNCT
cana-853	165	33	1	1	NUM
cana-853	165	34	−	−	NOUN
cana-853	165	35	𝑟)𝜇4	𝑟)𝜇4	PRON
cana-853	165	36	+	+	CCONJ
cana-853	165	37	𝜇5	𝜇5	PROPN
cana-853	165	38	using	use	VERB
cana-853	165	39	little	little	ADJ
cana-853	165	40	’s	’s	PART
cana-853	165	41	formula	formula	NOUN
cana-853	165	42	,	,	PUNCT
cana-853	165	43	we	we	PRON
cana-853	165	44	can	can	AUX
cana-853	165	45	calculate	calculate	VERB
cana-853	165	46	the	the	DET
cana-853	165	47	remaining	remain	VERB
cana-853	165	48	parameters	parameter	NOUN
cana-853	165	49	communications	communication	NOUN
cana-853	165	50	on	on	ADP
cana-853	165	51	applied	apply	VERB
cana-853	165	52	nonlinear	nonlinear	ADJ
cana-853	165	53	analysis	analysis	NOUN
cana-853	165	54	issn	issn	NOUN
cana-853	165	55	:	:	PUNCT
cana-853	165	56	1074	1074	NUM
cana-853	165	57	-	-	PUNCT
cana-853	165	58	133x	133x	NUM
cana-853	165	59	vol	vol	NOUN
cana-853	165	60	31	31	NUM
cana-853	165	61	no	no	NOUN
cana-853	165	62	.	.	PUNCT
cana-853	166	1	4s	4s	NUM
cana-853	166	2	(	(	PUNCT
cana-853	166	3	2024	2024	NUM
cana-853	166	4	)	)	PUNCT
cana-853	166	5	303	303	NUM
cana-853	166	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-853	166	7	wq1	wq1	ADJ
cana-853	166	8	,	,	PUNCT
cana-853	166	9	ls1	ls1	NOUN
cana-853	166	10	,	,	PUNCT
cana-853	166	11	ws1	ws1	INTJ
cana-853	166	12	,	,	PUNCT
cana-853	166	13	wq2	wq2	PRON
cana-853	166	14	,	,	PUNCT
cana-853	166	15	ls2	ls2	PROPN
cana-853	166	16	,	,	PUNCT
cana-853	166	17	ws2	ws2	NOUN
cana-853	166	18	,	,	PUNCT
cana-853	166	19	wq3	wq3	NOUN
cana-853	166	20	,	,	PUNCT
cana-853	166	21	ls3	ls3	PROPN
cana-853	166	22	,	,	PUNCT
cana-853	166	23	ws3	ws3	VERB
cana-853	166	24	5	5	NUM
cana-853	166	25	.	.	PUNCT
cana-853	166	26	particular	particular	ADJ
cana-853	166	27	case	case	NOUN
cana-853	166	28	whenμ1	whenμ1	PROPN
cana-853	167	1	=	=	SYM
cana-853	167	2	3μ1	3μ1	NUM
cana-853	167	3	,	,	PUNCT
cana-853	167	4	μ2	μ2	NOUN
cana-853	167	5	=	=	SYM
cana-853	167	6	3μ2	3μ2	NUM
cana-853	167	7	and	and	CCONJ
cana-853	167	8	μ3	μ3	ADJ
cana-853	167	9	=	=	PROPN
cana-853	167	10	μ4	μ4	NOUN
cana-853	167	11	=	=	SYM
cana-853	167	12	μ5	μ5	PROPN
cana-853	167	13	=	=	SYM
cana-853	167	14	0and	0and	PROPN
cana-853	167	15	�	�	PROPN
cana-853	167	16	̅	̅	NOUN
cana-853	167	17	�	�	PROPN
cana-853	167	18	=	=	SYM
cana-853	167	19	�	�	PROPN
cana-853	167	20	̅	̅	NOUN
cana-853	167	21	�	�	PROPN
cana-853	167	22	,	,	PUNCT
cana-853	167	23	�	�	PROPN
cana-853	167	24	̅	̅	NOUN
cana-853	167	25	�	�	NOUN
cana-853	167	26	=	=	SYM
cana-853	167	27	1	1	NUM
cana-853	167	28	−	−	NOUN
cana-853	167	29	�	�	NOUN
cana-853	167	30	̅	̅	NOUN
cana-853	167	31	�	�	NOUN
cana-853	167	32	,	,	PUNCT
cana-853	167	33	there	there	PRON
cana-853	167	34	is	be	VERB
cana-853	167	35	a	a	DET
cana-853	167	36	customer	customer	NOUN
cana-853	167	37	with	with	ADP
cana-853	167	38	and	and	CCONJ
cana-853	167	39	without	without	ADP
cana-853	167	40	preparatory	preparatory	ADJ
cana-853	167	41	wօrk	wօrk	NOUN
cana-853	167	42	,	,	PUNCT
cana-853	167	43	then	then	ADV
cana-853	167	44	the	the	DET
cana-853	167	45	system	system	NOUN
cana-853	167	46	's	's	PART
cana-853	167	47	average	average	ADJ
cana-853	167	48	queue	queue	NOUN
cana-853	167	49	length	length	NOUN
cana-853	167	50	's	's	PART
cana-853	167	51	asymptotic	asymptotic	ADJ
cana-853	167	52	naturelq	naturelq	NOUN
cana-853	167	53	for	for	ADP
cana-853	167	54	the	the	DET
cana-853	167	55	feedback	feedback	NOUN
cana-853	167	56	when	when	SCONJ
cana-853	167	57	γ	γ	X
cana-853	167	58	>	>	X
cana-853	167	59	0	0	NUM
cana-853	167	60	is	be	AUX
cana-853	167	61	lq	lq	ADP
cana-853	167	62	=	=	PUNCT
cana-853	167	63	λ	λ	X
cana-853	167	64	−	−	PROPN
cana-853	167	65	(	(	PUNCT
cana-853	167	66	�	�	NOUN
cana-853	167	67	̅	̅	NOUN
cana-853	167	68	�	�	NOUN
cana-853	167	69	μ1	μ1	NOUN
cana-853	167	70	+	+	SYM
cana-853	167	71	�	�	NOUN
cana-853	167	72	̅	̅	NOUN
cana-853	167	73	�	�	NOUN
cana-853	167	74	μ2	μ2	NOUN
cana-853	167	75	)	)	PUNCT
cana-853	167	76	γ	γ	PROPN
cana-853	167	77	+	+	NOUN
cana-853	167	78	2(	2(	NUM
cana-853	167	79	�	�	NOUN
cana-853	167	80	̅	̅	NOUN
cana-853	167	81	�	�	NOUN
cana-853	167	82	μ1	μ1	NOUN
cana-853	167	83	+	+	SYM
cana-853	167	84	�	�	NOUN
cana-853	167	85	̅	̅	NOUN
cana-853	167	86	�	�	NOUN
cana-853	167	87	μ2	μ2	NOUN
cana-853	167	88	)	)	PUNCT
cana-853	168	1	2(λ	2(λ	NUM
cana-853	169	1	+	+	CCONJ
cana-853	169	2	γ	γ	X
cana-853	169	3	)	)	PUNCT
cana-853	169	4	−	−	PROPN
cana-853	170	1	[	[	X
cana-853	170	2	(	(	PUNCT
cana-853	170	3	λ	λ	X
cana-853	170	4	+	+	CCONJ
cana-853	170	5	(	(	PUNCT
cana-853	170	6	�	�	NOUN
cana-853	170	7	̅	̅	NOUN
cana-853	170	8	�	�	NOUN
cana-853	170	9	μ1	μ1	NOUN
cana-853	170	10	+	+	SYM
cana-853	170	11	�	�	NOUN
cana-853	170	12	̅	̅	NOUN
cana-853	170	13	�	�	NOUN
cana-853	170	14	μ2	μ2	NOUN
cana-853	170	15	)	)	PUNCT
cana-853	171	1	+	+	CCONJ
cana-853	171	2	γ	γ	X
cana-853	171	3	)	)	PUNCT
cana-853	171	4	−	−	PROPN
cana-853	171	5	√(λ	√(λ	NOUN
cana-853	172	1	+	+	CCONJ
cana-853	172	2	(	(	PUNCT
cana-853	172	3	�	�	NOUN
cana-853	172	4	̅	̅	NOUN
cana-853	172	5	�	�	NOUN
cana-853	172	6	μ1	μ1	NOUN
cana-853	172	7	+	+	SYM
cana-853	172	8	�	�	NOUN
cana-853	172	9	̅	̅	NOUN
cana-853	172	10	�	�	NOUN
cana-853	172	11	μ2	μ2	NOUN
cana-853	172	12	)	)	PUNCT
cana-853	173	1	+	+	NUM
cana-853	173	2	γ)2	γ)2	NOUN
cana-853	173	3	−	−	PROPN
cana-853	173	4	4λ(	4λ(	NUM
cana-853	173	5	�	�	NOUN
cana-853	173	6	̅	̅	NOUN
cana-853	173	7	�	�	NOUN
cana-853	173	8	μ1	μ1	NOUN
cana-853	173	9	+	+	SYM
cana-853	173	10	�	�	NOUN
cana-853	173	11	̅	̅	NOUN
cana-853	173	12	�	�	NOUN
cana-853	173	13	μ2	μ2	NOUN
cana-853	173	14	)	)	PUNCT
cana-853	173	15	]	]	PUNCT
cana-853	173	16	using	use	VERB
cana-853	173	17	little	little	ADJ
cana-853	173	18	’s	’s	PART
cana-853	173	19	formula	formula	NOUN
cana-853	173	20	,	,	PUNCT
cana-853	173	21	we	we	PRON
cana-853	173	22	can	can	AUX
cana-853	173	23	calculate	calculate	VERB
cana-853	173	24	the	the	DET
cana-853	173	25	remaining	remain	VERB
cana-853	173	26	parameters	parameter	NOUN
cana-853	173	27	𝐖𝐪𝟏	𝐖𝐪𝟏	VERB
cana-853	173	28	,	,	PUNCT
cana-853	173	29	𝐋𝐬𝟏	𝐋𝐬𝟏	NOUN
cana-853	173	30	,	,	PUNCT
cana-853	173	31	𝐖𝐬𝟏	𝐖𝐬𝟏	NOUN
cana-853	173	32	,	,	PUNCT
cana-853	173	33	𝐖𝐪𝟐	𝐖𝐪𝟐	NOUN
cana-853	173	34	,	,	PUNCT
cana-853	173	35	𝐋𝐬𝟐	𝐋𝐬𝟐	NOUN
cana-853	173	36	,	,	PUNCT
cana-853	173	37	𝐖𝐬𝟐	𝐖𝐬𝟐	ADJ
cana-853	173	38	,	,	PUNCT
cana-853	173	39	𝐖𝐪𝟑	𝐖𝐪𝟑	NOUN
cana-853	173	40	,	,	PUNCT
cana-853	173	41	𝐋𝐬𝟑	𝐋𝐬𝟑	NOUN
cana-853	173	42	,	,	PUNCT
cana-853	173	43	𝐖𝐬𝟑	𝐖𝐬𝟑	NOUN
cana-853	173	44	.	.	PUNCT
cana-853	174	1	6	6	X
cana-853	174	2	.	.	X
cana-853	174	3	numerical	numerical	ADJ
cana-853	174	4	examples	example	NOUN
cana-853	174	5	number	number	NOUN
cana-853	174	6	of	of	ADP
cana-853	174	7	customers	customer	NOUN
cana-853	174	8	in	in	ADP
cana-853	174	9	all	all	DET
cana-853	174	10	the	the	DET
cana-853	174	11	three	three	NUM
cana-853	174	12	queues	queue	NOUN
cana-853	174	13	for	for	ADP
cana-853	174	14	the	the	DET
cana-853	174	15	system	system	NOUN
cana-853	174	16	the	the	DET
cana-853	174	17	consumers	consumer	NOUN
cana-853	174	18	in	in	ADP
cana-853	174	19	all	all	DET
cana-853	174	20	the	the	DET
cana-853	174	21	three	three	NUM
cana-853	174	22	queues	queue	NOUN
cana-853	174	23	for	for	ADP
cana-853	174	24	the	the	DET
cana-853	174	25	system	system	NOUN
cana-853	174	26	are	be	AUX
cana-853	174	27	calculated	calculate	VERB
cana-853	174	28	in	in	ADP
cana-853	174	29	table	table	NOUN
cana-853	174	30	1	1	NUM
cana-853	174	31	for	for	ADP
cana-853	174	32	�	�	NOUN
cana-853	174	33	̅	̅	NOUN
cana-853	174	34	�	�	NOUN
cana-853	174	35	=	=	SYM
cana-853	174	36	0.3	0.3	NUM
cana-853	174	37	,	,	PUNCT
cana-853	174	38	�	�	NOUN
cana-853	174	39	̅	̅	NOUN
cana-853	174	40	�	�	NOUN
cana-853	174	41	=	=	SYM
cana-853	174	42	0.5	0.5	NUM
cana-853	174	43	,	,	PUNCT
cana-853	174	44	r	r	NOUN
cana-853	174	45	=	=	SYM
cana-853	174	46	0.4	0.4	NUM
cana-853	174	47	,	,	PUNCT
cana-853	174	48	μ1	μ1	PROPN
cana-853	174	49	=	=	SYM
cana-853	174	50	6	6	NUM
cana-853	174	51	,	,	PUNCT
cana-853	174	52	μ2	μ2	NOUN
cana-853	174	53	=	=	SYM
cana-853	174	54	4	4	NUM
cana-853	174	55	,	,	PUNCT
cana-853	174	56	μ3	μ3	NOUN
cana-853	174	57	=	=	SYM
cana-853	174	58	8	8	NUM
cana-853	174	59	,	,	PUNCT
cana-853	174	60	μ4	μ4	NOUN
cana-853	174	61	=	=	SYM
cana-853	174	62	9	9	NUM
cana-853	174	63	,	,	PUNCT
cana-853	174	64	μ5	μ5	NOUN
cana-853	174	65	=	=	NOUN
cana-853	174	66	10	10	NUM
cana-853	174	67	,	,	PUNCT
cana-853	174	68	λ	λ	X
cana-853	174	69	=	=	NOUN
cana-853	174	70	1,2,3	1,2,3	NUM
cana-853	174	71	…	…	PUNCT
cana-853	174	72	.10	.10	NUM
cana-853	174	73	,	,	PUNCT
cana-853	174	74	γ	γ	X
cana-853	174	75	=	=	SYM
cana-853	174	76	3	3	NUM
cana-853	174	77	,	,	PUNCT
cana-853	174	78	6	6	NUM
cana-853	174	79	,	,	PUNCT
cana-853	174	80	9	9	NUM
cana-853	174	81	,	,	PUNCT
cana-853	174	82	12	12	NUM
cana-853	174	83	,	,	PUNCT
cana-853	174	84	15	15	NUM
cana-853	174	85	(	(	PUNCT
cana-853	174	86	catastrophe	catastrophe	NOUN
cana-853	174	87	effect	effect	NOUN
cana-853	174	88	)	)	PUNCT
cana-853	174	89	.	.	PUNCT
cana-853	175	1	in	in	ADP
cana-853	175	2	fig	fig	NOUN
cana-853	175	3	2,as	2,as	NUM
cana-853	175	4	the	the	DET
cana-853	175	5	value	value	NOUN
cana-853	175	6	of	of	ADP
cana-853	175	7	λ	λ	NOUN
cana-853	175	8	increases	increase	NOUN
cana-853	175	9	,	,	PUNCT
cana-853	175	10	the	the	DET
cana-853	175	11	number	number	NOUN
cana-853	175	12	of	of	ADP
cana-853	175	13	customers	customer	NOUN
cana-853	175	14	in	in	ADP
cana-853	175	15	each	each	PRON
cana-853	175	16	of	of	ADP
cana-853	175	17	the	the	DET
cana-853	175	18	three	three	NUM
cana-853	175	19	queues	queue	NOUN
cana-853	175	20	increases	increase	NOUN
cana-853	175	21	,	,	PUNCT
cana-853	175	22	and	and	CCONJ
cana-853	175	23	as	as	ADP
cana-853	175	24	the	the	DET
cana-853	175	25	value	value	NOUN
cana-853	175	26	of	of	ADP
cana-853	175	27	γ	γ	NOUN
cana-853	175	28	increases	increase	NOUN
cana-853	175	29	,	,	PUNCT
cana-853	175	30	the	the	DET
cana-853	175	31	number	number	NOUN
cana-853	175	32	of	of	ADP
cana-853	175	33	customers	customer	NOUN
cana-853	175	34	in	in	ADP
cana-853	175	35	each	each	PRON
cana-853	175	36	of	of	ADP
cana-853	175	37	the	the	DET
cana-853	175	38	queues	queue	NOUN
cana-853	175	39	decreases	decrease	VERB
cana-853	175	40	.	.	PUNCT
cana-853	176	1	table	table	NOUN
cana-853	176	2	:	:	PUNCT
cana-853	176	3	1	1	NUM
cana-853	176	4	3	3	NUM
cana-853	176	5	6	6	NUM
cana-853	176	6	9	9	NUM
cana-853	176	7	12	12	NUM
cana-853	176	8	15	15	NUM
cana-853	176	9	1	1	NUM
cana-853	176	10	0.0102	0.0102	NUM
cana-853	176	11	0.0099	0.0099	NUM
cana-853	176	12	0.0096	0.0096	NUM
cana-853	176	13	0.0094	0.0094	NUM
cana-853	176	14	0.0091	0.0091	NUM
cana-853	176	15	2	2	NUM
cana-853	176	16	0.0206	0.0206	NUM
cana-853	176	17	0.02	0.02	NUM
cana-853	176	18	0.0194	0.0194	NUM
cana-853	176	19	0.0189	0.0189	NUM
cana-853	176	20	0.0183	0.0183	NUM
cana-853	176	21	3	3	NUM
cana-853	176	22	0.0313	0.0313	NUM
cana-853	176	23	0.0303	0.0303	NUM
cana-853	176	24	0.0294	0.0294	NUM
cana-853	176	25	0.0285	0.0285	NUM
cana-853	176	26	0.0277	0.0277	NUM
cana-853	176	27	4	4	NUM
cana-853	176	28	0.0421	0.0421	NUM
cana-853	176	29	0.0408	0.0408	NUM
cana-853	176	30	0.0395	0.0395	NUM
cana-853	176	31	0.0384	0.0384	NUM
cana-853	176	32	0.0373	0.0373	NUM
cana-853	176	33	5	5	NUM
cana-853	176	34	0.0532	0.0532	NUM
cana-853	176	35	0.0515	0.0515	NUM
cana-853	176	36	0.0499	0.0499	NUM
cana-853	176	37	0.0484	0.0484	NUM
cana-853	176	38	0.0469	0.0469	NUM
cana-853	176	39	6	6	NUM
cana-853	176	40	0.0645	0.0645	NUM
cana-853	176	41	0.0624	0.0624	NUM
cana-853	177	1	0.0604	0.0604	NUM
cana-853	177	2	0.0585	0.0585	NUM
cana-853	177	3	0.0568	0.0568	NUM
cana-853	177	4	7	7	NUM
cana-853	177	5	0.0761	0.0761	NUM
cana-853	177	6	0.0735	0.0735	NUM
cana-853	177	7	0.0711	0.0711	NUM
cana-853	177	8	0.0689	0.0689	NUM
cana-853	177	9	0.0668	0.0668	NUM
cana-853	177	10	8	8	NUM
cana-853	177	11	0.0879	0.0879	NUM
cana-853	177	12	0.0848	0.0848	NUM
cana-853	177	13	0.082	0.082	NUM
cana-853	177	14	0.0794	0.0794	NUM
cana-853	177	15	0.077	0.077	NUM
cana-853	177	16	9	9	NUM
cana-853	177	17	0.0999	0.0999	NUM
cana-853	177	18	0.0964	0.0964	NUM
cana-853	177	19	0.0931	0.0931	NUM
cana-853	177	20	0.0901	0.0901	NUM
cana-853	177	21	0.0873	0.0873	NUM
cana-853	177	22	10	10	NUM
cana-853	177	23	0.1122	0.1122	NUM
cana-853	177	24	0.1082	0.1082	NUM
cana-853	177	25	0.1044	0.1044	NUM
cana-853	177	26	0.101	0.101	NUM
cana-853	177	27	0.0978	0.0978	NUM
cana-853	177	28	fig	fig	NOUN
cana-853	177	29	:	:	PUNCT
cana-853	177	30	2	2	NUM
cana-853	177	31	number	number	NOUN
cana-853	177	32	of	of	ADP
cana-853	177	33	customers	customer	NOUN
cana-853	177	34	in	in	ADP
cana-853	177	35	all	all	DET
cana-853	177	36	the	the	DET
cana-853	177	37	queues	queue	NOUN
cana-853	177	38	communications	communication	NOUN
cana-853	177	39	on	on	ADP
cana-853	177	40	applied	apply	VERB
cana-853	177	41	nonlinear	nonlinear	ADJ
cana-853	177	42	analysis	analysis	NOUN
cana-853	177	43	issn	issn	NOUN
cana-853	177	44	:	:	PUNCT
cana-853	177	45	1074	1074	NUM
cana-853	177	46	-	-	PUNCT
cana-853	177	47	133x	133x	NUM
cana-853	177	48	vol	vol	NOUN
cana-853	177	49	31	31	NUM
cana-853	177	50	no	no	NOUN
cana-853	177	51	.	.	PUNCT
cana-853	178	1	4s	4s	NUM
cana-853	178	2	(	(	PUNCT
cana-853	178	3	2024	2024	NUM
cana-853	178	4	)	)	PUNCT
cana-853	178	5	304	304	NUM
cana-853	179	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-853	179	2	waiting	waiting	NOUN
cana-853	179	3	time	time	NOUN
cana-853	179	4	of	of	ADP
cana-853	179	5	a	a	DET
cana-853	179	6	customer	customer	NOUN
cana-853	179	7	in	in	ADP
cana-853	179	8	all	all	DET
cana-853	179	9	the	the	DET
cana-853	179	10	three	three	NUM
cana-853	179	11	queues	queue	NOUN
cana-853	179	12	the	the	DET
cana-853	179	13	waiting	waiting	NOUN
cana-853	179	14	time	time	NOUN
cana-853	179	15	of	of	ADP
cana-853	179	16	the	the	DET
cana-853	179	17	customers	customer	NOUN
cana-853	179	18	in	in	ADP
cana-853	179	19	all	all	DET
cana-853	179	20	the	the	DET
cana-853	179	21	three	three	NUM
cana-853	179	22	queues	queue	NOUN
cana-853	179	23	are	be	AUX
cana-853	179	24	calculated	calculate	VERB
cana-853	179	25	in	in	ADP
cana-853	179	26	table	table	NOUN
cana-853	179	27	2	2	NUM
cana-853	179	28	for	for	ADP
cana-853	179	29	�	�	NOUN
cana-853	179	30	̅	̅	NOUN
cana-853	179	31	�	�	NOUN
cana-853	179	32	=	=	SYM
cana-853	179	33	0.3	0.3	NUM
cana-853	179	34	,	,	PUNCT
cana-853	179	35	�	�	NOUN
cana-853	179	36	̅	̅	NOUN
cana-853	179	37	�	�	NOUN
cana-853	179	38	=	=	SYM
cana-853	179	39	0.5	0.5	NUM
cana-853	179	40	,	,	PUNCT
cana-853	179	41	r	r	NOUN
cana-853	179	42	=	=	SYM
cana-853	179	43	0.4	0.4	NUM
cana-853	179	44	,	,	PUNCT
cana-853	179	45	μ1	μ1	PROPN
cana-853	179	46	=	=	SYM
cana-853	179	47	6	6	NUM
cana-853	179	48	,	,	PUNCT
cana-853	179	49	μ2	μ2	NOUN
cana-853	179	50	=	=	SYM
cana-853	179	51	4	4	NUM
cana-853	179	52	,	,	PUNCT
cana-853	179	53	μ3	μ3	NOUN
cana-853	179	54	=	=	SYM
cana-853	179	55	8	8	NUM
cana-853	179	56	,	,	PUNCT
cana-853	179	57	μ4	μ4	NOUN
cana-853	179	58	=	=	SYM
cana-853	179	59	9	9	NUM
cana-853	179	60	,	,	PUNCT
cana-853	179	61	μ5	μ5	NOUN
cana-853	179	62	=	=	NOUN
cana-853	179	63	10	10	NUM
cana-853	179	64	,	,	PUNCT
cana-853	179	65	λ	λ	X
cana-853	179	66	=	=	NOUN
cana-853	179	67	1,2,3	1,2,3	NUM
cana-853	179	68	…	…	PUNCT
cana-853	179	69	.10	.10	NUM
cana-853	179	70	,	,	PUNCT
cana-853	179	71	γ	γ	X
cana-853	179	72	=	=	SYM
cana-853	179	73	3	3	NUM
cana-853	179	74	,	,	PUNCT
cana-853	179	75	6	6	NUM
cana-853	179	76	,	,	PUNCT
cana-853	179	77	9	9	NUM
cana-853	179	78	,	,	PUNCT
cana-853	179	79	12	12	NUM
cana-853	179	80	,	,	PUNCT
cana-853	179	81	15	15	NUM
cana-853	179	82	(	(	PUNCT
cana-853	179	83	catastrophe	catastrophe	NOUN
cana-853	179	84	effect	effect	NOUN
cana-853	179	85	)	)	PUNCT
cana-853	179	86	.	.	PUNCT
cana-853	180	1	in	in	ADP
cana-853	180	2	fig	fig	NOUN
cana-853	180	3	2	2	NUM
cana-853	180	4	,	,	PUNCT
cana-853	180	5	as	as	ADP
cana-853	180	6	the	the	DET
cana-853	180	7	value	value	NOUN
cana-853	180	8	of	of	ADP
cana-853	180	9	λ	λ	NOUN
cana-853	180	10	increases	increase	NOUN
cana-853	180	11	,	,	PUNCT
cana-853	180	12	customers	customer	NOUN
cana-853	180	13	'	'	PART
cana-853	180	14	waiting	waiting	NOUN
cana-853	180	15	times	time	NOUN
cana-853	180	16	in	in	ADP
cana-853	180	17	each	each	PRON
cana-853	180	18	of	of	ADP
cana-853	180	19	the	the	DET
cana-853	180	20	three	three	NUM
cana-853	180	21	lines	line	NOUN
cana-853	180	22	are	be	AUX
cana-853	180	23	getting	get	VERB
cana-853	180	24	higher	high	ADJ
cana-853	180	25	,	,	PUNCT
cana-853	180	26	and	and	CCONJ
cana-853	180	27	as	as	ADP
cana-853	180	28	the	the	DET
cana-853	180	29	value	value	NOUN
cana-853	180	30	of	of	ADP
cana-853	180	31	γ	γ	NOUN
cana-853	180	32	increases	increase	NOUN
cana-853	180	33	,	,	PUNCT
cana-853	180	34	the	the	DET
cana-853	180	35	waiting	waiting	NOUN
cana-853	180	36	time	time	NOUN
cana-853	180	37	of	of	ADP
cana-853	180	38	customers	customer	NOUN
cana-853	180	39	in	in	ADP
cana-853	180	40	each	each	PRON
cana-853	180	41	of	of	ADP
cana-853	180	42	the	the	DET
cana-853	180	43	queues	queue	NOUN
cana-853	180	44	decreases	decrease	VERB
cana-853	180	45	.	.	PUNCT
cana-853	181	1	table	table	NOUN
cana-853	181	2	:	:	PUNCT
cana-853	181	3	2	2	NUM
cana-853	181	4	3	3	NUM
cana-853	181	5	6	6	NUM
cana-853	181	6	9	9	NUM
cana-853	181	7	12	12	NUM
cana-853	181	8	15	15	NUM
cana-853	181	9	1	1	NUM
cana-853	181	10	0.0102	0.0102	NUM
cana-853	181	11	0.0099	0.0099	NUM
cana-853	181	12	0.0096	0.0096	NUM
cana-853	181	13	0.0094	0.0094	NUM
cana-853	181	14	0.0091	0.0091	NUM
cana-853	181	15	2	2	NUM
cana-853	181	16	0.0103	0.0103	NUM
cana-853	181	17	0.01	0.01	NUM
cana-853	181	18	0.0097	0.0097	NUM
cana-853	181	19	0.0094	0.0094	NUM
cana-853	181	20	0.0092	0.0092	NUM
cana-853	181	21	3	3	NUM
cana-853	181	22	0.0104	0.0104	NUM
cana-853	181	23	0.0101	0.0101	NUM
cana-853	181	24	0.0098	0.0098	NUM
cana-853	181	25	0.0095	0.0095	NUM
cana-853	181	26	0.0092	0.0092	NUM
cana-853	181	27	4	4	NUM
cana-853	181	28	0.0105	0.0105	NUM
cana-853	181	29	0.0102	0.0102	NUM
cana-853	181	30	0.0099	0.0099	NUM
cana-853	181	31	0.0096	0.0096	NUM
cana-853	181	32	0.0093	0.0093	NUM
cana-853	181	33	5	5	NUM
cana-853	181	34	0.0106	0.0106	NUM
cana-853	181	35	0.0103	0.0103	NUM
cana-853	181	36	0.01	0.01	NUM
cana-853	181	37	0.0097	0.0097	NUM
cana-853	181	38	0.0094	0.0094	NUM
cana-853	181	39	6	6	NUM
cana-853	181	40	0.0108	0.0108	NUM
cana-853	181	41	0.0104	0.0104	NUM
cana-853	181	42	0.0101	0.0101	NUM
cana-853	181	43	0.0098	0.0098	NUM
cana-853	181	44	0.0095	0.0095	NUM
cana-853	181	45	7	7	NUM
cana-853	181	46	0.0109	0.0109	NUM
cana-853	181	47	0.0105	0.0105	NUM
cana-853	181	48	0.0102	0.0102	NUM
cana-853	181	49	0.0098	0.0098	NUM
cana-853	181	50	0.0095	0.0095	NUM
cana-853	181	51	8	8	NUM
cana-853	181	52	0.011	0.011	NUM
cana-853	181	53	0.0106	0.0106	NUM
cana-853	181	54	0.0103	0.0103	NUM
cana-853	181	55	0.0099	0.0099	NUM
cana-853	181	56	0.0096	0.0096	NUM
cana-853	181	57	9	9	NUM
cana-853	181	58	0.0111	0.0111	NUM
cana-853	181	59	0.0107	0.0107	NUM
cana-853	181	60	0.0103	0.0103	NUM
cana-853	181	61	0.01	0.01	NUM
cana-853	181	62	0.0097	0.0097	NUM
cana-853	181	63	10	10	NUM
cana-853	181	64	0.0112	0.0112	NUM
cana-853	181	65	0.0108	0.0108	NUM
cana-853	181	66	0.0104	0.0104	NUM
cana-853	181	67	0.0101	0.0101	NUM
cana-853	181	68	0.0098	0.0098	NUM
cana-853	181	69	fig	fig	NOUN
cana-853	181	70	:	:	PUNCT
cana-853	181	71	3	3	NUM
cana-853	181	72	waiting	waiting	NOUN
cana-853	181	73	time	time	NOUN
cana-853	181	74	of	of	ADP
cana-853	181	75	consumers	consumer	NOUN
cana-853	181	76	in	in	ADP
cana-853	181	77	all	all	DET
cana-853	181	78	the	the	DET
cana-853	181	79	three	three	NUM
cana-853	181	80	queues	queue	NOUN
cana-853	181	81	communications	communication	NOUN
cana-853	181	82	on	on	ADP
cana-853	181	83	applied	apply	VERB
cana-853	181	84	nonlinear	nonlinear	ADJ
cana-853	181	85	analysis	analysis	NOUN
cana-853	181	86	issn	issn	NOUN
cana-853	181	87	:	:	PUNCT
cana-853	181	88	1074	1074	NUM
cana-853	181	89	-	-	PUNCT
cana-853	181	90	133x	133x	NUM
cana-853	181	91	vol	vol	NOUN
cana-853	181	92	31	31	NUM
cana-853	181	93	no	no	NOUN
cana-853	181	94	.	.	PUNCT
cana-853	182	1	4s	4s	NUM
cana-853	182	2	(	(	PUNCT
cana-853	182	3	2024	2024	NUM
cana-853	182	4	)	)	PUNCT
cana-853	182	5	305	305	NUM
cana-853	182	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-853	182	7	number	number	NOUN
cana-853	182	8	of	of	ADP
cana-853	182	9	consumers	consumer	NOUN
cana-853	182	10	in	in	ADP
cana-853	182	11	the	the	DET
cana-853	182	12	system	system	NOUN
cana-853	182	13	the	the	DET
cana-853	182	14	number	number	NOUN
cana-853	182	15	of	of	ADP
cana-853	182	16	the	the	DET
cana-853	182	17	vendors	vendor	NOUN
cana-853	182	18	in	in	ADP
cana-853	182	19	the	the	DET
cana-853	182	20	system	system	NOUN
cana-853	182	21	are	be	AUX
cana-853	182	22	calculated	calculate	VERB
cana-853	182	23	in	in	ADP
cana-853	182	24	table	table	NOUN
cana-853	182	25	3	3	NUM
cana-853	182	26	for	for	ADP
cana-853	182	27	�	�	NOUN
cana-853	182	28	̅	̅	NOUN
cana-853	182	29	�	�	NOUN
cana-853	182	30	=	=	SYM
cana-853	182	31	0.3,	0.3,	NUM
cana-853	182	32	�	�	NOUN
cana-853	182	33	̅	̅	NOUN
cana-853	182	34	�	�	NOUN
cana-853	182	35	=	=	SYM
cana-853	182	36	0.5	0.5	NUM
cana-853	182	37	,	,	PUNCT
cana-853	182	38	r	r	NOUN
cana-853	182	39	=	=	SYM
cana-853	182	40	0.4,μ1	0.4,μ1	NUM
cana-853	182	41	=	=	SYM
cana-853	182	42	5	5	NUM
cana-853	182	43	,	,	PUNCT
cana-853	182	44	6	6	NUM
cana-853	182	45	,	,	PUNCT
cana-853	182	46	7	7	NUM
cana-853	182	47	,	,	PUNCT
cana-853	182	48	8	8	NUM
cana-853	182	49	,	,	PUNCT
cana-853	182	50	9	9	NUM
cana-853	182	51	,	,	PUNCT
cana-853	182	52	10	10	NUM
cana-853	182	53	,	,	PUNCT
cana-853	182	54	11	11	NUM
cana-853	182	55	,	,	PUNCT
cana-853	182	56	12	12	NUM
cana-853	182	57	,	,	PUNCT
cana-853	182	58	13	13	NUM
cana-853	182	59	,	,	PUNCT
cana-853	182	60	14	14	NUM
cana-853	182	61	,	,	PUNCT
cana-853	182	62	μ2	μ2	NOUN
cana-853	182	63	=	=	SYM
cana-853	182	64	4	4	NUM
cana-853	182	65	,	,	PUNCT
cana-853	182	66	μ3	μ3	NOUN
cana-853	182	67	=	=	SYM
cana-853	182	68	8	8	NUM
cana-853	182	69	,	,	PUNCT
cana-853	182	70	μ4	μ4	NOUN
cana-853	182	71	=	=	SYM
cana-853	182	72	9	9	NUM
cana-853	182	73	,	,	PUNCT
cana-853	182	74	μ5	μ5	NOUN
cana-853	182	75	=	=	NOUN
cana-853	182	76	10	10	NUM
cana-853	182	77	,	,	PUNCT
cana-853	182	78	λ	λ	X
cana-853	182	79	=	=	SYM
cana-853	182	80	5	5	NUM
cana-853	182	81	,	,	PUNCT
cana-853	182	82	γ	γ	NOUN
cana-853	182	83	=	=	SYM
cana-853	182	84	3	3	NUM
cana-853	182	85	,	,	PUNCT
cana-853	182	86	6	6	NUM
cana-853	182	87	,	,	PUNCT
cana-853	182	88	9	9	NUM
cana-853	182	89	,	,	PUNCT
cana-853	182	90	12	12	NUM
cana-853	182	91	,	,	PUNCT
cana-853	182	92	15	15	NUM
cana-853	182	93	(	(	PUNCT
cana-853	182	94	catastrophe	catastrophe	NOUN
cana-853	182	95	effect	effect	NOUN
cana-853	182	96	)	)	PUNCT
cana-853	182	97	.	.	PUNCT
cana-853	183	1	in	in	ADP
cana-853	183	2	fig	fig	NOUN
cana-853	183	3	4	4	NUM
cana-853	183	4	,	,	PUNCT
cana-853	183	5	as	as	SCONJ
cana-853	183	6	the	the	DET
cana-853	183	7	service	service	NOUN
cana-853	183	8	cost	cost	NOUN
cana-853	183	9	rises	rise	NOUN
cana-853	183	10	and	and	CCONJ
cana-853	183	11	for	for	ADP
cana-853	183	12	distinct	distinct	ADJ
cana-853	183	13	values	value	NOUN
cana-853	183	14	of	of	ADP
cana-853	183	15	γ	γ	X
cana-853	183	16	,	,	PUNCT
cana-853	183	17	the	the	DET
cana-853	183	18	number	number	NOUN
cana-853	183	19	of	of	ADP
cana-853	183	20	consumers	consumer	NOUN
cana-853	183	21	in	in	ADP
cana-853	183	22	the	the	DET
cana-853	183	23	system	system	NOUN
cana-853	183	24	decreases	decrease	VERB
cana-853	183	25	.	.	PUNCT
cana-853	184	1	table	table	NOUN
cana-853	184	2	:	:	PUNCT
cana-853	184	3	3	3	NUM
cana-853	184	4	3	3	NUM
cana-853	184	5	6	6	NUM
cana-853	184	6	9	9	NUM
cana-853	184	7	12	12	NUM
cana-853	184	8	15	15	NUM
cana-853	184	9	5	5	NUM
cana-853	184	10	1.0537	1.0537	NUM
cana-853	184	11	1.052	1.052	NUM
cana-853	184	12	1.0503	1.0503	NUM
cana-853	184	13	1.0488	1.0488	NUM
cana-853	184	14	1.0473	1.0473	NUM
cana-853	184	15	6	6	NUM
cana-853	184	16	0.8865	0.8865	NUM
cana-853	184	17	0.8848	0.8848	NUM
cana-853	184	18	0.8832	0.8832	NUM
cana-853	184	19	0.8817	0.8817	NUM
cana-853	184	20	0.8803	0.8803	NUM
cana-853	184	21	7	7	NUM
cana-853	184	22	0.767	0.767	NUM
cana-853	184	23	0.7653	0.7653	NUM
cana-853	184	24	0.7637	0.7637	NUM
cana-853	184	25	0.7622	0.7622	NUM
cana-853	184	26	0.7608	0.7608	NUM
cana-853	184	27	8	8	NUM
cana-853	184	28	0.6772	0.6772	NUM
cana-853	184	29	0.6756	0.6756	NUM
cana-853	184	30	0.674	0.674	NUM
cana-853	184	31	0.6725	0.6725	NUM
cana-853	184	32	0.6712	0.6712	NUM
cana-853	184	33	9	9	NUM
cana-853	184	34	0.6073	0.6073	NUM
cana-853	184	35	0.6057	0.6057	NUM
cana-853	184	36	0.6041	0.6041	NUM
cana-853	184	37	0.6027	0.6027	NUM
cana-853	184	38	0.6013	0.6013	NUM
cana-853	185	1	10	10	NUM
cana-853	185	2	0.5513	0.5513	NUM
cana-853	185	3	0.5497	0.5497	NUM
cana-853	185	4	0.5482	0.5482	NUM
cana-853	186	1	0.5467	0.5467	NUM
cana-853	186	2	0.5454	0.5454	NUM
cana-853	186	3	11	11	NUM
cana-853	186	4	0.5053	0.5053	NUM
cana-853	186	5	0.5038	0.5038	NUM
cana-853	186	6	0.5023	0.5023	NUM
cana-853	186	7	0.5009	0.5009	NUM
cana-853	186	8	0.4996	0.4996	NUM
cana-853	186	9	12	12	NUM
cana-853	186	10	0.467	0.467	NUM
cana-853	186	11	0.4655	0.4655	NUM
cana-853	186	12	0.464	0.464	NUM
cana-853	186	13	0.4626	0.4626	NUM
cana-853	186	14	0.4614	0.4614	NUM
cana-853	186	15	13	13	NUM
cana-853	186	16	0.4345	0.4345	NUM
cana-853	186	17	0.433	0.433	NUM
cana-853	186	18	0.4316	0.4316	NUM
cana-853	186	19	0.4302	0.4302	NUM
cana-853	186	20	0.429	0.429	NUM
cana-853	186	21	14	14	NUM
cana-853	186	22	0.4066	0.4066	NUM
cana-853	186	23	0.4051	0.4051	NUM
cana-853	186	24	0.4037	0.4037	NUM
cana-853	186	25	0.4024	0.4024	NUM
cana-853	186	26	0.4011	0.4011	NUM
cana-853	186	27	fig	fig	NOUN
cana-853	186	28	:	:	PUNCT
cana-853	186	29	4total	4total	NUM
cana-853	186	30	amount	amount	NOUN
cana-853	186	31	of	of	ADP
cana-853	186	32	consumers	consumer	NOUN
cana-853	186	33	in	in	ADP
cana-853	186	34	the	the	DET
cana-853	186	35	system	system	NOUN
cana-853	186	36	communications	communication	NOUN
cana-853	186	37	on	on	ADP
cana-853	186	38	applied	apply	VERB
cana-853	186	39	nonlinear	nonlinear	ADJ
cana-853	186	40	analysis	analysis	NOUN
cana-853	186	41	issn	issn	NOUN
cana-853	186	42	:	:	PUNCT
cana-853	186	43	1074	1074	NUM
cana-853	186	44	-	-	PUNCT
cana-853	186	45	133x	133x	NUM
cana-853	186	46	vol	vol	NOUN
cana-853	186	47	31	31	NUM
cana-853	186	48	no	no	NOUN
cana-853	186	49	.	.	PUNCT
cana-853	187	1	4s	4s	NUM
cana-853	187	2	(	(	PUNCT
cana-853	187	3	2024	2024	NUM
cana-853	187	4	)	)	PUNCT
cana-853	187	5	306	306	NUM
cana-853	187	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-853	187	7	waiting	waiting	NOUN
cana-853	187	8	time	time	NOUN
cana-853	187	9	of	of	ADP
cana-853	187	10	the	the	DET
cana-853	187	11	consumers	consumer	NOUN
cana-853	187	12	in	in	ADP
cana-853	187	13	the	the	DET
cana-853	187	14	system	system	NOUN
cana-853	187	15	the	the	DET
cana-853	187	16	total	total	ADJ
cana-853	187	17	amount	amount	NOUN
cana-853	187	18	of	of	ADP
cana-853	187	19	consumers	consumer	NOUN
cana-853	187	20	in	in	ADP
cana-853	187	21	the	the	DET
cana-853	187	22	system	system	NOUN
cana-853	187	23	are	be	AUX
cana-853	187	24	calculated	calculate	VERB
cana-853	187	25	in	in	ADP
cana-853	187	26	table	table	NOUN
cana-853	187	27	4	4	NUM
cana-853	187	28	for	for	ADP
cana-853	187	29	�	�	NOUN
cana-853	187	30	̅	̅	NOUN
cana-853	187	31	�	�	NOUN
cana-853	187	32	=	=	SYM
cana-853	187	33	0.3,	0.3,	NUM
cana-853	187	34	�	�	NOUN
cana-853	187	35	̅	̅	NOUN
cana-853	187	36	�	�	NOUN
cana-853	187	37	=	=	SYM
cana-853	187	38	0.5	0.5	NUM
cana-853	187	39	,	,	PUNCT
cana-853	187	40	r	r	NOUN
cana-853	187	41	=	=	SYM
cana-853	187	42	0.4,μ1	0.4,μ1	NUM
cana-853	187	43	=	=	SYM
cana-853	187	44	5	5	NUM
cana-853	187	45	,	,	PUNCT
cana-853	187	46	6	6	NUM
cana-853	187	47	,	,	PUNCT
cana-853	187	48	7	7	NUM
cana-853	187	49	,	,	PUNCT
cana-853	187	50	8	8	NUM
cana-853	187	51	,	,	PUNCT
cana-853	187	52	9	9	NUM
cana-853	187	53	,	,	PUNCT
cana-853	187	54	10	10	NUM
cana-853	187	55	,	,	PUNCT
cana-853	187	56	11	11	NUM
cana-853	187	57	,	,	PUNCT
cana-853	187	58	12	12	NUM
cana-853	187	59	,	,	PUNCT
cana-853	187	60	13	13	NUM
cana-853	187	61	,	,	PUNCT
cana-853	187	62	14	14	NUM
cana-853	187	63	,	,	PUNCT
cana-853	187	64	μ2	μ2	NOUN
cana-853	187	65	=	=	SYM
cana-853	187	66	4	4	NUM
cana-853	187	67	,	,	PUNCT
cana-853	187	68	μ3	μ3	NOUN
cana-853	187	69	=	=	SYM
cana-853	187	70	8	8	NUM
cana-853	187	71	,	,	PUNCT
cana-853	187	72	μ4	μ4	NOUN
cana-853	187	73	=	=	SYM
cana-853	187	74	9	9	NUM
cana-853	187	75	,	,	PUNCT
cana-853	187	76	μ5	μ5	NOUN
cana-853	187	77	=	=	NOUN
cana-853	187	78	10	10	NUM
cana-853	187	79	,	,	PUNCT
cana-853	187	80	λ	λ	X
cana-853	187	81	=	=	SYM
cana-853	187	82	5	5	NUM
cana-853	187	83	,	,	PUNCT
cana-853	187	84	γ	γ	NOUN
cana-853	187	85	=	=	SYM
cana-853	187	86	3	3	NUM
cana-853	187	87	,	,	PUNCT
cana-853	187	88	6	6	NUM
cana-853	187	89	,	,	PUNCT
cana-853	187	90	9	9	NUM
cana-853	187	91	,	,	PUNCT
cana-853	187	92	12	12	NUM
cana-853	187	93	,	,	PUNCT
cana-853	187	94	15	15	NUM
cana-853	187	95	(	(	PUNCT
cana-853	187	96	catastrophe	catastrophe	NOUN
cana-853	187	97	effect	effect	NOUN
cana-853	187	98	)	)	PUNCT
cana-853	187	99	.	.	PUNCT
cana-853	188	1	in	in	ADP
cana-853	188	2	fig	fig	NOUN
cana-853	188	3	5	5	NUM
cana-853	188	4	,	,	PUNCT
cana-853	188	5	when	when	SCONJ
cana-853	188	6	the	the	DET
cana-853	188	7	service	service	NOUN
cana-853	188	8	cost	cost	NOUN
cana-853	188	9	rises	rise	NOUN
cana-853	188	10	and	and	CCONJ
cana-853	188	11	for	for	ADP
cana-853	188	12	different	different	ADJ
cana-853	188	13	values	value	NOUN
cana-853	188	14	ofγ	ofγ	VERB
cana-853	188	15	,	,	PUNCT
cana-853	188	16	thetotal	thetotal	ADJ
cana-853	188	17	amount	amount	NOUN
cana-853	188	18	of	of	ADP
cana-853	188	19	vendors	vendor	NOUN
cana-853	188	20	in	in	ADP
cana-853	188	21	the	the	DET
cana-853	188	22	system	system	NOUN
cana-853	188	23	decreases	decrease	VERB
cana-853	188	24	.	.	PUNCT
cana-853	189	1	table	table	NOUN
cana-853	189	2	:	:	PUNCT
cana-853	189	3	4	4	NUM
cana-853	189	4	3	3	NUM
cana-853	189	5	6	6	NUM
cana-853	189	6	9	9	NUM
cana-853	189	7	12	12	NUM
cana-853	189	8	15	15	NUM
cana-853	189	9	5	5	NUM
cana-853	189	10	0.2107	0.2107	NUM
cana-853	189	11	0.2104	0.2104	NUM
cana-853	190	1	0.2101	0.2101	NUM
cana-853	190	2	0.2098	0.2098	NUM
cana-853	190	3	0.2095	0.2095	NUM
cana-853	190	4	6	6	NUM
cana-853	190	5	0.1773	0.1773	NUM
cana-853	190	6	0.177	0.177	NUM
cana-853	190	7	0.1766	0.1766	NUM
cana-853	190	8	0.1763	0.1763	NUM
cana-853	190	9	0.1761	0.1761	NUM
cana-853	190	10	7	7	NUM
cana-853	190	11	0.1534	0.1534	NUM
cana-853	190	12	0.1531	0.1531	NUM
cana-853	190	13	0.1527	0.1527	NUM
cana-853	190	14	0.1524	0.1524	NUM
cana-853	190	15	0.1522	0.1522	NUM
cana-853	190	16	8	8	NUM
cana-853	190	17	0.1354	0.1354	NUM
cana-853	190	18	0.1351	0.1351	NUM
cana-853	190	19	0.1348	0.1348	NUM
cana-853	190	20	0.1345	0.1345	NUM
cana-853	190	21	0.1342	0.1342	NUM
cana-853	190	22	9	9	NUM
cana-853	190	23	0.1215	0.1215	NUM
cana-853	190	24	0.1211	0.1211	NUM
cana-853	190	25	0.1208	0.1208	NUM
cana-853	190	26	0.1205	0.1205	NUM
cana-853	190	27	0.1203	0.1203	NUM
cana-853	190	28	10	10	NUM
cana-853	190	29	0.1103	0.1103	NUM
cana-853	190	30	0.1099	0.1099	NUM
cana-853	190	31	0.1096	0.1096	NUM
cana-853	190	32	0.1093	0.1093	NUM
cana-853	190	33	0.1091	0.1091	NUM
cana-853	190	34	11	11	NUM
cana-853	190	35	0.1011	0.1011	NUM
cana-853	190	36	0.1008	0.1008	NUM
cana-853	190	37	0.1005	0.1005	NUM
cana-853	190	38	0.1002	0.1002	NUM
cana-853	190	39	0.0999	0.0999	NUM
cana-853	190	40	12	12	NUM
cana-853	190	41	0.0934	0.0934	NUM
cana-853	190	42	0.0931	0.0931	NUM
cana-853	190	43	0.0928	0.0928	NUM
cana-853	190	44	0.0925	0.0925	NUM
cana-853	190	45	0.0923	0.0923	NUM
cana-853	190	46	13	13	NUM
cana-853	190	47	0.0869	0.0869	NUM
cana-853	190	48	0.0866	0.0866	NUM
cana-853	190	49	0.0863	0.0863	NUM
cana-853	190	50	0.086	0.086	NUM
cana-853	190	51	0.0858	0.0858	NUM
cana-853	190	52	14	14	NUM
cana-853	190	53	0.0813	0.0813	NUM
cana-853	190	54	0.081	0.081	NUM
cana-853	190	55	0.0807	0.0807	NUM
cana-853	190	56	0.0805	0.0805	NUM
cana-853	190	57	0.0802	0.0802	NUM
cana-853	190	58	fig	fig	NOUN
cana-853	190	59	:	:	PUNCT
cana-853	190	60	5	5	NUM
cana-853	190	61	waiting	waiting	NOUN
cana-853	190	62	time	time	NOUN
cana-853	190	63	of	of	ADP
cana-853	190	64	the	the	DET
cana-853	190	65	customer	customer	NOUN
cana-853	190	66	in	in	ADP
cana-853	190	67	the	the	DET
cana-853	190	68	system	system	NOUN
cana-853	190	69	node	node	VERB
cana-853	190	70	one	one	NUM
cana-853	190	71	-number	-number	NOUN
cana-853	190	72	of	of	ADP
cana-853	190	73	customers	customer	NOUN
cana-853	190	74	the	the	DET
cana-853	190	75	customers	customer	NOUN
cana-853	190	76	in	in	ADP
cana-853	190	77	node	node	NOUN
cana-853	190	78	one	one	NUM
cana-853	190	79	are	be	AUX
cana-853	190	80	calculated	calculate	VERB
cana-853	190	81	in	in	ADP
cana-853	190	82	table	table	NOUN
cana-853	190	83	5	5	NUM
cana-853	190	84	for	for	ADP
cana-853	190	85	�	�	NOUN
cana-853	190	86	̅	̅	NOUN
cana-853	190	87	�	�	NOUN
cana-853	190	88	=	=	SYM
cana-853	190	89	0.3	0.3	NUM
cana-853	190	90	,	,	PUNCT
cana-853	190	91	�	�	NOUN
cana-853	190	92	̅	̅	NOUN
cana-853	190	93	�	�	NOUN
cana-853	190	94	=	=	SYM
cana-853	190	95	0.5	0.5	NUM
cana-853	190	96	,	,	PUNCT
cana-853	190	97	r	r	NOUN
cana-853	190	98	=	=	SYM
cana-853	190	99	0.4	0.4	NUM
cana-853	190	100	,	,	PUNCT
cana-853	190	101	μ1	μ1	PROPN
cana-853	190	102	=	=	SYM
cana-853	190	103	6	6	NUM
cana-853	190	104	,	,	PUNCT
cana-853	190	105	μ2	μ2	NOUN
cana-853	190	106	=	=	SYM
cana-853	190	107	4	4	NUM
cana-853	190	108	,	,	PUNCT
cana-853	190	109	μ3	μ3	NOUN
cana-853	190	110	=	=	SYM
cana-853	190	111	8	8	NUM
cana-853	190	112	,	,	PUNCT
cana-853	190	113	μ4	μ4	NOUN
cana-853	190	114	=	=	SYM
cana-853	190	115	9	9	NUM
cana-853	190	116	,	,	PUNCT
cana-853	190	117	μ5	μ5	NOUN
cana-853	190	118	=	=	NOUN
cana-853	190	119	10	10	NUM
cana-853	190	120	,	,	PUNCT
cana-853	190	121	λ	λ	X
cana-853	190	122	=	=	NOUN
cana-853	190	123	1,2,3	1,2,3	NUM
cana-853	190	124	…	…	PUNCT
cana-853	190	125	.10	.10	NUM
cana-853	190	126	,	,	PUNCT
cana-853	190	127	γ	γ	X
cana-853	190	128	=	=	SYM
cana-853	190	129	3	3	NUM
cana-853	190	130	,	,	PUNCT
cana-853	190	131	6	6	NUM
cana-853	190	132	,	,	PUNCT
cana-853	190	133	9	9	NUM
cana-853	190	134	,	,	PUNCT
cana-853	190	135	12	12	NUM
cana-853	190	136	,	,	PUNCT
cana-853	190	137	15	15	NUM
cana-853	190	138	(	(	PUNCT
cana-853	190	139	catastrophe	catastrophe	NOUN
cana-853	190	140	effect	effect	NOUN
cana-853	190	141	)	)	PUNCT
cana-853	190	142	.	.	PUNCT
cana-853	191	1	communications	communication	NOUN
cana-853	191	2	on	on	ADP
cana-853	191	3	applied	apply	VERB
cana-853	191	4	nonlinear	nonlinear	ADJ
cana-853	191	5	analysis	analysis	NOUN
cana-853	191	6	issn	issn	NOUN
cana-853	191	7	:	:	PUNCT
cana-853	191	8	1074	1074	NUM
cana-853	191	9	-	-	PUNCT
cana-853	191	10	133x	133x	NUM
cana-853	191	11	vol	vol	NOUN
cana-853	191	12	31	31	NUM
cana-853	191	13	no	no	NOUN
cana-853	191	14	.	.	PUNCT
cana-853	192	1	4s	4s	NUM
cana-853	192	2	(	(	PUNCT
cana-853	192	3	2024	2024	NUM
cana-853	192	4	)	)	PUNCT
cana-853	192	5	307	307	NUM
cana-853	192	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-853	192	7	in	in	ADP
cana-853	192	8	fig	fig	NOUN
cana-853	192	9	6	6	NUM
cana-853	192	10	,	,	PUNCT
cana-853	192	11	as	as	ADP
cana-853	192	12	the	the	DET
cana-853	192	13	value	value	NOUN
cana-853	192	14	of	of	ADP
cana-853	192	15	λ	λ	PROPN
cana-853	192	16	increases	increase	NOUN
cana-853	192	17	,	,	PUNCT
cana-853	192	18	the	the	DET
cana-853	192	19	number	number	NOUN
cana-853	192	20	of	of	ADP
cana-853	192	21	customers	customer	NOUN
cana-853	192	22	in	in	ADP
cana-853	192	23	node	node	ADJ
cana-853	192	24	one	one	NUM
cana-853	192	25	increases	increase	NOUN
cana-853	192	26	,	,	PUNCT
cana-853	192	27	and	and	CCONJ
cana-853	192	28	as	as	ADP
cana-853	192	29	the	the	DET
cana-853	192	30	value	value	NOUN
cana-853	192	31	of	of	ADP
cana-853	192	32	γ	γ	NOUN
cana-853	192	33	increases	increase	NOUN
cana-853	192	34	,	,	PUNCT
cana-853	192	35	the	the	DET
cana-853	192	36	number	number	NOUN
cana-853	192	37	of	of	ADP
cana-853	192	38	customers	customer	NOUN
cana-853	192	39	in	in	ADP
cana-853	192	40	node	node	NOUN
cana-853	192	41	one	one	NUM
cana-853	192	42	decreases	decrease	NOUN
cana-853	192	43	.	.	PUNCT
cana-853	193	1	table	table	NOUN
cana-853	193	2	:	:	PUNCT
cana-853	193	3	5	5	NUM
cana-853	193	4	3	3	NUM
cana-853	193	5	6	6	NUM
cana-853	193	6	9	9	NUM
cana-853	193	7	12	12	NUM
cana-853	193	8	15	15	NUM
cana-853	193	9	1	1	NUM
cana-853	193	10	0.0919	0.0919	NUM
cana-853	193	11	0.0713	0.0713	NUM
cana-853	194	1	0.0584	0.0584	NUM
cana-853	194	2	0.0495	0.0495	NUM
cana-853	194	3	0.043	0.043	NUM
cana-853	194	4	2	2	NUM
cana-853	194	5	0.1963	0.1963	NUM
cana-853	194	6	0.1483	0.1483	NUM
cana-853	194	7	0.1199	0.1199	NUM
cana-853	194	8	0.101	0.101	NUM
cana-853	194	9	0.0873	0.0873	NUM
cana-853	194	10	3	3	NUM
cana-853	194	11	0.3144	0.3144	NUM
cana-853	194	12	0.231	0.231	NUM
cana-853	194	13	0.1845	0.1845	NUM
cana-853	194	14	0.1542	0.1542	NUM
cana-853	194	15	0.1328	0.1328	NUM
cana-853	194	16	4	4	NUM
cana-853	194	17	0.4473	0.4473	NUM
cana-853	194	18	0.3196	0.3196	NUM
cana-853	194	19	0.2521	0.2521	NUM
cana-853	194	20	0.2093	0.2093	NUM
cana-853	194	21	0.1794	0.1794	NUM
cana-853	194	22	5	5	NUM
cana-853	194	23	0.5961	0.5961	NUM
cana-853	194	24	0.4138	0.4138	NUM
cana-853	194	25	0.3225	0.3225	NUM
cana-853	194	26	0.2661	0.2661	NUM
cana-853	194	27	0.2272	0.2272	NUM
cana-853	194	28	6	6	NUM
cana-853	194	29	0.7611	0.7611	NUM
cana-853	194	30	0.5136	0.5136	NUM
cana-853	194	31	0.3957	0.3957	NUM
cana-853	194	32	0.3244	0.3244	NUM
cana-853	194	33	0.276	0.276	NUM
cana-853	194	34	7	7	NUM
cana-853	194	35	0.9425	0.9425	NUM
cana-853	194	36	0.6188	0.6188	NUM
cana-853	194	37	0.4716	0.4716	NUM
cana-853	194	38	0.3844	0.3844	NUM
cana-853	194	39	0.3258	0.3258	NUM
cana-853	194	40	8	8	NUM
cana-853	194	41	1.1397	1.1397	NUM
cana-853	194	42	0.729	0.729	NUM
cana-853	194	43	0.5499	0.5499	NUM
cana-853	194	44	0.4457	0.4457	NUM
cana-853	194	45	0.3765	0.3765	NUM
cana-853	194	46	9	9	NUM
cana-853	194	47	1.3521	1.3521	NUM
cana-853	194	48	0.844	0.844	NUM
cana-853	194	49	0.6305	0.6305	NUM
cana-853	194	50	0.5084	0.5084	NUM
cana-853	194	51	0.4281	0.4281	NUM
cana-853	194	52	10	10	NUM
cana-853	194	53	1.5784	1.5784	NUM
cana-853	194	54	0.9634	0.9634	NUM
cana-853	194	55	0.7133	0.7133	NUM
cana-853	194	56	0.5724	0.5724	NUM
cana-853	194	57	0.4806	0.4806	NUM
cana-853	194	58	fig	fig	NOUN
cana-853	194	59	:	:	PUNCT
cana-853	194	60	6	6	NUM
cana-853	194	61	number	number	NOUN
cana-853	194	62	of	of	ADP
cana-853	194	63	customers	customer	NOUN
cana-853	194	64	in	in	ADP
cana-853	194	65	node	node	PROPN
cana-853	194	66	one	one	NUM
cana-853	194	67	the	the	DET
cana-853	194	68	total	total	ADJ
cana-853	194	69	amount	amount	NOUN
cana-853	194	70	of	of	ADP
cana-853	194	71	consumers	consumer	NOUN
cana-853	194	72	in	in	ADP
cana-853	194	73	the	the	DET
cana-853	194	74	node	node	NOUN
cana-853	194	75	two	two	NUM
cana-853	194	76	the	the	DET
cana-853	194	77	customers	customer	NOUN
cana-853	194	78	in	in	ADP
cana-853	194	79	node	node	NOUN
cana-853	194	80	two	two	NUM
cana-853	194	81	are	be	AUX
cana-853	194	82	calculated	calculate	VERB
cana-853	194	83	in	in	ADP
cana-853	194	84	table	table	NOUN
cana-853	194	85	6	6	NUM
cana-853	194	86	for	for	ADP
cana-853	194	87	�	�	NOUN
cana-853	194	88	̅	̅	NOUN
cana-853	194	89	�	�	NOUN
cana-853	194	90	=	=	SYM
cana-853	194	91	0.3,	0.3,	NUM
cana-853	194	92	�	�	NOUN
cana-853	194	93	̅	̅	NOUN
cana-853	194	94	�	�	NOUN
cana-853	194	95	=	=	SYM
cana-853	194	96	0.5	0.5	NUM
cana-853	194	97	,	,	PUNCT
cana-853	194	98	r	r	NOUN
cana-853	194	99	=	=	SYM
cana-853	194	100	0.4,μ1	0.4,μ1	NUM
cana-853	194	101	=	=	SYM
cana-853	194	102	6	6	NUM
cana-853	194	103	,	,	PUNCT
cana-853	194	104	μ2	μ2	NOUN
cana-853	194	105	=	=	SYM
cana-853	194	106	4	4	NUM
cana-853	194	107	,	,	PUNCT
cana-853	194	108	μ3	μ3	NOUN
cana-853	194	109	=	=	SYM
cana-853	194	110	8	8	NUM
cana-853	194	111	,	,	PUNCT
cana-853	194	112	μ4	μ4	NOUN
cana-853	194	113	=	=	SYM
cana-853	194	114	9	9	NUM
cana-853	194	115	,	,	PUNCT
cana-853	194	116	μ5	μ5	NOUN
cana-853	194	117	=	=	NOUN
cana-853	194	118	10	10	NUM
cana-853	194	119	,	,	PUNCT
cana-853	194	120	λ	λ	X
cana-853	194	121	=	=	NOUN
cana-853	194	122	1,2,3	1,2,3	NUM
cana-853	194	123	…	…	PUNCT
cana-853	194	124	.10	.10	NUM
cana-853	194	125	,	,	PUNCT
cana-853	194	126	γ	γ	X
cana-853	194	127	=	=	SYM
cana-853	194	128	3	3	NUM
cana-853	194	129	,	,	PUNCT
cana-853	194	130	6	6	NUM
cana-853	194	131	,	,	PUNCT
cana-853	194	132	9	9	NUM
cana-853	194	133	,	,	PUNCT
cana-853	194	134	12	12	NUM
cana-853	194	135	,	,	PUNCT
cana-853	194	136	15	15	NUM
cana-853	194	137	(	(	PUNCT
cana-853	194	138	catastrophe	catastrophe	NOUN
cana-853	194	139	effect	effect	NOUN
cana-853	194	140	)	)	PUNCT
cana-853	194	141	.	.	PUNCT
cana-853	195	1	in	in	ADP
cana-853	195	2	fig	fig	NOUN
cana-853	195	3	7	7	NUM
cana-853	195	4	,	,	PUNCT
cana-853	195	5	as	as	ADP
cana-853	195	6	the	the	DET
cana-853	195	7	value	value	NOUN
cana-853	195	8	of	of	ADP
cana-853	195	9	λ	λ	PROPN
cana-853	195	10	increases	increase	NOUN
cana-853	195	11	,	,	PUNCT
cana-853	195	12	the	the	DET
cana-853	195	13	number	number	NOUN
cana-853	195	14	of	of	ADP
cana-853	195	15	vendors	vendor	NOUN
cana-853	195	16	in	in	ADP
cana-853	195	17	node	node	ADJ
cana-853	195	18	two	two	NUM
cana-853	195	19	increases	increase	NOUN
cana-853	195	20	,	,	PUNCT
cana-853	195	21	and	and	CCONJ
cana-853	195	22	as	as	ADP
cana-853	195	23	the	the	DET
cana-853	195	24	value	value	NOUN
cana-853	195	25	of	of	ADP
cana-853	195	26	γ	γ	NOUN
cana-853	195	27	increases	increase	NOUN
cana-853	195	28	,	,	PUNCT
cana-853	195	29	the	the	DET
cana-853	195	30	number	number	NOUN
cana-853	195	31	of	of	ADP
cana-853	195	32	customers	customer	NOUN
cana-853	195	33	in	in	ADP
cana-853	195	34	node	node	NOUN
cana-853	195	35	two	two	NUM
cana-853	195	36	decreases	decrease	NOUN
cana-853	195	37	.	.	PUNCT
cana-853	196	1	communications	communication	NOUN
cana-853	196	2	on	on	ADP
cana-853	196	3	applied	apply	VERB
cana-853	196	4	nonlinear	nonlinear	ADJ
cana-853	196	5	analysis	analysis	NOUN
cana-853	196	6	issn	issn	NOUN
cana-853	196	7	:	:	PUNCT
cana-853	196	8	1074	1074	NUM
cana-853	196	9	-	-	PUNCT
cana-853	196	10	133x	133x	NUM
cana-853	196	11	vol	vol	NOUN
cana-853	196	12	31	31	NUM
cana-853	196	13	no	no	NOUN
cana-853	196	14	.	.	PUNCT
cana-853	197	1	4s	4s	NUM
cana-853	197	2	(	(	PUNCT
cana-853	197	3	2024	2024	NUM
cana-853	197	4	)	)	PUNCT
cana-853	197	5	308	308	NUM
cana-853	197	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-853	197	7	table	table	NOUN
cana-853	197	8	:	:	PUNCT
cana-853	197	9	6	6	NUM
cana-853	197	10	3	3	NUM
cana-853	197	11	6	6	NUM
cana-853	197	12	9	9	NUM
cana-853	197	13	12	12	NUM
cana-853	197	14	15	15	NUM
cana-853	197	15	1	1	NUM
cana-853	197	16	0.0694	0.0694	NUM
cana-853	197	17	0.057	0.057	NUM
cana-853	197	18	0.0485	0.0485	NUM
cana-853	197	19	0.0422	0.0422	NUM
cana-853	197	20	0.0374	0.0374	NUM
cana-853	197	21	2	2	NUM
cana-853	197	22	0.1466	0.1466	NUM
cana-853	197	23	0.1183	0.1183	NUM
cana-853	197	24	0.0995	0.0995	NUM
cana-853	197	25	0.0861	0.0861	NUM
cana-853	197	26	0.0759	0.0759	NUM
cana-853	197	27	3	3	NUM
cana-853	197	28	0.2326	0.2326	NUM
cana-853	197	29	0.184	0.184	NUM
cana-853	197	30	0.1532	0.1532	NUM
cana-853	197	31	0.1317	0.1317	NUM
cana-853	197	32	0.1157	0.1157	NUM
cana-853	197	33	4	4	NUM
cana-853	197	34	0.3283	0.3283	NUM
cana-853	197	35	0.2544	0.2544	NUM
cana-853	197	36	0.2096	0.2096	NUM
cana-853	197	37	0.179	0.179	NUM
cana-853	197	38	0.1566	0.1566	NUM
cana-853	197	39	5	5	NUM
cana-853	197	40	0.4346	0.4346	NUM
cana-853	197	41	0.3295	0.3295	NUM
cana-853	197	42	0.2686	0.2686	NUM
cana-853	197	43	0.2279	0.2279	NUM
cana-853	197	44	0.1986	0.1986	NUM
cana-853	197	45	6	6	NUM
cana-853	197	46	0.5526	0.5526	NUM
cana-853	197	47	0.4094	0.4094	NUM
cana-853	197	48	0.3302	0.3302	NUM
cana-853	197	49	0.2785	0.2785	NUM
cana-853	197	50	0.2417	0.2417	NUM
cana-853	197	51	7	7	NUM
cana-853	197	52	0.683	0.683	NUM
cana-853	197	53	0.4942	0.4942	NUM
cana-853	197	54	0.3944	0.3944	NUM
cana-853	197	55	0.3307	0.3307	NUM
cana-853	197	56	0.2859	0.2859	NUM
cana-853	197	57	8	8	NUM
cana-853	197	58	0.8265	0.8265	NUM
cana-853	197	59	0.5838	0.5838	NUM
cana-853	197	60	0.4611	0.4611	NUM
cana-853	197	61	0.3844	0.3844	NUM
cana-853	197	62	0.331	0.331	NUM
cana-853	197	63	9	9	NUM
cana-853	197	64	0.9835	0.9835	NUM
cana-853	197	65	0.6782	0.6782	NUM
cana-853	197	66	0.5303	0.5303	NUM
cana-853	197	67	0.4396	0.4396	NUM
cana-853	197	68	0.3772	0.3772	NUM
cana-853	197	69	10	10	NUM
cana-853	197	70	1.1543	1.1543	NUM
cana-853	197	71	0.7774	0.7774	NUM
cana-853	197	72	0.6018	0.6018	NUM
cana-853	197	73	0.4962	0.4962	NUM
cana-853	197	74	0.4244	0.4244	NUM
cana-853	197	75	fig	fig	NOUN
cana-853	197	76	:	:	PUNCT
cana-853	197	77	7	7	NUM
cana-853	197	78	the	the	DET
cana-853	197	79	total	total	ADJ
cana-853	197	80	amount	amount	NOUN
cana-853	197	81	of	of	ADP
cana-853	197	82	consumers	consumer	NOUN
cana-853	197	83	in	in	ADP
cana-853	197	84	the	the	DET
cana-853	197	85	node	node	NOUN
cana-853	197	86	two	two	NUM
cana-853	197	87	number	number	NOUN
cana-853	197	88	of	of	ADP
cana-853	197	89	consumers	consumer	NOUN
cana-853	197	90	in	in	ADP
cana-853	197	91	node	node	NOUN
cana-853	197	92	three	three	NUM
cana-853	197	93	the	the	DET
cana-853	197	94	customers	customer	NOUN
cana-853	197	95	in	in	ADP
cana-853	197	96	node	node	NOUN
cana-853	197	97	three	three	NUM
cana-853	197	98	are	be	AUX
cana-853	197	99	calculated	calculate	VERB
cana-853	197	100	in	in	ADP
cana-853	197	101	table	table	NOUN
cana-853	197	102	7	7	NUM
cana-853	197	103	for	for	ADP
cana-853	197	104	�	�	NOUN
cana-853	197	105	̅	̅	NOUN
cana-853	197	106	�	�	NOUN
cana-853	197	107	=	=	SYM
cana-853	197	108	0.3	0.3	NUM
cana-853	197	109	,	,	PUNCT
cana-853	197	110	�	�	NOUN
cana-853	197	111	̅	̅	NOUN
cana-853	197	112	�	�	NOUN
cana-853	197	113	=	=	SYM
cana-853	197	114	0.5	0.5	NUM
cana-853	197	115	,	,	PUNCT
cana-853	197	116	r	r	NOUN
cana-853	197	117	=	=	SYM
cana-853	197	118	0.4	0.4	NUM
cana-853	197	119	,	,	PUNCT
cana-853	197	120	μ1	μ1	PROPN
cana-853	197	121	=	=	SYM
cana-853	197	122	6	6	NUM
cana-853	197	123	,	,	PUNCT
cana-853	197	124	μ2	μ2	NOUN
cana-853	197	125	=	=	SYM
cana-853	197	126	4	4	NUM
cana-853	197	127	,	,	PUNCT
cana-853	197	128	μ3	μ3	NOUN
cana-853	197	129	=	=	SYM
cana-853	197	130	8	8	NUM
cana-853	197	131	,	,	PUNCT
cana-853	197	132	μ4	μ4	NOUN
cana-853	197	133	=	=	SYM
cana-853	197	134	9	9	NUM
cana-853	197	135	,	,	PUNCT
cana-853	197	136	μ5	μ5	NOUN
cana-853	197	137	=	=	NOUN
cana-853	197	138	10	10	NUM
cana-853	197	139	,	,	PUNCT
cana-853	197	140	λ	λ	X
cana-853	197	141	=	=	NOUN
cana-853	197	142	1,2,3	1,2,3	NUM
cana-853	197	143	…	…	PUNCT
cana-853	197	144	.10	.10	NUM
cana-853	197	145	,	,	PUNCT
cana-853	197	146	γ	γ	X
cana-853	197	147	=	=	SYM
cana-853	197	148	3	3	NUM
cana-853	197	149	,	,	PUNCT
cana-853	197	150	6	6	NUM
cana-853	197	151	,	,	PUNCT
cana-853	197	152	9	9	NUM
cana-853	197	153	,	,	PUNCT
cana-853	197	154	12	12	NUM
cana-853	197	155	,	,	PUNCT
cana-853	197	156	15	15	NUM
cana-853	197	157	(	(	PUNCT
cana-853	197	158	catastrophe	catastrophe	NOUN
cana-853	197	159	effect	effect	NOUN
cana-853	197	160	)	)	PUNCT
cana-853	197	161	.	.	PUNCT
cana-853	198	1	in	in	ADP
cana-853	198	2	fig	fig	NOUN
cana-853	198	3	8	8	NUM
cana-853	198	4	,	,	PUNCT
cana-853	198	5	as	as	ADP
cana-853	198	6	the	the	DET
cana-853	198	7	value	value	NOUN
cana-853	198	8	of	of	ADP
cana-853	198	9	λ	λ	PROPN
cana-853	198	10	increases	increase	NOUN
cana-853	198	11	,	,	PUNCT
cana-853	198	12	the	the	DET
cana-853	198	13	quantity	quantity	NOUN
cana-853	198	14	of	of	ADP
cana-853	198	15	consumers	consumer	NOUN
cana-853	198	16	in	in	ADP
cana-853	198	17	node	node	ADJ
cana-853	198	18	three	three	NUM
cana-853	198	19	increases	increase	NOUN
cana-853	198	20	,	,	PUNCT
cana-853	198	21	and	and	CCONJ
cana-853	198	22	as	as	ADP
cana-853	198	23	the	the	DET
cana-853	198	24	value	value	NOUN
cana-853	198	25	of	of	ADP
cana-853	198	26	γ	γ	NOUN
cana-853	198	27	increases	increase	NOUN
cana-853	198	28	,	,	PUNCT
cana-853	198	29	the	the	DET
cana-853	198	30	quantity	quantity	NOUN
cana-853	198	31	of	of	ADP
cana-853	198	32	customers	customer	NOUN
cana-853	198	33	in	in	ADP
cana-853	198	34	node	node	NOUN
cana-853	198	35	three	three	NUM
cana-853	198	36	decreases	decrease	NOUN
cana-853	198	37	.	.	PUNCT
cana-853	199	1	communications	communication	NOUN
cana-853	199	2	on	on	ADP
cana-853	199	3	applied	apply	VERB
cana-853	199	4	nonlinear	nonlinear	ADJ
cana-853	199	5	analysis	analysis	NOUN
cana-853	199	6	issn	issn	NOUN
cana-853	199	7	:	:	PUNCT
cana-853	199	8	1074	1074	NUM
cana-853	199	9	-	-	PUNCT
cana-853	199	10	133x	133x	NUM
cana-853	199	11	vol	vol	NOUN
cana-853	199	12	31	31	NUM
cana-853	199	13	no	no	NOUN
cana-853	199	14	.	.	PUNCT
cana-853	200	1	4s	4s	NUM
cana-853	200	2	(	(	PUNCT
cana-853	200	3	2024	2024	NUM
cana-853	200	4	)	)	PUNCT
cana-853	200	5	309	309	NUM
cana-853	200	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-853	200	7	table	table	NOUN
cana-853	200	8	:	:	PUNCT
cana-853	200	9	7	7	NUM
cana-853	200	10	3	3	NUM
cana-853	200	11	6	6	NUM
cana-853	200	12	9	9	NUM
cana-853	200	13	12	12	NUM
cana-853	200	14	15	15	NUM
cana-853	200	15	1	1	NUM
cana-853	200	16	0.0383	0.0383	NUM
cana-853	200	17	0.0342	0.0342	NUM
cana-853	200	18	0.031	0.031	NUM
cana-853	200	19	0.0283	0.0283	NUM
cana-853	200	20	0.026	0.026	NUM
cana-853	200	21	2	2	NUM
cana-853	200	22	0.0792	0.0792	NUM
cana-853	200	23	0.0704	0.0704	NUM
cana-853	200	24	0.0634	0.0634	NUM
cana-853	200	25	0.0577	0.0577	NUM
cana-853	200	26	0.0529	0.0529	NUM
cana-853	200	27	3	3	NUM
cana-853	200	28	0.1231	0.1231	NUM
cana-853	200	29	0.1085	0.1085	NUM
cana-853	200	30	0.0972	0.0972	NUM
cana-853	200	31	0.0881	0.0881	NUM
cana-853	200	32	0.0806	0.0806	NUM
cana-853	200	33	4	4	NUM
cana-853	200	34	0.1701	0.1701	NUM
cana-853	200	35	0.1487	0.1487	NUM
cana-853	200	36	0.1325	0.1325	NUM
cana-853	200	37	0.1196	0.1196	NUM
cana-853	200	38	0.1092	0.1092	NUM
cana-853	200	39	5	5	NUM
cana-853	200	40	0.2206	0.2206	NUM
cana-853	200	41	0.1912	0.1912	NUM
cana-853	200	42	0.1694	0.1694	NUM
cana-853	200	43	0.1523	0.1523	NUM
cana-853	200	44	0.1386	0.1386	NUM
cana-853	200	45	6	6	NUM
cana-853	200	46	0.2749	0.2749	NUM
cana-853	200	47	0.2361	0.2361	NUM
cana-853	200	48	0.2078	0.2078	NUM
cana-853	200	49	0.1861	0.1861	NUM
cana-853	200	50	0.1689	0.1689	NUM
cana-853	200	51	7	7	NUM
cana-853	200	52	0.3333	0.3333	NUM
cana-853	200	53	0.2834	0.2834	NUM
cana-853	200	54	0.2479	0.2479	NUM
cana-853	200	55	0.2211	0.2211	NUM
cana-853	200	56	0.2	0.2	NUM
cana-853	200	57	8	8	NUM
cana-853	200	58	0.3963	0.3963	NUM
cana-853	200	59	0.3333	0.3333	NUM
cana-853	200	60	0.2898	0.2898	NUM
cana-853	200	61	0.2573	0.2573	NUM
cana-853	200	62	0.232	0.232	NUM
cana-853	200	63	9	9	NUM
cana-853	200	64	0.4641	0.4641	NUM
cana-853	200	65	0.386	0.386	NUM
cana-853	200	66	0.3333	0.3333	NUM
cana-853	200	67	0.2947	0.2947	NUM
cana-853	200	68	0.2649	0.2649	NUM
cana-853	200	69	10	10	NUM
cana-853	200	70	0.5373	0.5373	NUM
cana-853	200	71	0.4415	0.4415	NUM
cana-853	200	72	0.3787	0.3787	NUM
cana-853	200	73	0.3333	0.3333	NUM
cana-853	200	74	0.2987	0.2987	NUM
cana-853	200	75	fig	fig	NOUN
cana-853	200	76	:	:	PUNCT
cana-853	200	77	8	8	NUM
cana-853	200	78	count	count	NOUN
cana-853	200	79	of	of	ADP
cana-853	200	80	vendors	vendor	NOUN
cana-853	200	81	in	in	ADP
cana-853	200	82	node	node	NOUN
cana-853	200	83	three	three	NUM
cana-853	200	84	7	7	NUM
cana-853	200	85	.	.	PUNCT
cana-853	200	86	conclusion	conclusion	NOUN
cana-853	200	87	in	in	ADP
cana-853	200	88	this	this	DET
cana-853	200	89	study	study	NOUN
cana-853	200	90	,	,	PUNCT
cana-853	200	91	we	we	PRON
cana-853	200	92	derive	derive	VERB
cana-853	200	93	probability	probability	NOUN
cana-853	200	94	of	of	ADP
cana-853	200	95	n	n	PRON
cana-853	200	96	count	count	NOUN
cana-853	200	97	of	of	ADP
cana-853	200	98	vendorsin	vendorsin	NOUN
cana-853	200	99	the	the	DET
cana-853	200	100	system	system	NOUN
cana-853	200	101	with	with	ADP
cana-853	200	102	queue	queue	NOUN
cana-853	200	103	length	length	NOUN
cana-853	200	104	,	,	PUNCT
cana-853	200	105	queue	queue	NOUN
cana-853	200	106	time	time	NOUN
cana-853	200	107	and	and	CCONJ
cana-853	200	108	system	system	NOUN
cana-853	200	109	time	time	NOUN
cana-853	200	110	of	of	ADP
cana-853	200	111	markovian	markovian	ADJ
cana-853	200	112	queue	queue	NOUN
cana-853	200	113	with	with	ADP
cana-853	200	114	single	single	ADJ
cana-853	200	115	server	server	NOUN
cana-853	200	116	netwօrk	netwօrk	NOUN
cana-853	200	117	along	along	ADP
cana-853	200	118	with	with	ADP
cana-853	200	119	preparatory	preparatory	ADJ
cana-853	200	120	wօrk	wօrk	NOUN
cana-853	200	121	and	and	CCONJ
cana-853	200	122	feedback	feedback	VERB
cana-853	200	123	for	for	ADP
cana-853	200	124	three	three	NUM
cana-853	200	125	nodes	node	NOUN
cana-853	200	126	when	when	SCONJ
cana-853	200	127	catastrophes	catastrophe	NOUN
cana-853	200	128	occur	occur	VERB
cana-853	200	129	.	.	PUNCT
cana-853	201	1	the	the	DET
cana-853	201	2	numerical	numerical	ADJ
cana-853	201	3	examples	example	NOUN
cana-853	201	4	shows	show	VERB
cana-853	201	5	that	that	SCONJ
cana-853	201	6	when	when	SCONJ
cana-853	201	7	the	the	DET
cana-853	201	8	number	number	NOUN
cana-853	201	9	of	of	ADP
cana-853	201	10	customers	customer	NOUN
cana-853	201	11	increases	increase	VERB
cana-853	201	12	with	with	ADP
cana-853	201	13	arrival	arrival	NOUN
cana-853	201	14	(	(	PUNCT
cana-853	201	15	fig.2	fig.2	PROPN
cana-853	201	16	)	)	PUNCT
cana-853	201	17	waiting	wait	VERB
cana-853	201	18	time	time	NOUN
cana-853	201	19	increase	increase	NOUN
cana-853	201	20	with	with	ADP
cana-853	201	21	arrival	arrival	NOUN
cana-853	201	22	(	(	PUNCT
cana-853	201	23	fig.3	fig.3	PROPN
cana-853	201	24	)	)	PUNCT
cana-853	201	25	,	,	PUNCT
cana-853	201	26	the	the	DET
cana-853	201	27	count	count	NOUN
cana-853	201	28	of	of	ADP
cana-853	201	29	consumers	consumer	NOUN
cana-853	201	30	in	in	ADP
cana-853	201	31	the	the	DET
cana-853	201	32	nodes	node	NOUN
cana-853	201	33	one	one	NUM
cana-853	201	34	,	,	PUNCT
cana-853	201	35	two	two	NUM
cana-853	201	36	,	,	PUNCT
cana-853	201	37	three	three	NUM
cana-853	201	38	increases	increase	NOUN
cana-853	201	39	with	with	ADP
cana-853	201	40	arrival	arrival	NOUN
cana-853	201	41	rate	rate	NOUN
cana-853	201	42	(	(	PUNCT
cana-853	201	43	fig	fig	NOUN
cana-853	201	44	.	.	NOUN
cana-853	201	45	6	6	NUM
cana-853	201	46	,	,	PUNCT
cana-853	201	47	7	7	NUM
cana-853	201	48	,	,	PUNCT
cana-853	201	49	8)	8)	NUM
cana-853	201	50	.	.	PUNCT
cana-853	202	1	it	it	PRON
cana-853	202	2	shows	show	VERB
cana-853	202	3	thecoincides	thecoincide	NOUN
cana-853	202	4	of	of	ADP
cana-853	202	5	the	the	DET
cana-853	202	6	result	result	NOUN
cana-853	202	7	.	.	PUNCT
cana-853	203	1	references	reference	NOUN
cana-853	203	2	[	[	X
cana-853	203	3	1	1	X
cana-853	203	4	]	]	PUNCT
cana-853	203	5	chandrasekaran	chandrasekaran	ADJ
cana-853	203	6	v.m	v.m	PROPN
cana-853	203	7	,	,	PUNCT
cana-853	203	8	saravanarajan	saravanarajan	PROPN
cana-853	203	9	m.c	m.c	PROPN
cana-853	203	10	,	,	PUNCT
cana-853	203	11	transient	transient	NOUN
cana-853	203	12	and	and	CCONJ
cana-853	203	13	reliability	reliability	NOUN
cana-853	203	14	analysis	analysis	NOUN
cana-853	203	15	of	of	ADP
cana-853	203	16	m	m	PROPN
cana-853	203	17	/	/	SYM
cana-853	203	18	m/1	m/1	NOUN
cana-853	203	19	feedback	feedback	NOUN
cana-853	203	20	queue	queue	NOUN
cana-853	203	21	subject	subject	NOUN
cana-853	203	22	to	to	ADP
cana-853	203	23	catastrophes	catastrophe	NOUN
cana-853	203	24	,	,	PUNCT
cana-853	203	25	server	server	NOUN
cana-853	203	26	failures	failure	NOUN
cana-853	203	27	and	and	CCONJ
cana-853	203	28	repairs	repair	NOUN
cana-853	203	29	,	,	PUNCT
cana-853	203	30	international	international	ADJ
cana-853	203	31	journal	journal	NOUN
cana-853	203	32	of	of	ADP
cana-853	203	33	pure	pure	ADJ
cana-853	203	34	and	and	CCONJ
cana-853	203	35	applied	apply	VERB
cana-853	203	36	mathematics.volume	mathematics.volume	PROPN
cana-853	203	37	77	77	NUM
cana-853	203	38	no.5	no.5	PROPN
cana-853	203	39	(	(	PUNCT
cana-853	203	40	2012	2012	NUM
cana-853	203	41	)	)	PUNCT
cana-853	204	1	pp	pp	CCONJ
cana-853	204	2	:	:	PUNCT
cana-853	204	3	605	605	NUM
cana-853	204	4	-625	-625	NOUN
cana-853	204	5	.	.	PUNCT
cana-853	205	1	[	[	X
cana-853	205	2	2	2	NUM
cana-853	205	3	]	]	X
cana-853	205	4	chaox	chaox	NOUN
cana-853	205	5	.	.	PUNCT
cana-853	205	6	,aqueuingnetwօrk	,aqueuingnetwօrk	PUNCT
cana-853	205	7	model	model	NOUN
cana-853	205	8	with	with	ADP
cana-853	205	9	catastrophes	catastrophe	NOUN
cana-853	205	10	and	and	CCONJ
cana-853	205	11	product	product	NOUN
cana-853	205	12	form	form	NOUN
cana-853	205	13	solution	solution	NOUN
cana-853	205	14	,	,	PUNCT
cana-853	205	15	operation	operation	NOUN
cana-853	205	16	research	research	PROPN
cana-853	205	17	letters.18(1995)75	letters.18(1995)75	PROPN
cana-853	205	18	-	-	PUNCT
cana-853	205	19	79	79	NUM
cana-853	205	20	.	.	PUNCT
cana-853	206	1	communications	communication	NOUN
cana-853	206	2	on	on	ADP
cana-853	206	3	applied	apply	VERB
cana-853	206	4	nonlinear	nonlinear	ADJ
cana-853	206	5	analysis	analysis	NOUN
cana-853	206	6	issn	issn	NOUN
cana-853	206	7	:	:	PUNCT
cana-853	206	8	1074	1074	NUM
cana-853	206	9	-	-	PUNCT
cana-853	206	10	133x	133x	NUM
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cana-853	206	12	31	31	NUM
cana-853	206	13	no	no	NOUN
cana-853	206	14	.	.	PUNCT
cana-853	207	1	4s	4s	NUM
cana-853	207	2	(	(	PUNCT
cana-853	207	3	2024	2024	NUM
cana-853	207	4	)	)	PUNCT
cana-853	207	5	310	310	NUM
cana-853	207	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-853	208	1	[	[	X
cana-853	208	2	3	3	X
cana-853	208	3	]	]	X
cana-853	208	4	erlang	erlang	PROPN
cana-853	208	5	a.k	a.k	PROPN
cana-853	208	6	,	,	PUNCT
cana-853	208	7	the	the	DET
cana-853	208	8	theory	theory	NOUN
cana-853	208	9	of	of	ADP
cana-853	208	10	probabilities	probability	NOUN
cana-853	208	11	and	and	CCONJ
cana-853	208	12	telephone	telephone	NOUN
cana-853	208	13	conversations	conversation	NOUN
cana-853	208	14	,	,	PUNCT
cana-853	208	15	nytjindsskriffmath.b20	nytjindsskriffmath.b20	NOUN
cana-853	208	16	(	(	PUNCT
cana-853	208	17	1909	1909	NUM
cana-853	208	18	)	)	PUNCT
cana-853	208	19	33	33	NUM
cana-853	208	20	-	-	SYM
cana-853	208	21	39	39	NUM
cana-853	208	22	.	.	PUNCT
cana-853	209	1	[	[	X
cana-853	209	2	4	4	X
cana-853	209	3	]	]	X
cana-853	209	4	gelenbe	gelenbe	NOUN
cana-853	209	5	e	e	NOUN
cana-853	209	6	,	,	PUNCT
cana-853	209	7	productformqueueingnetwօrkswithpositiveandnegativecustomers	productformqueueingnetwօrkswithpositiveandnegativecustomer	NOUN
cana-853	209	8	,	,	PUNCT
cana-853	209	9	journalofappliedprobability.28(3)(1991)6	journalofappliedprobability.28(3)(1991)6	X
cana-853	209	10	56	56	NUM
cana-853	209	11	-	-	SYM
cana-853	209	12	663	663	NUM
cana-853	209	13	.	.	PUNCT
cana-853	210	1	[	[	X
cana-853	210	2	5	5	NUM
cana-853	210	3	]	]	PUNCT
cana-853	210	4	jackson	jackson	PROPN
cana-853	210	5	j.r	j.r	PROPN
cana-853	210	6	.	.	PROPN
cana-853	210	7	,	,	PUNCT
cana-853	210	8	“	"	PUNCT
cana-853	210	9	job	job	NOUN
cana-853	210	10	shop	shop	NOUN
cana-853	210	11	-	-	PUNCT
cana-853	210	12	like	like	ADJ
cana-853	210	13	queueing	queue	VERB
cana-853	210	14	systems	system	NOUN
cana-853	210	15	”	"	PUNCT
cana-853	210	16	,	,	PUNCT
cana-853	210	17	management	management	NOUN
cana-853	210	18	science	science	NOUN
cana-853	210	19	,	,	PUNCT
cana-853	210	20	10	10	NUM
cana-853	210	21	131	131	NUM
cana-853	210	22	-	-	SYM
cana-853	210	23	142	142	NUM
cana-853	210	24	(	(	PUNCT
cana-853	210	25	1963	1963	NUM
cana-853	210	26	)	)	PUNCT
cana-853	210	27	.	.	PUNCT
cana-853	211	1	[	[	X
cana-853	211	2	6	6	NUM
cana-853	211	3	]	]	X
cana-853	211	4	krishnakumar	krishnakumar	PROPN
cana-853	211	5	b	b	PROPN
cana-853	211	6	,	,	PUNCT
cana-853	211	7	arivudainambi	arivudainambi	PROPN
cana-853	211	8	d	d	NOUN
cana-853	211	9	,	,	PUNCT
cana-853	211	10	transient	transient	ADJ
cana-853	211	11	solution	solution	NOUN
cana-853	211	12	of	of	ADP
cana-853	211	13	an	an	DET
cana-853	211	14	m	m	NOUN
cana-853	211	15	/	/	SYM
cana-853	211	16	m/1queue	m/1queue	NOUN
cana-853	211	17	with	with	ADP
cana-853	211	18	catastrophes	catastrophe	NOUN
cana-853	211	19	,	,	PUNCT
cana-853	211	20	computers	computer	NOUN
cana-853	211	21	and	and	CCONJ
cana-853	211	22	mathematics	mathematic	NOUN
cana-853	211	23	with	with	ADP
cana-853	211	24	applications.40	applications.40	PROPN
cana-853	211	25	(	(	PUNCT
cana-853	211	26	2000)1233	2000)1233	NOUN
cana-853	211	27	-	-	SYM
cana-853	211	28	1240	1240	NUM
cana-853	211	29	.	.	PUNCT
cana-853	212	1	[	[	X
cana-853	212	2	7	7	X
cana-853	212	3	]	]	SYM
cana-853	212	4	parthasarathy	parthasarathy	NOUN
cana-853	212	5	p	p	NOUN
cana-853	212	6	r	r	NOUN
cana-853	212	7	,	,	PUNCT
cana-853	212	8	a	a	DET
cana-853	212	9	transiet	transiet	ADJ
cana-853	212	10	solution	solution	NOUN
cana-853	212	11	to	to	ADP
cana-853	212	12	an	an	DET
cana-853	212	13	m	m	NOUN
cana-853	212	14	/	/	SYM
cana-853	212	15	m/1	m/1	NOUN
cana-853	212	16	queue	queue	NOUN
cana-853	212	17	:	:	PUNCT
cana-853	212	18	a	a	DET
cana-853	212	19	simple	simple	ADJ
cana-853	212	20	approach	approach	NOUN
cana-853	212	21	,	,	PUNCT
cana-853	212	22	advappl.prob	advappl.prob	INTJ
cana-853	212	23	,	,	PUNCT
cana-853	212	24	volume	volume	NOUN
cana-853	212	25	19,(1987	19,(1987	NUM
cana-853	212	26	)	)	PUNCT
cana-853	212	27	pp	pp	CCONJ
cana-853	212	28	:	:	PUNCT
cana-853	212	29	997	997	NUM
cana-853	212	30	–	–	PUNCT
cana-853	212	31	998	998	NUM
cana-853	212	32	.	.	PUNCT
cana-853	213	1	[	[	X
cana-853	213	2	8	8	NUM
cana-853	213	3	]	]	SYM
cana-853	213	4	parthasarathy	parthasarathy	NOUN
cana-853	213	5	p.r	p.r	NOUN
cana-853	213	6	and	and	CCONJ
cana-853	213	7	sharafalim	sharafalim	NOUN
cana-853	213	8	,	,	PUNCT
cana-853	213	9	transient	transient	ADJ
cana-853	213	10	solution	solution	NOUN
cana-853	213	11	to	to	ADP
cana-853	213	12	the	the	DET
cana-853	213	13	many	many	ADJ
cana-853	213	14	server	server	NOUN
cana-853	213	15	poisson	poisson	NOUN
cana-853	213	16	queues	queue	NOUN
cana-853	213	17	,	,	PUNCT
cana-853	213	18	j.appl.prob	j.appl.prob	PROPN
cana-853	213	19	.	.	PROPN
cana-853	213	20	,26	,26	PROPN
cana-853	213	21	,	,	PUNCT
cana-853	213	22	(	(	PUNCT
cana-853	213	23	1989	1989	NUM
cana-853	213	24	)	)	PUNCT
cana-853	213	25	pp	pp	CCONJ
cana-853	213	26	:	:	PUNCT
cana-853	213	27	584	584	NUM
cana-853	213	28	594	594	NUM
cana-853	213	29	.	.	PUNCT
cana-853	214	1	[	[	X
cana-853	214	2	9	9	NUM
cana-853	214	3	]	]	PUNCT
cana-853	214	4	santhakumaran	santhakumaran	VERB
cana-853	214	5	a	a	PRON
cana-853	214	6	and	and	CCONJ
cana-853	214	7	shanmugasundaram	shanmugasundaram	PROPN
cana-853	214	8	s	s	PART
cana-853	214	9	,	,	PUNCT
cana-853	214	10	preparatory	preparatory	ADJ
cana-853	214	11	wօrk	wօrk	NOUN
cana-853	214	12	on	on	ADP
cana-853	214	13	arrival	arrival	NOUN
cana-853	214	14	customers	customer	NOUN
cana-853	214	15	with	with	ADP
cana-853	214	16	a	a	DET
cana-853	214	17	single	single	ADJ
cana-853	214	18	server	server	NOUN
cana-853	214	19	feedback	feedback	NOUN
cana-853	214	20	queue	queue	NOUN
cana-853	214	21	,	,	PUNCT
cana-853	214	22	journal	journal	NOUN
cana-853	214	23	of	of	ADP
cana-853	214	24	information	information	NOUN
cana-853	214	25	and	and	CCONJ
cana-853	214	26	management	management	NOUN
cana-853	214	27	sciences	science	NOUN
cana-853	214	28	,	,	PUNCT
cana-853	214	29	volume	volume	NOUN
cana-853	214	30	19	19	NUM
cana-853	214	31	,	,	PUNCT
cana-853	214	32	no	no	INTJ
cana-853	214	33	.	.	NOUN
cana-853	214	34	2	2	NUM
cana-853	214	35	,	,	PUNCT
cana-853	214	36	(	(	PUNCT
cana-853	214	37	2008	2008	NUM
cana-853	214	38	)	)	PUNCT
cana-853	215	1	pp	pp	CCONJ
cana-853	215	2	:	:	PUNCT
cana-853	215	3	301	301	NUM
cana-853	215	4	-	-	SYM
cana-853	215	5	313	313	NUM
cana-853	215	6	.	.	PUNCT
cana-853	216	1	[	[	X
cana-853	216	2	10	10	NUM
cana-853	216	3	]	]	X
cana-853	216	4	shanmugasundaram	shanmugasundaram	PROPN
cana-853	216	5	s	s	PROPN
cana-853	216	6	and	and	CCONJ
cana-853	216	7	chitras	chitras	PROPN
cana-853	216	8	,	,	PUNCT
cana-853	216	9	time	time	NOUN
cana-853	216	10	dependent	dependent	ADJ
cana-853	216	11	solution	solution	NOUN
cana-853	216	12	of	of	ADP
cana-853	216	13	single	single	ADJ
cana-853	216	14	server	server	NOUN
cana-853	216	15	feedback	feedback	NOUN
cana-853	216	16	queue	queue	NOUN
cana-853	216	17	customer	customer	NOUN
cana-853	216	18	having	have	VERB
cana-853	216	19	a	a	DET
cana-853	216	20	service	service	NOUN
cana-853	216	21	with	with	ADP
cana-853	216	22	and	and	CCONJ
cana-853	216	23	without	without	ADP
cana-853	216	24	preparatory	preparatory	ADJ
cana-853	216	25	wօrk	wօrk	NOUN
cana-853	216	26	when	when	SCONJ
cana-853	216	27	catastrophe	catastrophe	NOUN
cana-853	216	28	occurs	occur	VERB
cana-853	216	29	,	,	PUNCT
cana-853	216	30	international	international	ADJ
cana-853	216	31	journal	journal	NOUN
cana-853	216	32	of	of	ADP
cana-853	216	33	applied	apply	VERB
cana-853	216	34	engineering	engineering	NOUN
cana-853	216	35	research	research	NOUN
cana-853	216	36	,	,	PUNCT
cana-853	216	37	volume	volume	NOUN
cana-853	216	38	11	11	NUM
cana-853	216	39	,	,	PUNCT
cana-853	216	40	no	no	DET
cana-853	216	41	1	1	NUM
cana-853	216	42	(	(	PUNCT
cana-853	216	43	2016	2016	NUM
cana-853	216	44	)	)	PUNCT
cana-853	217	1	pp	pp	CCONJ
cana-853	217	2	:	:	PUNCT
cana-853	217	3	384	384	NUM
cana-853	217	4	-	-	SYM
cana-853	217	5	391	391	NUM
cana-853	217	6	.	.	PUNCT
cana-853	218	1	[	[	X
cana-853	218	2	11	11	NUM
cana-853	218	3	]	]	PUNCT
cana-853	218	4	shanmugasundarams	shanmugasundaram	NOUN
cana-853	218	5	,	,	PUNCT
cana-853	218	6	vanitha	vanitha	PROPN
cana-853	218	7	s	s	PART
cana-853	218	8	,	,	PUNCT
cana-853	218	9	“	"	PUNCT
cana-853	218	10	steady	steady	ADJ
cana-853	218	11	state	state	NOUN
cana-853	218	12	analysis	analysis	NOUN
cana-853	218	13	of	of	ADP
cana-853	218	14	m	m	PROPN
cana-853	218	15	/	/	SYM
cana-853	218	16	m/1	m/1	NOUN
cana-853	218	17	retrial	retrial	NOUN
cana-853	218	18	queueing	queueing	NOUN
cana-853	218	19	netwօrk	netwօrk	VERB
cana-853	218	20	with	with	ADP
cana-853	218	21	catastrophes	catastrophe	NOUN
cana-853	218	22	”	"	PUNCT
cana-853	218	23	,	,	PUNCT
cana-853	218	24	international	international	ADJ
cana-853	218	25	journal	journal	NOUN
cana-853	218	26	of	of	ADP
cana-853	218	27	mathematics	mathematics	NOUN
cana-853	218	28	trends	trend	NOUN
cana-853	218	29	and	and	CCONJ
cana-853	218	30	technology	technology	NOUN
cana-853	218	31	.	.	PUNCT
cana-853	219	1	26(12	26(12	NUM
cana-853	219	2	)	)	PUNCT
cana-853	219	3	(	(	PUNCT
cana-853	219	4	2020	2020	NUM
cana-853	219	5	)	)	PUNCT
cana-853	219	6	170	170	NUM
cana-853	219	7	–	–	PUNCT
cana-853	219	8	181	181	NUM
cana-853	219	9	.	.	PUNCT
cana-853	220	1	[	[	X
cana-853	220	2	12	12	NUM
cana-853	220	3	]	]	X
cana-853	220	4	takacs	takacs	PROPN
cana-853	220	5	l.	l.	PROPN
cana-853	220	6	,	,	PUNCT
cana-853	220	7	“	"	PUNCT
cana-853	220	8	a	a	DET
cana-853	220	9	single	single	ADJ
cana-853	220	10	server	server	NOUN
cana-853	220	11	queue	queue	NOUN
cana-853	220	12	with	with	ADP
cana-853	220	13	feedback	feedback	NOUN
cana-853	220	14	”	"	PUNCT
cana-853	220	15	,	,	PUNCT
cana-853	220	16	the	the	DET
cana-853	220	17	bell	bell	NOUN
cana-853	220	18	system	system	NOUN
cana-853	220	19	technical	technical	ADJ
cana-853	220	20	journal	journal	NOUN
cana-853	220	21	,	,	PUNCT
cana-853	220	22	42	42	NUM
cana-853	220	23	,	,	PUNCT
cana-853	220	24	505	505	NUM
cana-853	220	25	-	-	SYM
cana-853	220	26	519	519	NUM
cana-853	220	27	,	,	PUNCT
cana-853	220	28	(	(	PUNCT
cana-853	220	29	1963	1963	NUM
cana-853	220	30	)	)	PUNCT
cana-853	220	31	.	.	PUNCT
cana-853	221	1	[	[	X
cana-853	221	2	13	13	NUM
cana-853	221	3	]	]	PUNCT
cana-853	221	4	thangaraj	thangaraj	PROPN
cana-853	221	5	v	v	NOUN
cana-853	221	6	and	and	CCONJ
cana-853	221	7	vanitha	vanitha	PROPN
cana-853	221	8	s	s	PROPN
cana-853	221	9	,	,	PUNCT
cana-853	221	10	m	m	PROPN
cana-853	221	11	/	/	SYM
cana-853	221	12	m/1	m/1	NOUN
cana-853	221	13	queue	queue	NOUN
cana-853	221	14	with	with	ADP
cana-853	221	15	feedback	feedback	NOUN
cana-853	221	16	a	a	DET
cana-853	221	17	continued	continue	VERB
cana-853	221	18	fraction	fraction	NOUN
cana-853	221	19	approach	approach	NOUN
cana-853	221	20	,	,	PUNCT
cana-853	221	21	international	international	ADJ
cana-853	221	22	journal	journal	NOUN
cana-853	221	23	of	of	ADP
cana-853	221	24	computational	computational	ADJ
cana-853	221	25	and	and	CCONJ
cana-853	221	26	applied	applied	ADJ
cana-853	221	27	mathematics	mathematic	NOUN
cana-853	221	28	,	,	PUNCT
cana-853	221	29	volume	volume	NOUN
cana-853	221	30	5	5	NUM
cana-853	221	31	,	,	PUNCT
cana-853	221	32	(	(	PUNCT
cana-853	221	33	2010	2010	NUM
cana-853	221	34	)	)	PUNCT
cana-853	222	1	pp	pp	CCONJ
cana-853	222	2	:	:	PUNCT
cana-853	222	3	129	129	NUM
cana-853	222	4	-	-	SYM
cana-853	222	5	139	139	NUM
cana-853	223	1	[	[	X
cana-853	223	2	14	14	NUM
cana-853	223	3	]	]	PUNCT
cana-853	223	4	thangarajv	thangarajv	ADJ
cana-853	223	5	,	,	PUNCT
cana-853	223	6	vanitha	vanitha	PROPN
cana-853	223	7	s	s	X
cana-853	223	8	,	,	PUNCT
cana-853	223	9	on	on	ADP
cana-853	223	10	the	the	DET
cana-853	223	11	analysis	analysis	NOUN
cana-853	223	12	of	of	ADP
cana-853	223	13	m	m	PROPN
cana-853	223	14	/	/	SYM
cana-853	223	15	m/1	m/1	NOUN
cana-853	223	16	feedback	feedback	NOUN
cana-853	223	17	queue	queue	NOUN
cana-853	223	18	with	with	ADP
cana-853	223	19	catastrophes	catastrophe	NOUN
cana-853	223	20	using	use	VERB
cana-853	223	21	continued	continued	ADJ
cana-853	223	22	fractions	fraction	NOUN
cana-853	223	23	,	,	PUNCT
cana-853	223	24	international	international	ADJ
cana-853	223	25	journal	journal	NOUN
cana-853	223	26	of	of	ADP
cana-853	223	27	pure	pure	ADJ
cana-853	223	28	and	and	CCONJ
cana-853	223	29	applied	apply	VERB
cana-853	223	30	mathematics.53(1)(2009)133	mathematics.53(1)(2009)133	NOUN
cana-853	223	31	-	-	PUNCT
cana-853	223	32	151	151	NUM
cana-853	223	33	.	.	PUNCT