id	sid	tid	token	lemma	pos
cana-3949	1	1	communications	communication	NOUN
cana-3949	1	2	on	on	ADP
cana-3949	1	3	applied	apply	VERB
cana-3949	1	4	nonlinear	nonlinear	ADJ
cana-3949	1	5	analysis	analysis	NOUN
cana-3949	1	6	issn	issn	NOUN
cana-3949	1	7	:	:	PUNCT
cana-3949	1	8	1074	1074	NUM
cana-3949	1	9	-	-	PUNCT
cana-3949	1	10	133x	133x	NUM
cana-3949	1	11	vol	vol	NOUN
cana-3949	1	12	32	32	NUM
cana-3949	1	13	no	no	NOUN
cana-3949	1	14	.	.	PUNCT
cana-3949	2	1	9s	9s	NUM
cana-3949	2	2	(	(	PUNCT
cana-3949	2	3	2025	2025	NUM
cana-3949	2	4	)	)	PUNCT
cana-3949	2	5	377	377	NUM
cana-3949	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3949	2	7	m	m	PROPN
cana-3949	2	8	/	/	SYM
cana-3949	2	9	g/1	g/1	NOUN
cana-3949	2	10	queue	queue	NOUN
cana-3949	2	11	with	with	ADP
cana-3949	2	12	two	two	NUM
cana-3949	2	13	stage	stage	NOUN
cana-3949	2	14	heterogeneous	heterogeneous	ADJ
cana-3949	2	15	service	service	NOUN
cana-3949	2	16	and	and	CCONJ
cana-3949	2	17	compulsory	compulsory	ADJ
cana-3949	2	18	deterministic	deterministic	ADJ
cana-3949	2	19	server	server	NOUN
cana-3949	2	20	vacations	vacation	NOUN
cana-3949	2	21	s.	s.	PROPN
cana-3949	3	1	vanitha1	vanitha1	PROPN
cana-3949	4	1	1assistant	1assistant	NUM
cana-3949	4	2	professor	professor	NOUN
cana-3949	4	3	,	,	PUNCT
cana-3949	4	4	department	department	NOUN
cana-3949	4	5	of	of	ADP
cana-3949	4	6	mathematics	mathematics	PROPN
cana-3949	4	7	sri	sri	PROPN
cana-3949	5	1	sivasubramaniya	sivasubramaniya	PROPN
cana-3949	5	2	nadar	nadar	PROPN
cana-3949	5	3	college	college	PROPN
cana-3949	5	4	of	of	ADP
cana-3949	5	5	engineering	engineering	NOUN
cana-3949	5	6	,	,	PUNCT
cana-3949	5	7	tamilnadu	tamilnadu	PROPN
cana-3949	5	8	,	,	PUNCT
cana-3949	5	9	india	india	PROPN
cana-3949	5	10	vanithas@ssn.edu.in	vanithas@ssn.edu.in	PROPN
cana-3949	5	11	article	article	NOUN
cana-3949	5	12	history	history	NOUN
cana-3949	5	13	:	:	PUNCT
cana-3949	5	14	received	receive	VERB
cana-3949	5	15	:	:	PUNCT
cana-3949	5	16	16	16	NUM
cana-3949	5	17	-	-	SYM
cana-3949	5	18	11	11	NUM
cana-3949	5	19	-	-	PUNCT
cana-3949	5	20	2024	2024	NUM
cana-3949	5	21	revised	revise	VERB
cana-3949	5	22	:	:	PUNCT
cana-3949	5	23	15	15	NUM
cana-3949	5	24	-	-	SYM
cana-3949	5	25	12	12	NUM
cana-3949	5	26	-	-	PUNCT
cana-3949	5	27	2024	2024	NUM
cana-3949	5	28	accepted	accept	VERB
cana-3949	5	29	:	:	PUNCT
cana-3949	5	30	02	02	NUM
cana-3949	5	31	-	-	PUNCT
cana-3949	5	32	01	01	NUM
cana-3949	5	33	-	-	PUNCT
cana-3949	5	34	2025	2025	NUM
cana-3949	5	35	abstract	abstract	NOUN
cana-3949	5	36	:	:	PUNCT
cana-3949	5	37	we	we	PRON
cana-3949	5	38	analyze	analyze	VERB
cana-3949	5	39	a	a	DET
cana-3949	5	40	single	single	ADJ
cana-3949	5	41	server	server	NOUN
cana-3949	5	42	vacation	vacation	NOUN
cana-3949	5	43	queue	queue	NOUN
cana-3949	5	44	with	with	ADP
cana-3949	5	45	poisson	poisson	PROPN
cana-3949	5	46	arrivals	arrival	NOUN
cana-3949	5	47	,	,	PUNCT
cana-3949	5	48	two	two	NUM
cana-3949	5	49	stages	stage	NOUN
cana-3949	5	50	of	of	ADP
cana-3949	5	51	heterogeneous	heterogeneous	ADJ
cana-3949	5	52	service	service	NOUN
cana-3949	5	53	with	with	ADP
cana-3949	5	54	different	different	ADJ
cana-3949	5	55	(	(	PUNCT
cana-3949	5	56	arbitrary	arbitrary	ADJ
cana-3949	5	57	)	)	PUNCT
cana-3949	5	58	service	service	NOUN
cana-3949	5	59	time	time	NOUN
cana-3949	5	60	distributions	distribution	NOUN
cana-3949	5	61	subject	subject	ADJ
cana-3949	5	62	to	to	ADP
cana-3949	5	63	deterministic	deterministic	ADJ
cana-3949	5	64	vacation	vacation	NOUN
cana-3949	5	65	of	of	ADP
cana-3949	5	66	constant	constant	ADJ
cana-3949	5	67	duration	duration	NOUN
cana-3949	5	68	𝑑	𝑑	NOUN
cana-3949	5	69	(	(	PUNCT
cana-3949	5	70	>	>	X
cana-3949	5	71	0	0	NUM
cana-3949	5	72	)	)	PUNCT
cana-3949	5	73	.	.	PUNCT
cana-3949	6	1	after	after	ADP
cana-3949	6	2	the	the	DET
cana-3949	6	3	first	first	ADJ
cana-3949	6	4	stage	stage	NOUN
cana-3949	6	5	service	service	NOUN
cana-3949	6	6	,	,	PUNCT
cana-3949	6	7	the	the	DET
cana-3949	6	8	server	server	NOUN
cana-3949	6	9	must	must	AUX
cana-3949	6	10	provide	provide	VERB
cana-3949	6	11	the	the	DET
cana-3949	6	12	second	second	ADJ
cana-3949	6	13	stage	stage	NOUN
cana-3949	6	14	service	service	NOUN
cana-3949	6	15	.	.	PUNCT
cana-3949	7	1	we	we	PRON
cana-3949	7	2	assume	assume	VERB
cana-3949	7	3	that	that	SCONJ
cana-3949	7	4	after	after	ADP
cana-3949	7	5	completion	completion	NOUN
cana-3949	7	6	of	of	ADP
cana-3949	7	7	second	second	ADJ
cana-3949	7	8	stage	stage	NOUN
cana-3949	7	9	service	service	NOUN
cana-3949	7	10	,	,	PUNCT
cana-3949	7	11	the	the	DET
cana-3949	7	12	server	server	NOUN
cana-3949	7	13	may	may	AUX
cana-3949	7	14	decide	decide	VERB
cana-3949	7	15	to	to	PART
cana-3949	7	16	take	take	VERB
cana-3949	7	17	a	a	DET
cana-3949	7	18	vacation	vacation	NOUN
cana-3949	7	19	of	of	ADP
cana-3949	7	20	fixed	fix	VERB
cana-3949	7	21	length	length	NOUN
cana-3949	7	22	𝑑	𝑑	PROPN
cana-3949	7	23	(	(	PUNCT
cana-3949	7	24	>	>	X
cana-3949	7	25	0	0	NUM
cana-3949	7	26	)	)	PUNCT
cana-3949	7	27	.	.	PUNCT
cana-3949	8	1	the	the	DET
cana-3949	8	2	time	time	NOUN
cana-3949	8	3	dependent	dependent	ADJ
cana-3949	8	4	probability	probability	NOUN
cana-3949	8	5	generating	generating	NOUN
cana-3949	8	6	functions	function	NOUN
cana-3949	8	7	using	use	VERB
cana-3949	8	8	supplementary	supplementary	ADJ
cana-3949	8	9	variable	variable	ADJ
cana-3949	8	10	technique	technique	NOUN
cana-3949	8	11	have	have	AUX
cana-3949	8	12	been	be	AUX
cana-3949	8	13	obtained	obtain	VERB
cana-3949	8	14	in	in	ADP
cana-3949	8	15	terms	term	NOUN
cana-3949	8	16	of	of	ADP
cana-3949	8	17	their	their	PRON
cana-3949	8	18	laplace	laplace	NOUN
cana-3949	8	19	transforms	transform	VERB
cana-3949	8	20	and	and	CCONJ
cana-3949	8	21	the	the	DET
cana-3949	8	22	corresponding	correspond	VERB
cana-3949	8	23	steady	steady	ADJ
cana-3949	8	24	state	state	NOUN
cana-3949	8	25	results	result	NOUN
cana-3949	8	26	are	be	AUX
cana-3949	8	27	also	also	ADV
cana-3949	8	28	obtained	obtain	VERB
cana-3949	8	29	explicitly	explicitly	ADV
cana-3949	8	30	.	.	PUNCT
cana-3949	9	1	keywords	keyword	NOUN
cana-3949	9	2	:	:	PUNCT
cana-3949	9	3	poisson	poisson	NOUN
cana-3949	9	4	arrivals	arrival	NOUN
cana-3949	9	5	,	,	PUNCT
cana-3949	9	6	probability	probability	NOUN
cana-3949	9	7	generating	generating	NOUN
cana-3949	9	8	function	function	NOUN
cana-3949	9	9	,	,	PUNCT
cana-3949	9	10	transient	transient	ADJ
cana-3949	9	11	state	state	NOUN
cana-3949	9	12	,	,	PUNCT
cana-3949	9	13	steady	steady	ADJ
cana-3949	9	14	state	state	NOUN
cana-3949	9	15	,	,	PUNCT
cana-3949	9	16	supplementary	supplementary	ADJ
cana-3949	9	17	variable	variable	ADJ
cana-3949	9	18	technique	technique	NOUN
cana-3949	9	19	.	.	PUNCT
cana-3949	10	1	1	1	X
cana-3949	10	2	.	.	X
cana-3949	10	3	introduction	introduction	NOUN
cana-3949	10	4	in	in	ADP
cana-3949	10	5	recent	recent	ADJ
cana-3949	10	6	years	year	NOUN
cana-3949	10	7	queues	queue	NOUN
cana-3949	10	8	with	with	ADP
cana-3949	10	9	server	server	NOUN
cana-3949	10	10	vacations	vacation	NOUN
cana-3949	10	11	have	have	AUX
cana-3949	10	12	emerged	emerge	VERB
cana-3949	10	13	as	as	ADP
cana-3949	10	14	an	an	DET
cana-3949	10	15	important	important	ADJ
cana-3949	10	16	area	area	NOUN
cana-3949	10	17	of	of	ADP
cana-3949	10	18	queueing	queue	VERB
cana-3949	10	19	theory	theory	NOUN
cana-3949	10	20	and	and	CCONJ
cana-3949	10	21	have	have	AUX
cana-3949	10	22	been	be	AUX
cana-3949	10	23	studied	study	VERB
cana-3949	10	24	extensively	extensively	ADV
cana-3949	10	25	due	due	ADP
cana-3949	10	26	to	to	ADP
cana-3949	10	27	their	their	PRON
cana-3949	10	28	various	various	ADJ
cana-3949	10	29	applications	application	NOUN
cana-3949	10	30	in	in	ADP
cana-3949	10	31	production	production	NOUN
cana-3949	10	32	,	,	PUNCT
cana-3949	10	33	inventory	inventory	NOUN
cana-3949	10	34	systems	system	NOUN
cana-3949	10	35	,	,	PUNCT
cana-3949	10	36	communication	communication	NOUN
cana-3949	10	37	systems	system	NOUN
cana-3949	10	38	,	,	PUNCT
cana-3949	10	39	computer	computer	NOUN
cana-3949	10	40	networks	network	NOUN
cana-3949	10	41	etc	etc	X
cana-3949	10	42	.	.	PUNCT
cana-3949	11	1	some	some	PRON
cana-3949	11	2	of	of	ADP
cana-3949	11	3	the	the	DET
cana-3949	11	4	few	few	ADJ
cana-3949	11	5	important	important	ADJ
cana-3949	11	6	monographs	monograph	NOUN
cana-3949	11	7	on	on	ADP
cana-3949	11	8	queueing	queue	VERB
cana-3949	11	9	theory	theory	NOUN
cana-3949	11	10	for	for	ADP
cana-3949	11	11	the	the	DET
cana-3949	11	12	performance	performance	NOUN
cana-3949	11	13	prediction	prediction	NOUN
cana-3949	11	14	of	of	ADP
cana-3949	11	15	computer	computer	NOUN
cana-3949	11	16	networks	network	NOUN
cana-3949	11	17	and	and	CCONJ
cana-3949	11	18	communication	communication	NOUN
cana-3949	11	19	systems	system	NOUN
cana-3949	11	20	include	include	VERB
cana-3949	11	21	kleinrock	kleinrock	PROPN
cana-3949	11	22	[	[	X
cana-3949	11	23	11	11	NUM
cana-3949	11	24	]	]	PUNCT
cana-3949	11	25	,	,	PUNCT
cana-3949	11	26	cohen	cohen	PROPN
cana-3949	11	27	(	(	PUNCT
cana-3949	11	28	[	[	X
cana-3949	11	29	2],[3	2],[3	NUM
cana-3949	11	30	]	]	PUNCT
cana-3949	11	31	)	)	PUNCT
cana-3949	11	32	,	,	PUNCT
cana-3949	11	33	doshi	doshi	PROPN
cana-3949	11	34	(	(	PUNCT
cana-3949	11	35	[	[	X
cana-3949	11	36	4	4	NUM
cana-3949	11	37	]	]	PUNCT
cana-3949	11	38	,	,	PUNCT
cana-3949	11	39	[	[	X
cana-3949	11	40	5	5	NUM
cana-3949	11	41	]	]	PUNCT
cana-3949	11	42	,	,	PUNCT
cana-3949	11	43	[	[	X
cana-3949	11	44	6	6	NUM
cana-3949	11	45	]	]	NUM
cana-3949	11	46	)	)	PUNCT
cana-3949	11	47	,	,	PUNCT
cana-3949	11	48	lavenberg	lavenberg	PROPN
cana-3949	12	1	[	[	X
cana-3949	12	2	13	13	NUM
cana-3949	12	3	]	]	PUNCT
cana-3949	12	4	,	,	PUNCT
cana-3949	12	5	takagi	takagi	PROPN
cana-3949	13	1	[	[	X
cana-3949	13	2	17	17	NUM
cana-3949	13	3	]	]	PUNCT
cana-3949	13	4	and	and	CCONJ
cana-3949	13	5	several	several	ADJ
cana-3949	13	6	others	other	NOUN
cana-3949	13	7	.	.	PUNCT
cana-3949	14	1	the	the	DET
cana-3949	14	2	single	single	ADJ
cana-3949	14	3	server	server	NOUN
cana-3949	14	4	queue	queue	NOUN
cana-3949	14	5	with	with	ADP
cana-3949	14	6	two	two	NUM
cana-3949	14	7	phases	phase	NOUN
cana-3949	14	8	of	of	ADP
cana-3949	14	9	service	service	NOUN
cana-3949	14	10	subject	subject	NOUN
cana-3949	14	11	to	to	ADP
cana-3949	14	12	vacation	vacation	NOUN
cana-3949	14	13	has	have	AUX
cana-3949	14	14	paid	pay	VERB
cana-3949	14	15	attention	attention	NOUN
cana-3949	14	16	recently	recently	ADV
cana-3949	14	17	by	by	ADP
cana-3949	14	18	several	several	ADJ
cana-3949	14	19	researchers	researcher	NOUN
cana-3949	14	20	.	.	PUNCT
cana-3949	15	1	presently	presently	ADV
cana-3949	15	2	such	such	ADJ
cana-3949	15	3	type	type	NOUN
cana-3949	15	4	of	of	ADP
cana-3949	15	5	models	model	NOUN
cana-3949	15	6	has	have	AUX
cana-3949	15	7	been	be	AUX
cana-3949	15	8	the	the	DET
cana-3949	15	9	subject	subject	ADJ
cana-3949	15	10	matter	matter	NOUN
cana-3949	15	11	of	of	ADP
cana-3949	15	12	current	current	ADJ
cana-3949	15	13	research	research	NOUN
cana-3949	15	14	mainly	mainly	ADV
cana-3949	15	15	due	due	ADP
cana-3949	15	16	to	to	ADP
cana-3949	15	17	its	its	PRON
cana-3949	15	18	applications	application	NOUN
cana-3949	15	19	in	in	ADP
cana-3949	15	20	computer	computer	NOUN
cana-3949	15	21	and	and	CCONJ
cana-3949	15	22	communication	communication	NOUN
cana-3949	15	23	systems	system	NOUN
cana-3949	15	24	.	.	PUNCT
cana-3949	16	1	one	one	NUM
cana-3949	16	2	of	of	ADP
cana-3949	16	3	the	the	DET
cana-3949	16	4	most	most	ADV
cana-3949	16	5	important	important	ADJ
cana-3949	16	6	results	result	NOUN
cana-3949	16	7	that	that	PRON
cana-3949	16	8	deals	deal	VERB
cana-3949	16	9	with	with	ADP
cana-3949	16	10	such	such	ADJ
cana-3949	16	11	models	model	NOUN
cana-3949	16	12	is	be	AUX
cana-3949	16	13	”	"	PUNCT
cana-3949	16	14	stochastic	stochastic	ADJ
cana-3949	16	15	decomposition	decomposition	NOUN
cana-3949	16	16	result	result	NOUN
cana-3949	16	17	”	"	PUNCT
cana-3949	16	18	which	which	PRON
cana-3949	16	19	was	be	AUX
cana-3949	16	20	first	first	ADV
cana-3949	16	21	established	establish	VERB
cana-3949	16	22	by	by	ADP
cana-3949	16	23	fuhrmann	fuhrmann	NOUN
cana-3949	16	24	and	and	CCONJ
cana-3949	16	25	cooper	cooper	NOUN
cana-3949	17	1	[	[	X
cana-3949	17	2	8	8	NUM
cana-3949	17	3	]	]	PUNCT
cana-3949	17	4	for	for	ADP
cana-3949	17	5	m	m	PROPN
cana-3949	17	6	/	/	SYM
cana-3949	17	7	g/1	g/1	NOUN
cana-3949	17	8	type	type	NOUN
cana-3949	17	9	queues	queue	NOUN
cana-3949	17	10	with	with	ADP
cana-3949	17	11	generalized	generalized	ADJ
cana-3949	17	12	vacations	vacation	NOUN
cana-3949	17	13	.	.	PUNCT
cana-3949	18	1	the	the	DET
cana-3949	18	2	queueing	queue	VERB
cana-3949	18	3	system	system	NOUN
cana-3949	18	4	with	with	ADP
cana-3949	18	5	two	two	NUM
cana-3949	18	6	phase	phase	NOUN
cana-3949	18	7	service	service	NOUN
cana-3949	18	8	has	have	AUX
cana-3949	18	9	been	be	AUX
cana-3949	18	10	first	first	ADV
cana-3949	18	11	studied	study	VERB
cana-3949	18	12	by	by	ADP
cana-3949	18	13	krishna	krishna	PROPN
cana-3949	18	14	and	and	CCONJ
cana-3949	18	15	lee	lee	PROPN
cana-3949	19	1	[	[	X
cana-3949	19	2	12	12	NUM
cana-3949	19	3	]	]	PUNCT
cana-3949	19	4	.	.	PUNCT
cana-3949	20	1	doshi	doshi	PROPN
cana-3949	21	1	[	[	X
cana-3949	21	2	7	7	NUM
cana-3949	21	3	]	]	PUNCT
cana-3949	21	4	has	have	AUX
cana-3949	21	5	expanded	expand	VERB
cana-3949	21	6	two	two	NUM
cana-3949	21	7	phase	phase	NOUN
cana-3949	21	8	queueing	queue	VERB
cana-3949	21	9	system	system	NOUN
cana-3949	21	10	of	of	ADP
cana-3949	21	11	krishna	krishna	PROPN
cana-3949	21	12	and	and	CCONJ
cana-3949	21	13	lee	lee	PROPN
cana-3949	21	14	into	into	ADP
cana-3949	21	15	the	the	DET
cana-3949	21	16	case	case	NOUN
cana-3949	21	17	of	of	ADP
cana-3949	21	18	batch	batch	NOUN
cana-3949	21	19	and	and	CCONJ
cana-3949	21	20	individual	individual	ADJ
cana-3949	21	21	service	service	NOUN
cana-3949	21	22	times	time	NOUN
cana-3949	21	23	with	with	ADP
cana-3949	21	24	general	general	ADJ
cana-3949	21	25	distributions	distribution	NOUN
cana-3949	21	26	.	.	PUNCT
cana-3949	22	1	by	by	ADP
cana-3949	22	2	using	use	VERB
cana-3949	22	3	an	an	DET
cana-3949	22	4	embedded	embed	VERB
cana-3949	22	5	markov	markov	NOUN
cana-3949	22	6	chain	chain	NOUN
cana-3949	22	7	approach	approach	NOUN
cana-3949	22	8	,	,	PUNCT
cana-3949	22	9	the	the	DET
cana-3949	22	10	distribution	distribution	NOUN
cana-3949	22	11	for	for	ADP
cana-3949	22	12	the	the	DET
cana-3949	22	13	system	system	NOUN
cana-3949	22	14	size	size	NOUN
cana-3949	22	15	and	and	CCONJ
cana-3949	22	16	sojourn	sojourn	NOUN
cana-3949	22	17	time	time	NOUN
cana-3949	22	18	of	of	ADP
cana-3949	22	19	a	a	DET
cana-3949	22	20	customer	customer	NOUN
cana-3949	22	21	is	be	AUX
cana-3949	22	22	derived	derive	VERB
cana-3949	22	23	.	.	PUNCT
cana-3949	23	1	recently	recently	ADV
cana-3949	23	2	there	there	PRON
cana-3949	23	3	have	have	AUX
cana-3949	23	4	been	be	AUX
cana-3949	23	5	several	several	ADJ
cana-3949	23	6	contributions	contribution	NOUN
cana-3949	23	7	considering	consider	VERB
cana-3949	23	8	queueing	queue	VERB
cana-3949	23	9	systems	system	NOUN
cana-3949	23	10	of	of	ADP
cana-3949	23	11	m	m	NOUN
cana-3949	23	12	/	/	SYM
cana-3949	23	13	g/1	g/1	NOUN
cana-3949	23	14	type	type	NOUN
cana-3949	23	15	in	in	ADP
cana-3949	23	16	which	which	PRON
cana-3949	23	17	the	the	DET
cana-3949	23	18	server	server	NOUN
cana-3949	23	19	may	may	AUX
cana-3949	23	20	provide	provide	VERB
cana-3949	23	21	a	a	DET
cana-3949	23	22	second	second	ADJ
cana-3949	23	23	phase	phase	NOUN
cana-3949	23	24	of	of	ADP
cana-3949	23	25	service	service	NOUN
cana-3949	23	26	.	.	PUNCT
cana-3949	24	1	the	the	DET
cana-3949	24	2	steady	steady	ADJ
cana-3949	24	3	state	state	NOUN
cana-3949	24	4	behaviour	behaviour	NOUN
cana-3949	24	5	of	of	ADP
cana-3949	24	6	a	a	DET
cana-3949	24	7	m	m	NOUN
cana-3949	24	8	/	/	SYM
cana-3949	24	9	g/1	g/1	NOUN
cana-3949	24	10	queue	queue	NOUN
cana-3949	24	11	with	with	ADP
cana-3949	24	12	two	two	NUM
cana-3949	24	13	types	type	NOUN
cana-3949	24	14	of	of	ADP
cana-3949	24	15	general	general	ADJ
cana-3949	24	16	heterogeneous	heterogeneous	ADJ
cana-3949	24	17	service	service	NOUN
cana-3949	24	18	and	and	CCONJ
cana-3949	24	19	optional	optional	ADJ
cana-3949	24	20	repeated	repeat	VERB
cana-3949	24	21	service	service	NOUN
cana-3949	24	22	subject	subject	NOUN
cana-3949	24	23	to	to	ADP
cana-3949	24	24	server	server	NOUN
cana-3949	24	25	’s	’s	PART
cana-3949	24	26	breakdowns	breakdown	NOUN
cana-3949	24	27	and	and	CCONJ
cana-3949	24	28	delayed	delay	VERB
cana-3949	24	29	repair	repair	NOUN
cana-3949	24	30	is	be	AUX
cana-3949	24	31	studied	study	VERB
cana-3949	24	32	by	by	ADP
cana-3949	24	33	choudhury	choudhury	PROPN
cana-3949	24	34	and	and	CCONJ
cana-3949	24	35	chandi	chandi	PROPN
cana-3949	24	36	ram	ram	PROPN
cana-3949	24	37	kalita	kalita	PROPN
cana-3949	25	1	[	[	X
cana-3949	25	2	1	1	NUM
cana-3949	25	3	]	]	PUNCT
cana-3949	25	4	.	.	PUNCT
cana-3949	26	1	the	the	DET
cana-3949	26	2	joint	joint	ADJ
cana-3949	26	3	distribution	distribution	NOUN
cana-3949	26	4	of	of	ADP
cana-3949	26	5	state	state	NOUN
cana-3949	26	6	of	of	ADP
cana-3949	26	7	the	the	DET
cana-3949	26	8	server	server	NOUN
cana-3949	26	9	and	and	CCONJ
cana-3949	26	10	queue	queue	NOUN
cana-3949	26	11	size	size	NOUN
cana-3949	26	12	by	by	ADP
cana-3949	26	13	considering	consider	VERB
cana-3949	26	14	both	both	PRON
cana-3949	26	15	elapsed	elapse	VERB
cana-3949	26	16	and	and	CCONJ
cana-3949	26	17	remaining	remaining	ADJ
cana-3949	26	18	time	time	NOUN
cana-3949	26	19	are	be	AUX
cana-3949	26	20	https://www.researchgate.net/profile/chandi-kalita?_tp=eyjjb250zxh0ijp7imzpcnn0ugfnzsi6inb1ymxpy2f0aw9uiiwicgfnzsi6inb1ymxpy2f0aw9uin19	https://www.researchgate.net/profile/chandi-kalita?_tp=eyjjb250zxh0ijp7imzpcnn0ugfnzsi6inb1ymxpy2f0aw9uiiwicgfnzsi6inb1ymxpy2f0aw9uin19	NOUN
cana-3949	26	21	communications	communication	NOUN
cana-3949	26	22	on	on	ADP
cana-3949	26	23	applied	apply	VERB
cana-3949	26	24	nonlinear	nonlinear	ADJ
cana-3949	26	25	analysis	analysis	NOUN
cana-3949	26	26	issn	issn	NOUN
cana-3949	26	27	:	:	PUNCT
cana-3949	26	28	1074	1074	NUM
cana-3949	26	29	-	-	PUNCT
cana-3949	26	30	133x	133x	NUM
cana-3949	26	31	vol	vol	NOUN
cana-3949	26	32	32	32	NUM
cana-3949	26	33	no	no	NOUN
cana-3949	26	34	.	.	PUNCT
cana-3949	27	1	9s	9s	NUM
cana-3949	27	2	(	(	PUNCT
cana-3949	27	3	2025	2025	NUM
cana-3949	27	4	)	)	PUNCT
cana-3949	27	5	378	378	NUM
cana-3949	27	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3949	27	7	derived	derive	VERB
cana-3949	27	8	explicitly	explicitly	ADV
cana-3949	27	9	for	for	ADP
cana-3949	27	10	that	that	DET
cana-3949	27	11	model	model	NOUN
cana-3949	27	12	.	.	PUNCT
cana-3949	28	1	a	a	DET
cana-3949	28	2	m	m	NOUN
cana-3949	28	3	/	/	SYM
cana-3949	28	4	g/1	g/1	NOUN
cana-3949	28	5	retrial	retrial	NOUN
cana-3949	28	6	queueing	queue	VERB
cana-3949	28	7	system	system	NOUN
cana-3949	28	8	with	with	ADP
cana-3949	28	9	two	two	NUM
cana-3949	28	10	phases	phase	NOUN
cana-3949	28	11	of	of	ADP
cana-3949	28	12	service	service	NOUN
cana-3949	28	13	in	in	ADP
cana-3949	28	14	which	which	PRON
cana-3949	28	15	the	the	DET
cana-3949	28	16	second	second	ADJ
cana-3949	28	17	phase	phase	NOUN
cana-3949	28	18	is	be	AUX
cana-3949	28	19	optional	optional	ADJ
cana-3949	28	20	and	and	CCONJ
cana-3949	28	21	the	the	DET
cana-3949	28	22	server	server	NOUN
cana-3949	28	23	operating	operate	VERB
cana-3949	28	24	under	under	ADP
cana-3949	28	25	bernoulli	bernoulli	NOUN
cana-3949	28	26	vacation	vacation	NOUN
cana-3949	28	27	schedule	schedule	NOUN
cana-3949	28	28	is	be	AUX
cana-3949	28	29	investigated	investigate	VERB
cana-3949	28	30	by	by	ADP
cana-3949	28	31	pavai	pavai	VERB
cana-3949	28	32	madheswari	madheswari	PROPN
cana-3949	28	33	et	et	NOUN
cana-3949	28	34	.	.	PUNCT
cana-3949	29	1	al	al	PROPN
cana-3949	30	1	[	[	X
cana-3949	30	2	14	14	NUM
cana-3949	30	3	]	]	PUNCT
cana-3949	30	4	.	.	PUNCT
cana-3949	31	1	in	in	ADP
cana-3949	31	2	that	that	DET
cana-3949	31	3	model	model	NOUN
cana-3949	31	4	,	,	PUNCT
cana-3949	31	5	the	the	DET
cana-3949	31	6	customer	customer	NOUN
cana-3949	31	7	is	be	AUX
cana-3949	31	8	allowed	allow	VERB
cana-3949	31	9	to	to	PART
cana-3949	31	10	balk	balk	VERB
cana-3949	31	11	upon	upon	SCONJ
cana-3949	31	12	arrival	arrival	NOUN
cana-3949	31	13	if	if	SCONJ
cana-3949	31	14	he	he	PRON
cana-3949	31	15	finds	find	VERB
cana-3949	31	16	the	the	DET
cana-3949	31	17	server	server	NOUN
cana-3949	31	18	unavailable	unavailable	ADJ
cana-3949	31	19	to	to	PART
cana-3949	31	20	serve	serve	VERB
cana-3949	31	21	his	his	PRON
cana-3949	31	22	request	request	NOUN
cana-3949	31	23	immediately	immediately	ADV
cana-3949	31	24	.	.	PUNCT
cana-3949	32	1	the	the	DET
cana-3949	32	2	joint	joint	ADJ
cana-3949	32	3	generating	generating	NOUN
cana-3949	32	4	functions	function	NOUN
cana-3949	32	5	of	of	ADP
cana-3949	32	6	orbit	orbit	NOUN
cana-3949	32	7	size	size	NOUN
cana-3949	32	8	and	and	CCONJ
cana-3949	32	9	server	server	NOUN
cana-3949	32	10	status	status	NOUN
cana-3949	32	11	are	be	AUX
cana-3949	32	12	derived	derive	VERB
cana-3949	32	13	using	use	VERB
cana-3949	32	14	supplementary	supplementary	ADJ
cana-3949	32	15	variable	variable	ADJ
cana-3949	32	16	technique	technique	NOUN
cana-3949	32	17	.	.	PUNCT
cana-3949	33	1	a	a	DET
cana-3949	33	2	non	non	ADJ
cana-3949	33	3	-	-	ADJ
cana-3949	33	4	markovian	markovian	ADJ
cana-3949	33	5	queueing	queueing	NOUN
cana-3949	33	6	model	model	NOUN
cana-3949	33	7	with	with	ADP
cana-3949	33	8	setup	setup	NOUN
cana-3949	33	9	time	time	NOUN
cana-3949	33	10	and	and	CCONJ
cana-3949	33	11	balking	balking	NOUN
cana-3949	33	12	is	be	AUX
cana-3949	33	13	studied	study	VERB
cana-3949	33	14	by	by	ADP
cana-3949	33	15	s.	s.	PROPN
cana-3949	33	16	shyamala	shyamala	PROPN
cana-3949	33	17	and	and	CCONJ
cana-3949	33	18	r.	r.	PROPN
cana-3949	33	19	vijayaraj	vijayaraj	VERB
cana-3949	34	1	[	[	X
cana-3949	34	2	15	15	NUM
cana-3949	34	3	]	]	PUNCT
cana-3949	34	4	.	.	PUNCT
cana-3949	35	1	in	in	ADP
cana-3949	35	2	this	this	DET
cana-3949	35	3	model	model	NOUN
cana-3949	35	4	,	,	PUNCT
cana-3949	35	5	the	the	DET
cana-3949	35	6	server	server	NOUN
cana-3949	35	7	provides	provide	VERB
cana-3949	35	8	two	two	NUM
cana-3949	35	9	stages	stage	NOUN
cana-3949	35	10	of	of	ADP
cana-3949	35	11	service	service	NOUN
cana-3949	35	12	in	in	ADP
cana-3949	35	13	which	which	PRON
cana-3949	35	14	the	the	DET
cana-3949	35	15	service	service	NOUN
cana-3949	35	16	time	time	NOUN
cana-3949	35	17	for	for	ADP
cana-3949	35	18	each	each	DET
cana-3949	35	19	customer	customer	NOUN
cana-3949	35	20	follows	follow	VERB
cana-3949	35	21	general	general	ADJ
cana-3949	35	22	distribution	distribution	NOUN
cana-3949	35	23	.	.	PUNCT
cana-3949	36	1	upon	upon	SCONJ
cana-3949	36	2	completion	completion	NOUN
cana-3949	36	3	of	of	ADP
cana-3949	36	4	a	a	DET
cana-3949	36	5	service	service	NOUN
cana-3949	36	6	the	the	DET
cana-3949	36	7	server	server	NOUN
cana-3949	36	8	may	may	AUX
cana-3949	36	9	go	go	VERB
cana-3949	36	10	for	for	ADP
cana-3949	36	11	a	a	DET
cana-3949	36	12	vacation	vacation	NOUN
cana-3949	36	13	with	with	ADP
cana-3949	36	14	probability	probability	NOUN
cana-3949	36	15	𝑝	𝑝	NOUN
cana-3949	36	16	or	or	CCONJ
cana-3949	36	17	stay	stay	VERB
cana-3949	36	18	back	back	ADV
cana-3949	36	19	in	in	ADP
cana-3949	36	20	the	the	DET
cana-3949	36	21	system	system	NOUN
cana-3949	36	22	to	to	PART
cana-3949	36	23	serve	serve	VERB
cana-3949	36	24	a	a	DET
cana-3949	36	25	next	next	ADJ
cana-3949	36	26	customer	customer	NOUN
cana-3949	36	27	with	with	ADP
cana-3949	36	28	probability	probability	NOUN
cana-3949	36	29	1−	1−	NUM
cana-3949	36	30	𝑝	𝑝	NOUN
cana-3949	36	31	if	if	SCONJ
cana-3949	36	32	any	any	PRON
cana-3949	36	33	.	.	PUNCT
cana-3949	37	1	a	a	DET
cana-3949	37	2	new	new	ADJ
cana-3949	37	3	model	model	NOUN
cana-3949	37	4	of	of	ADP
cana-3949	37	5	a	a	DET
cana-3949	37	6	queueing	queue	VERB
cana-3949	37	7	system	system	NOUN
cana-3949	37	8	which	which	PRON
cana-3949	37	9	provides	provide	VERB
cana-3949	37	10	two	two	NUM
cana-3949	37	11	stage	stage	NOUN
cana-3949	37	12	first	first	ADV
cana-3949	37	13	essential	essential	ADJ
cana-3949	37	14	service	service	NOUN
cana-3949	37	15	followed	follow	VERB
cana-3949	37	16	by	by	ADP
cana-3949	37	17	one	one	NUM
cana-3949	37	18	of	of	ADP
cana-3949	37	19	the	the	DET
cana-3949	37	20	two	two	NUM
cana-3949	37	21	types	type	NOUN
cana-3949	37	22	of	of	ADP
cana-3949	37	23	additional	additional	ADJ
cana-3949	37	24	optional	optional	ADJ
cana-3949	37	25	service	service	NOUN
cana-3949	37	26	is	be	AUX
cana-3949	37	27	analysed	analyse	VERB
cana-3949	37	28	by	by	ADP
cana-3949	37	29	k.	k.	PROPN
cana-3949	37	30	c	c	PROPN
cana-3949	37	31	madan	madan	PROPN
cana-3949	38	1	[	[	X
cana-3949	38	2	9	9	NUM
cana-3949	38	3	]	]	PUNCT
cana-3949	38	4	.	.	PUNCT
cana-3949	39	1	moreover	moreover	ADV
cana-3949	39	2	,	,	PUNCT
cana-3949	39	3	the	the	DET
cana-3949	39	4	server	server	NOUN
cana-3949	39	5	has	have	VERB
cana-3949	39	6	the	the	DET
cana-3949	39	7	option	option	NOUN
cana-3949	39	8	to	to	PART
cana-3949	39	9	take	take	VERB
cana-3949	39	10	a	a	DET
cana-3949	39	11	vacation	vacation	NOUN
cana-3949	39	12	of	of	ADP
cana-3949	39	13	constant	constant	ADJ
cana-3949	39	14	length	length	NOUN
cana-3949	39	15	.	.	PUNCT
cana-3949	40	1	a	a	DET
cana-3949	40	2	batch	batch	NOUN
cana-3949	40	3	arrival	arrival	NOUN
cana-3949	40	4	single	single	ADJ
cana-3949	40	5	service	service	NOUN
cana-3949	40	6	queue	queue	NOUN
cana-3949	40	7	with	with	ADP
cana-3949	40	8	two	two	NUM
cana-3949	40	9	stages	stage	NOUN
cana-3949	40	10	of	of	ADP
cana-3949	40	11	service	service	NOUN
cana-3949	40	12	(	(	PUNCT
cana-3949	40	13	second	second	ADJ
cana-3949	40	14	stage	stage	NOUN
cana-3949	40	15	is	be	AUX
cana-3949	40	16	optional	optional	ADJ
cana-3949	40	17	)	)	PUNCT
cana-3949	40	18	and	and	CCONJ
cana-3949	40	19	working	work	VERB
cana-3949	40	20	breakdown	breakdown	NOUN
cana-3949	40	21	is	be	AUX
cana-3949	40	22	investigated	investigate	VERB
cana-3949	40	23	by	by	ADP
cana-3949	40	24	b.	b.	PROPN
cana-3949	40	25	somasundaram	somasundaram	PROPN
cana-3949	40	26	et	et	PROPN
cana-3949	40	27	.	.	PUNCT
cana-3949	41	1	al	al	PROPN
cana-3949	42	1	[	[	X
cana-3949	42	2	16	16	NUM
cana-3949	42	3	]	]	PUNCT
cana-3949	42	4	.	.	PUNCT
cana-3949	43	1	when	when	SCONJ
cana-3949	43	2	the	the	DET
cana-3949	43	3	system	system	NOUN
cana-3949	43	4	is	be	AUX
cana-3949	43	5	in	in	ADP
cana-3949	43	6	operation	operation	NOUN
cana-3949	43	7	,	,	PUNCT
cana-3949	43	8	it	it	PRON
cana-3949	43	9	may	may	AUX
cana-3949	43	10	breakdown	breakdown	VERB
cana-3949	43	11	at	at	ADP
cana-3949	43	12	any	any	DET
cana-3949	43	13	time	time	NOUN
cana-3949	43	14	.	.	PUNCT
cana-3949	44	1	during	during	ADP
cana-3949	44	2	breakdown	breakdown	ADJ
cana-3949	44	3	period	period	NOUN
cana-3949	44	4	,	,	PUNCT
cana-3949	44	5	instead	instead	ADV
cana-3949	44	6	of	of	ADP
cana-3949	44	7	terminating	terminate	VERB
cana-3949	44	8	the	the	DET
cana-3949	44	9	service	service	NOUN
cana-3949	44	10	totally	totally	ADV
cana-3949	44	11	,	,	PUNCT
cana-3949	44	12	it	it	PRON
cana-3949	44	13	continues	continue	VERB
cana-3949	44	14	at	at	ADP
cana-3949	44	15	a	a	DET
cana-3949	44	16	slower	slow	ADJ
cana-3949	44	17	rate	rate	NOUN
cana-3949	44	18	.	.	PUNCT
cana-3949	45	1	k.	k.	PROPN
cana-3949	46	1	c.	c.	PROPN
cana-3949	46	2	madan	madan	PROPN
cana-3949	47	1	[	[	X
cana-3949	47	2	10	10	NUM
cana-3949	47	3	]	]	PUNCT
cana-3949	47	4	has	have	AUX
cana-3949	47	5	studied	study	VERB
cana-3949	47	6	a	a	DET
cana-3949	47	7	m	m	PROPN
cana-3949	47	8	/	/	SYM
cana-3949	47	9	g/1	g/1	NOUN
cana-3949	47	10	single	single	ADJ
cana-3949	47	11	server	server	NOUN
cana-3949	47	12	vacation	vacation	NOUN
cana-3949	47	13	queue	queue	NOUN
cana-3949	47	14	with	with	ADP
cana-3949	47	15	two	two	NUM
cana-3949	47	16	types	type	NOUN
cana-3949	47	17	of	of	ADP
cana-3949	47	18	service	service	NOUN
cana-3949	47	19	and	and	CCONJ
cana-3949	47	20	two	two	NUM
cana-3949	47	21	types	type	NOUN
cana-3949	47	22	of	of	ADP
cana-3949	47	23	vacation	vacation	NOUN
cana-3949	47	24	.	.	PUNCT
cana-3949	48	1	using	use	VERB
cana-3949	48	2	supplementary	supplementary	ADJ
cana-3949	48	3	variable	variable	ADJ
cana-3949	48	4	technique	technique	NOUN
cana-3949	48	5	,	,	PUNCT
cana-3949	48	6	a	a	DET
cana-3949	48	7	steady	steady	ADJ
cana-3949	48	8	state	state	NOUN
cana-3949	48	9	solution	solution	NOUN
cana-3949	48	10	in	in	ADP
cana-3949	48	11	terms	term	NOUN
cana-3949	48	12	of	of	ADP
cana-3949	48	13	the	the	DET
cana-3949	48	14	generating	generate	VERB
cana-3949	48	15	function	function	NOUN
cana-3949	48	16	of	of	ADP
cana-3949	48	17	the	the	DET
cana-3949	48	18	queue	queue	NOUN
cana-3949	48	19	length	length	NOUN
cana-3949	48	20	as	as	ADV
cana-3949	48	21	well	well	ADV
cana-3949	48	22	as	as	ADP
cana-3949	48	23	the	the	DET
cana-3949	48	24	steady	steady	ADJ
cana-3949	48	25	state	state	NOUN
cana-3949	48	26	probabilities	probability	NOUN
cana-3949	48	27	for	for	ADP
cana-3949	48	28	all	all	DET
cana-3949	48	29	different	different	ADJ
cana-3949	48	30	states	state	NOUN
cana-3949	48	31	of	of	ADP
cana-3949	48	32	the	the	DET
cana-3949	48	33	system	system	NOUN
cana-3949	48	34	are	be	AUX
cana-3949	48	35	derived	derive	VERB
cana-3949	48	36	.	.	PUNCT
cana-3949	49	1	many	many	ADJ
cana-3949	49	2	researchers	researcher	NOUN
cana-3949	49	3	have	have	AUX
cana-3949	49	4	developed	develop	VERB
cana-3949	49	5	several	several	ADJ
cana-3949	49	6	models	model	NOUN
cana-3949	49	7	involving	involve	VERB
cana-3949	49	8	single	single	ADJ
cana-3949	49	9	vacation	vacation	NOUN
cana-3949	49	10	policy	policy	NOUN
cana-3949	49	11	but	but	CCONJ
cana-3949	49	12	only	only	ADV
cana-3949	49	13	few	few	ADJ
cana-3949	49	14	models	model	NOUN
cana-3949	49	15	have	have	AUX
cana-3949	49	16	been	be	AUX
cana-3949	49	17	studied	study	VERB
cana-3949	49	18	subject	subject	ADJ
cana-3949	49	19	to	to	ADP
cana-3949	49	20	compulsory	compulsory	ADJ
cana-3949	49	21	vacation	vacation	NOUN
cana-3949	49	22	.	.	PUNCT
cana-3949	50	1	examples	example	NOUN
cana-3949	50	2	of	of	ADP
cana-3949	50	3	this	this	DET
cana-3949	50	4	kind	kind	NOUN
cana-3949	50	5	of	of	ADP
cana-3949	50	6	situation	situation	NOUN
cana-3949	50	7	may	may	AUX
cana-3949	50	8	well	well	ADV
cana-3949	50	9	be	be	AUX
cana-3949	50	10	found	find	VERB
cana-3949	50	11	in	in	ADP
cana-3949	50	12	some	some	DET
cana-3949	50	13	transport	transport	NOUN
cana-3949	50	14	systems	system	NOUN
cana-3949	50	15	in	in	ADP
cana-3949	50	16	which	which	PRON
cana-3949	50	17	a	a	DET
cana-3949	50	18	ferry	ferry	NOUN
cana-3949	50	19	driver	driver	NOUN
cana-3949	50	20	or	or	CCONJ
cana-3949	50	21	a	a	DET
cana-3949	50	22	locomotive	locomotive	ADJ
cana-3949	50	23	driver	driver	NOUN
cana-3949	50	24	may	may	AUX
cana-3949	50	25	like	like	VERB
cana-3949	50	26	to	to	PART
cana-3949	50	27	go	go	VERB
cana-3949	50	28	to	to	ADP
cana-3949	50	29	on	on	ADP
cana-3949	50	30	a	a	DET
cana-3949	50	31	vacation	vacation	NOUN
cana-3949	50	32	after	after	ADP
cana-3949	50	33	every	every	DET
cana-3949	50	34	round	round	ADJ
cana-3949	50	35	trip	trip	NOUN
cana-3949	50	36	.	.	PUNCT
cana-3949	51	1	such	such	DET
cana-3949	51	2	a	a	DET
cana-3949	51	3	trip	trip	NOUN
cana-3949	51	4	essentially	essentially	ADV
cana-3949	51	5	involves	involve	VERB
cana-3949	51	6	a	a	DET
cana-3949	51	7	two	two	NUM
cana-3949	51	8	stage	stage	NOUN
cana-3949	51	9	service	service	NOUN
cana-3949	51	10	,	,	PUNCT
cana-3949	51	11	that	that	PRON
cana-3949	51	12	is	be	AUX
cana-3949	51	13	trip	trip	NOUN
cana-3949	51	14	to	to	ADP
cana-3949	51	15	a	a	DET
cana-3949	51	16	particular	particular	ADJ
cana-3949	51	17	destination	destination	NOUN
cana-3949	51	18	and	and	CCONJ
cana-3949	51	19	back	back	ADV
cana-3949	51	20	to	to	ADP
cana-3949	51	21	the	the	DET
cana-3949	51	22	starting	starting	NOUN
cana-3949	51	23	point	point	NOUN
cana-3949	51	24	.	.	PUNCT
cana-3949	52	1	there	there	PRON
cana-3949	52	2	are	be	VERB
cana-3949	52	3	probably	probably	ADV
cana-3949	52	4	many	many	ADJ
cana-3949	52	5	other	other	ADJ
cana-3949	52	6	situations	situation	NOUN
cana-3949	52	7	such	such	ADJ
cana-3949	52	8	as	as	ADP
cana-3949	52	9	some	some	DET
cana-3949	52	10	manufacturing	manufacturing	NOUN
cana-3949	52	11	processes	process	NOUN
cana-3949	52	12	which	which	PRON
cana-3949	52	13	involves	involve	VERB
cana-3949	52	14	two	two	NUM
cana-3949	52	15	stages	stage	NOUN
cana-3949	52	16	of	of	ADP
cana-3949	52	17	service	service	NOUN
cana-3949	52	18	and	and	CCONJ
cana-3949	52	19	machines	machine	NOUN
cana-3949	52	20	that	that	PRON
cana-3949	52	21	need	need	VERB
cana-3949	52	22	to	to	PART
cana-3949	52	23	be	be	AUX
cana-3949	52	24	stopped	stop	VERB
cana-3949	52	25	for	for	ADP
cana-3949	52	26	overhauling	overhaul	VERB
cana-3949	52	27	,	,	PUNCT
cana-3949	52	28	etc	etc	X
cana-3949	52	29	.	.	X
cana-3949	52	30	,	,	PUNCT
cana-3949	52	31	after	after	SCONJ
cana-3949	52	32	each	each	DET
cana-3949	52	33	two	two	NUM
cana-3949	52	34	stage	stage	NOUN
cana-3949	52	35	service	service	NOUN
cana-3949	52	36	is	be	AUX
cana-3949	52	37	complete	complete	ADJ
cana-3949	52	38	.	.	PUNCT
cana-3949	53	1	in	in	ADP
cana-3949	53	2	the	the	DET
cana-3949	53	3	present	present	ADJ
cana-3949	53	4	work	work	NOUN
cana-3949	53	5	,	,	PUNCT
cana-3949	53	6	we	we	PRON
cana-3949	53	7	study	study	VERB
cana-3949	53	8	a	a	DET
cana-3949	53	9	single	single	ADJ
cana-3949	53	10	server	server	NOUN
cana-3949	53	11	vacation	vacation	NOUN
cana-3949	53	12	queue	queue	NOUN
cana-3949	53	13	with	with	ADP
cana-3949	53	14	poisson	poisson	PROPN
cana-3949	53	15	arrivals	arrival	NOUN
cana-3949	53	16	,	,	PUNCT
cana-3949	53	17	two	two	NUM
cana-3949	53	18	stages	stage	NOUN
cana-3949	53	19	of	of	ADP
cana-3949	53	20	heterogeneous	heterogeneous	ADJ
cana-3949	53	21	service	service	NOUN
cana-3949	53	22	with	with	ADP
cana-3949	53	23	different	different	ADJ
cana-3949	53	24	(	(	PUNCT
cana-3949	53	25	arbitrary	arbitrary	ADJ
cana-3949	53	26	)	)	PUNCT
cana-3949	53	27	service	service	NOUN
cana-3949	53	28	time	time	NOUN
cana-3949	53	29	distributions	distribution	NOUN
cana-3949	53	30	subject	subject	ADJ
cana-3949	53	31	to	to	ADP
cana-3949	53	32	deterministic	deterministic	ADJ
cana-3949	53	33	vacation	vacation	NOUN
cana-3949	53	34	of	of	ADP
cana-3949	53	35	constant	constant	ADJ
cana-3949	53	36	duration	duration	NOUN
cana-3949	53	37	d	d	PROPN
cana-3949	53	38	(	(	PUNCT
cana-3949	53	39	>	>	X
cana-3949	53	40	0	0	NUM
cana-3949	53	41	)	)	PUNCT
cana-3949	53	42	.	.	PUNCT
cana-3949	54	1	after	after	ADP
cana-3949	54	2	the	the	DET
cana-3949	54	3	first	first	ADJ
cana-3949	54	4	stage	stage	NOUN
cana-3949	54	5	service	service	NOUN
cana-3949	54	6	,	,	PUNCT
cana-3949	54	7	the	the	DET
cana-3949	54	8	server	server	NOUN
cana-3949	54	9	must	must	AUX
cana-3949	54	10	provide	provide	VERB
cana-3949	54	11	the	the	DET
cana-3949	54	12	second	second	ADJ
cana-3949	54	13	stage	stage	NOUN
cana-3949	54	14	service	service	NOUN
cana-3949	54	15	.	.	PUNCT
cana-3949	55	1	further	far	ADV
cana-3949	55	2	,	,	PUNCT
cana-3949	55	3	we	we	PRON
cana-3949	55	4	assume	assume	VERB
cana-3949	55	5	that	that	SCONJ
cana-3949	55	6	after	after	ADP
cana-3949	55	7	completion	completion	NOUN
cana-3949	55	8	of	of	ADP
cana-3949	55	9	second	second	ADJ
cana-3949	55	10	stage	stage	NOUN
cana-3949	55	11	service	service	NOUN
cana-3949	55	12	,	,	PUNCT
cana-3949	55	13	the	the	DET
cana-3949	55	14	server	server	NOUN
cana-3949	55	15	may	may	AUX
cana-3949	55	16	decide	decide	VERB
cana-3949	55	17	to	to	PART
cana-3949	55	18	take	take	VERB
cana-3949	55	19	a	a	DET
cana-3949	55	20	vacation	vacation	NOUN
cana-3949	55	21	of	of	ADP
cana-3949	55	22	fixed	fix	VERB
cana-3949	55	23	length	length	NOUN
cana-3949	56	1	d	d	PROPN
cana-3949	56	2	(	(	PUNCT
cana-3949	56	3	>	>	X
cana-3949	56	4	0	0	NUM
cana-3949	56	5	)	)	PUNCT
cana-3949	56	6	.	.	PUNCT
cana-3949	57	1	this	this	DET
cana-3949	57	2	kind	kind	NOUN
cana-3949	57	3	of	of	ADP
cana-3949	57	4	problems	problem	NOUN
cana-3949	57	5	in	in	ADP
cana-3949	57	6	real	real	ADJ
cana-3949	57	7	life	life	NOUN
cana-3949	57	8	can	can	AUX
cana-3949	57	9	be	be	AUX
cana-3949	57	10	seen	see	VERB
cana-3949	57	11	in	in	ADP
cana-3949	57	12	production	production	NOUN
cana-3949	57	13	and	and	CCONJ
cana-3949	57	14	manufacturing	manufacturing	NOUN
cana-3949	57	15	industries	industry	NOUN
cana-3949	57	16	.	.	PUNCT
cana-3949	58	1	the	the	DET
cana-3949	58	2	rest	rest	NOUN
cana-3949	58	3	of	of	ADP
cana-3949	58	4	the	the	DET
cana-3949	58	5	paper	paper	NOUN
cana-3949	58	6	is	be	AUX
cana-3949	58	7	organized	organize	VERB
cana-3949	58	8	as	as	SCONJ
cana-3949	58	9	follows	follow	VERB
cana-3949	58	10	.	.	PUNCT
cana-3949	59	1	the	the	DET
cana-3949	59	2	mathematical	mathematical	ADJ
cana-3949	59	3	description	description	NOUN
cana-3949	59	4	of	of	ADP
cana-3949	59	5	our	our	PRON
cana-3949	59	6	model	model	NOUN
cana-3949	59	7	is	be	AUX
cana-3949	59	8	in	in	ADP
cana-3949	59	9	section	section	NOUN
cana-3949	59	10	2	2	NUM
cana-3949	59	11	.	.	PUNCT
cana-3949	60	1	definitions	definition	NOUN
cana-3949	60	2	representing	represent	VERB
cana-3949	60	3	the	the	DET
cana-3949	60	4	model	model	NOUN
cana-3949	60	5	and	and	CCONJ
cana-3949	60	6	equations	equation	NOUN
cana-3949	60	7	governing	govern	VERB
cana-3949	60	8	the	the	DET
cana-3949	60	9	model	model	NOUN
cana-3949	60	10	are	be	AUX
cana-3949	60	11	there	there	ADV
cana-3949	60	12	in	in	ADP
cana-3949	60	13	section	section	NOUN
cana-3949	60	14	3	3	NUM
cana-3949	60	15	.	.	PUNCT
cana-3949	61	1	the	the	DET
cana-3949	61	2	time	time	NOUN
cana-3949	61	3	dependent	dependent	ADJ
cana-3949	61	4	solutions	solution	NOUN
cana-3949	61	5	have	have	AUX
cana-3949	61	6	been	be	AUX
cana-3949	61	7	obtained	obtain	VERB
cana-3949	61	8	in	in	ADP
cana-3949	61	9	section	section	NOUN
cana-3949	61	10	4	4	NUM
cana-3949	61	11	using	use	VERB
cana-3949	61	12	supplementary	supplementary	ADJ
cana-3949	61	13	variable	variable	ADJ
cana-3949	61	14	technique	technique	NOUN
cana-3949	61	15	and	and	CCONJ
cana-3949	61	16	the	the	DET
cana-3949	61	17	corresponding	correspond	VERB
cana-3949	61	18	steady	steady	ADJ
cana-3949	61	19	state	state	NOUN
cana-3949	61	20	results	result	NOUN
cana-3949	61	21	have	have	AUX
cana-3949	61	22	been	be	AUX
cana-3949	61	23	derived	derive	VERB
cana-3949	61	24	explicitly	explicitly	ADV
cana-3949	61	25	in	in	ADP
cana-3949	61	26	section	section	NOUN
cana-3949	61	27	5	5	NUM
cana-3949	61	28	.	.	NOUN
cana-3949	61	29	2	2	NUM
cana-3949	61	30	.	.	NOUN
cana-3949	61	31	assumptions	assumption	NOUN
cana-3949	61	32	underlying	underlie	VERB
cana-3949	61	33	the	the	DET
cana-3949	61	34	model	model	NOUN
cana-3949	61	35	the	the	DET
cana-3949	61	36	following	follow	VERB
cana-3949	61	37	assumptions	assumption	NOUN
cana-3949	61	38	describe	describe	VERB
cana-3949	61	39	the	the	DET
cana-3949	61	40	mathematical	mathematical	ADJ
cana-3949	61	41	model	model	NOUN
cana-3949	61	42	.	.	PUNCT
cana-3949	62	1	•	•	NUM
cana-3949	62	2	customers	customer	NOUN
cana-3949	62	3	arrive	arrive	VERB
cana-3949	62	4	at	at	ADP
cana-3949	62	5	the	the	DET
cana-3949	62	6	system	system	NOUN
cana-3949	62	7	one	one	NUM
cana-3949	62	8	by	by	ADP
cana-3949	62	9	one	one	NUM
cana-3949	62	10	in	in	ADP
cana-3949	62	11	according	accord	VERB
cana-3949	62	12	to	to	ADP
cana-3949	62	13	a	a	DET
cana-3949	62	14	poisson	poisson	NOUN
cana-3949	62	15	stream	stream	NOUN
cana-3949	62	16	with	with	ADP
cana-3949	62	17	arrival	arrival	NOUN
cana-3949	62	18	rate	rate	NOUN
cana-3949	62	19	𝜆	𝜆	NOUN
cana-3949	62	20	(	(	PUNCT
cana-3949	62	21	>	>	X
cana-3949	62	22	0	0	NUM
cana-3949	62	23	)	)	PUNCT
cana-3949	62	24	.	.	PUNCT
cana-3949	63	1	https://www.researchgate.net/profile/pavai-soundararajan?_tp=eyjjb250zxh0ijp7imzpcnn0ugfnzsi6inb1ymxpy2f0aw9uiiwicgfnzsi6inb1ymxpy2f0aw9uin19	https://www.researchgate.net/profile/pavai-soundararajan?_tp=eyjjb250zxh0ijp7imzpcnn0ugfnzsi6inb1ymxpy2f0aw9uiiwicgfnzsi6inb1ymxpy2f0aw9uin19	PROPN
cana-3949	63	2	javascript	javascript	NOUN
cana-3949	63	3	:	:	PUNCT
cana-3949	63	4	;	;	PUNCT
cana-3949	63	5	javascript	javascript	NOUN
cana-3949	63	6	:	:	PUNCT
cana-3949	63	7	;	;	PUNCT
cana-3949	63	8	communications	communication	NOUN
cana-3949	63	9	on	on	ADP
cana-3949	63	10	applied	apply	VERB
cana-3949	63	11	nonlinear	nonlinear	ADJ
cana-3949	63	12	analysis	analysis	NOUN
cana-3949	63	13	issn	issn	NOUN
cana-3949	63	14	:	:	PUNCT
cana-3949	63	15	1074	1074	NUM
cana-3949	63	16	-	-	PUNCT
cana-3949	63	17	133x	133x	NUM
cana-3949	63	18	vol	vol	NOUN
cana-3949	63	19	32	32	NUM
cana-3949	63	20	no	no	NOUN
cana-3949	63	21	.	.	PUNCT
cana-3949	64	1	9s	9s	NUM
cana-3949	64	2	(	(	PUNCT
cana-3949	64	3	2025	2025	NUM
cana-3949	64	4	)	)	PUNCT
cana-3949	64	5	379	379	NUM
cana-3949	64	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3949	64	7	•	•	NOUN
cana-3949	64	8	each	each	DET
cana-3949	64	9	customer	customer	NOUN
cana-3949	64	10	undergoes	undergo	VERB
cana-3949	64	11	two	two	NUM
cana-3949	64	12	stages	stage	NOUN
cana-3949	64	13	of	of	ADP
cana-3949	64	14	heterogeneous	heterogeneous	ADJ
cana-3949	64	15	service	service	NOUN
cana-3949	64	16	provided	provide	VERB
cana-3949	64	17	by	by	ADP
cana-3949	64	18	a	a	DET
cana-3949	64	19	single	single	ADJ
cana-3949	64	20	server	server	NOUN
cana-3949	64	21	on	on	ADP
cana-3949	64	22	a	a	DET
cana-3949	64	23	first	first	ADJ
cana-3949	64	24	come	come	NOUN
cana-3949	64	25	first	first	ADV
cana-3949	64	26	served	serve	VERB
cana-3949	64	27	basis	basis	NOUN
cana-3949	64	28	.	.	PUNCT
cana-3949	65	1	the	the	DET
cana-3949	65	2	service	service	NOUN
cana-3949	65	3	time	time	NOUN
cana-3949	65	4	of	of	ADP
cana-3949	65	5	two	two	NUM
cana-3949	65	6	stages	stage	NOUN
cana-3949	65	7	follow	follow	VERB
cana-3949	65	8	different	different	ADJ
cana-3949	65	9	general	general	ADJ
cana-3949	65	10	(	(	PUNCT
cana-3949	65	11	distributions	distribution	NOUN
cana-3949	65	12	)	)	PUNCT
cana-3949	65	13	with	with	ADP
cana-3949	65	14	distribution	distribution	NOUN
cana-3949	65	15	function	function	NOUN
cana-3949	65	16	𝐵𝑗(𝑣	𝐵𝑗(𝑣	NOUN
cana-3949	65	17	)	)	PUNCT
cana-3949	65	18	and	and	CCONJ
cana-3949	65	19	the	the	DET
cana-3949	65	20	density	density	NOUN
cana-3949	65	21	function	function	NOUN
cana-3949	65	22	𝑏𝑗(𝑣	𝑏𝑗(𝑣	NOUN
cana-3949	65	23	)	)	PUNCT
cana-3949	65	24	,	,	PUNCT
cana-3949	65	25	𝑗	𝑗	NOUN
cana-3949	65	26	=	=	SYM
cana-3949	65	27	1,2	1,2	NUM
cana-3949	65	28	.	.	PUNCT
cana-3949	65	29	•	•	NUM
cana-3949	65	30	let	let	VERB
cana-3949	65	31	𝜇𝑖(𝑥)𝑑𝑥	𝜇𝑖(𝑥)𝑑𝑥	PRON
cana-3949	65	32	be	be	AUX
cana-3949	65	33	the	the	DET
cana-3949	65	34	conditional	conditional	ADJ
cana-3949	65	35	probability	probability	NOUN
cana-3949	65	36	of	of	ADP
cana-3949	65	37	completion	completion	NOUN
cana-3949	65	38	of	of	ADP
cana-3949	65	39	the	the	DET
cana-3949	65	40	𝑖𝑡ℎ	𝑖𝑡ℎ	NOUN
cana-3949	65	41	stage	stage	NOUN
cana-3949	65	42	of	of	ADP
cana-3949	65	43	service	service	NOUN
cana-3949	65	44	during	during	ADP
cana-3949	65	45	the	the	DET
cana-3949	65	46	interval	interval	NOUN
cana-3949	65	47	(	(	PUNCT
cana-3949	65	48	𝑥	𝑥	NOUN
cana-3949	65	49	+	+	X
cana-3949	65	50	𝑑𝑥	𝑑𝑥	AUX
cana-3949	65	51	]	]	X
cana-3949	65	52	given	give	VERB
cana-3949	65	53	that	that	SCONJ
cana-3949	65	54	the	the	DET
cana-3949	65	55	elapsed	elapse	VERB
cana-3949	65	56	service	service	NOUN
cana-3949	65	57	time	time	NOUN
cana-3949	65	58	is	be	AUX
cana-3949	65	59	𝑥	𝑥	NOUN
cana-3949	65	60	,	,	PUNCT
cana-3949	65	61	so	so	SCONJ
cana-3949	65	62	that	that	SCONJ
cana-3949	65	63	𝜇𝑖(x	𝜇𝑖(x	NOUN
cana-3949	65	64	)	)	PUNCT
cana-3949	65	65	=	=	SYM
cana-3949	65	66	𝑏𝑖(𝑥	𝑏𝑖(𝑥	X
cana-3949	65	67	)	)	PUNCT
cana-3949	65	68	1−𝐵𝑖(𝑥	1−𝐵𝑖(𝑥	NUM
cana-3949	65	69	)	)	PUNCT
cana-3949	65	70	,	,	PUNCT
cana-3949	65	71	𝑖	𝑖	NOUN
cana-3949	65	72	=	=	SYM
cana-3949	65	73	1,2	1,2	NUM
cana-3949	65	74	.	.	PUNCT
cana-3949	66	1	(	(	PUNCT
cana-3949	66	2	1	1	NUM
cana-3949	66	3	)	)	PUNCT
cana-3949	66	4	and	and	CCONJ
cana-3949	66	5	therefore	therefore	ADV
cana-3949	66	6	𝑏𝑖(𝑣	𝑏𝑖(𝑣	X
cana-3949	66	7	)	)	PUNCT
cana-3949	66	8	=	=	PUNCT
cana-3949	66	9	𝜇𝑖(𝑣)𝑒	𝜇𝑖(𝑣)𝑒	NOUN
cana-3949	66	10	−∫	−∫	VERB
cana-3949	66	11	𝜇𝑖(𝑥)𝑑𝑥	𝜇𝑖(𝑥)𝑑𝑥	NUM
cana-3949	66	12	∞	∞	NUM
cana-3949	66	13	0	0	NUM
cana-3949	66	14	.	.	PUNCT
cana-3949	67	1	(	(	PUNCT
cana-3949	67	2	2	2	NUM
cana-3949	67	3	)	)	PUNCT
cana-3949	67	4	•	•	NOUN
cana-3949	67	5	as	as	ADV
cana-3949	67	6	soon	soon	ADV
cana-3949	67	7	as	as	SCONJ
cana-3949	67	8	the	the	DET
cana-3949	67	9	service	service	NOUN
cana-3949	67	10	of	of	ADP
cana-3949	67	11	the	the	DET
cana-3949	67	12	second	second	ADJ
cana-3949	67	13	stage	stage	NOUN
cana-3949	67	14	of	of	ADP
cana-3949	67	15	a	a	DET
cana-3949	67	16	customer	customer	NOUN
cana-3949	67	17	is	be	AUX
cana-3949	67	18	complete	complete	ADJ
cana-3949	67	19	,	,	PUNCT
cana-3949	67	20	then	then	ADV
cana-3949	67	21	the	the	DET
cana-3949	67	22	server	server	NOUN
cana-3949	67	23	goes	go	VERB
cana-3949	67	24	for	for	ADP
cana-3949	67	25	compulsory	compulsory	ADJ
cana-3949	67	26	vacation	vacation	NOUN
cana-3949	67	27	.	.	PUNCT
cana-3949	68	1	•	•	INTJ
cana-3949	68	2	we	we	PRON
cana-3949	68	3	assume	assume	VERB
cana-3949	68	4	that	that	SCONJ
cana-3949	68	5	whenever	whenever	SCONJ
cana-3949	68	6	the	the	DET
cana-3949	68	7	server	server	NOUN
cana-3949	68	8	takes	take	VERB
cana-3949	68	9	a	a	DET
cana-3949	68	10	vacation	vacation	NOUN
cana-3949	68	11	,	,	PUNCT
cana-3949	68	12	it	it	PRON
cana-3949	68	13	is	be	AUX
cana-3949	68	14	of	of	ADP
cana-3949	68	15	constant	constant	ADJ
cana-3949	68	16	duration	duration	NOUN
cana-3949	68	17	𝑑	𝑑	NOUN
cana-3949	68	18	(	(	PUNCT
cana-3949	68	19	>	>	X
cana-3949	68	20	0	0	NUM
cana-3949	68	21	)	)	PUNCT
cana-3949	68	22	.	.	PUNCT
cana-3949	69	1	•	•	NUM
cana-3949	69	2	on	on	ADP
cana-3949	69	3	returning	return	VERB
cana-3949	69	4	from	from	ADP
cana-3949	69	5	vacation	vacation	NOUN
cana-3949	69	6	the	the	DET
cana-3949	69	7	server	server	NOUN
cana-3949	69	8	instantly	instantly	ADV
cana-3949	69	9	starts	start	VERB
cana-3949	69	10	serving	serve	VERB
cana-3949	69	11	the	the	DET
cana-3949	69	12	customer	customer	NOUN
cana-3949	69	13	at	at	ADP
cana-3949	69	14	the	the	DET
cana-3949	69	15	head	head	NOUN
cana-3949	69	16	of	of	ADP
cana-3949	69	17	the	the	DET
cana-3949	69	18	queue	queue	NOUN
cana-3949	69	19	.	.	PUNCT
cana-3949	70	1	•	•	NOUN
cana-3949	70	2	the	the	DET
cana-3949	70	3	customers	customer	NOUN
cana-3949	70	4	are	be	AUX
cana-3949	70	5	served	serve	VERB
cana-3949	70	6	according	accord	VERB
cana-3949	70	7	to	to	ADP
cana-3949	70	8	the	the	DET
cana-3949	70	9	first	first	ADJ
cana-3949	70	10	come	come	NOUN
cana-3949	70	11	,	,	PUNCT
cana-3949	70	12	first	first	ADV
cana-3949	70	13	served	serve	VERB
cana-3949	70	14	rule	rule	NOUN
cana-3949	70	15	.	.	PUNCT
cana-3949	71	1	•	•	NUM
cana-3949	71	2	various	various	ADJ
cana-3949	71	3	stochastic	stochastic	ADJ
cana-3949	71	4	processes	process	NOUN
cana-3949	71	5	involved	involve	VERB
cana-3949	71	6	in	in	ADP
cana-3949	71	7	the	the	DET
cana-3949	71	8	system	system	NOUN
cana-3949	71	9	are	be	AUX
cana-3949	71	10	independent	independent	ADJ
cana-3949	71	11	of	of	ADP
cana-3949	71	12	each	each	DET
cana-3949	71	13	other	other	ADJ
cana-3949	71	14	.	.	PUNCT
cana-3949	72	1	3	3	X
cana-3949	72	2	.	.	X
cana-3949	72	3	definitions	definition	NOUN
cana-3949	72	4	,	,	PUNCT
cana-3949	72	5	notations	notation	NOUN
cana-3949	72	6	and	and	CCONJ
cana-3949	72	7	equations	equation	NOUN
cana-3949	72	8	governing	govern	VERB
cana-3949	72	9	the	the	DET
cana-3949	72	10	system	system	NOUN
cana-3949	72	11	we	we	PRON
cana-3949	72	12	define	define	VERB
cana-3949	72	13	•	•	NOUN
cana-3949	72	14	𝑃𝑛	𝑃𝑛	PROPN
cana-3949	72	15	(	(	PUNCT
cana-3949	72	16	1	1	NUM
cana-3949	72	17	)	)	PUNCT
cana-3949	72	18	(	(	PUNCT
cana-3949	72	19	𝑥	𝑥	NOUN
cana-3949	72	20	,	,	PUNCT
cana-3949	72	21	𝑡	𝑡	PROPN
cana-3949	72	22	)	)	PUNCT
cana-3949	72	23	:	:	PUNCT
cana-3949	72	24	probability	probability	NOUN
cana-3949	72	25	that	that	SCONJ
cana-3949	72	26	at	at	ADP
cana-3949	72	27	time	time	NOUN
cana-3949	72	28	𝑡	𝑡	PROPN
cana-3949	72	29	,	,	PUNCT
cana-3949	72	30	there	there	PRON
cana-3949	72	31	are	be	VERB
cana-3949	72	32	𝑛	𝑛	DET
cana-3949	72	33	≥	≥	NUM
cana-3949	72	34	0	0	NUM
cana-3949	72	35	customers	customer	NOUN
cana-3949	72	36	in	in	ADP
cana-3949	72	37	the	the	DET
cana-3949	72	38	queue	queue	NOUN
cana-3949	72	39	excluding	exclude	VERB
cana-3949	72	40	one	one	NUM
cana-3949	72	41	customer	customer	NOUN
cana-3949	72	42	in	in	ADP
cana-3949	72	43	first	first	ADJ
cana-3949	72	44	stage	stage	NOUN
cana-3949	72	45	of	of	ADP
cana-3949	72	46	service	service	NOUN
cana-3949	72	47	and	and	CCONJ
cana-3949	72	48	the	the	DET
cana-3949	72	49	elapsed	elapse	VERB
cana-3949	72	50	served	serve	VERB
cana-3949	72	51	time	time	NOUN
cana-3949	72	52	of	of	ADP
cana-3949	72	53	this	this	DET
cana-3949	72	54	customer	customer	NOUN
cana-3949	72	55	is	be	AUX
cana-3949	72	56	𝑥.	𝑥.	VERB
cana-3949	72	57	consequently	consequently	ADV
cana-3949	72	58	𝑃𝑛	𝑃𝑛	PROPN
cana-3949	72	59	(	(	PUNCT
cana-3949	72	60	1)(𝑡	1)(𝑡	NUM
cana-3949	72	61	)	)	PUNCT
cana-3949	72	62	=	=	SYM
cana-3949	73	1	∫	∫	PROPN
cana-3949	74	1	𝑃𝑛	𝑃𝑛	PROPN
cana-3949	74	2	(	(	PUNCT
cana-3949	74	3	1)(𝑥	1)(𝑥	NUM
cana-3949	74	4	,	,	PUNCT
cana-3949	74	5	𝑡)𝑑𝑥	𝑡)𝑑𝑥	PROPN
cana-3949	74	6	∞	∞	NUM
cana-3949	74	7	0	0	NUM
cana-3949	74	8	denotes	denote	VERB
cana-3949	74	9	the	the	DET
cana-3949	74	10	probability	probability	NOUN
cana-3949	74	11	that	that	SCONJ
cana-3949	74	12	at	at	ADP
cana-3949	74	13	time	time	NOUN
cana-3949	74	14	𝑡	𝑡	PROPN
cana-3949	74	15	,	,	PUNCT
cana-3949	74	16	there	there	PRON
cana-3949	74	17	are	be	VERB
cana-3949	74	18	𝑛	𝑛	DET
cana-3949	74	19	customers	customer	NOUN
cana-3949	74	20	in	in	ADP
cana-3949	74	21	the	the	DET
cana-3949	74	22	queue	queue	NOUN
cana-3949	74	23	excluding	exclude	VERB
cana-3949	74	24	the	the	DET
cana-3949	74	25	one	one	NUM
cana-3949	74	26	customer	customer	NOUN
cana-3949	74	27	in	in	ADP
cana-3949	74	28	first	first	ADJ
cana-3949	74	29	stage	stage	NOUN
cana-3949	74	30	of	of	ADP
cana-3949	74	31	service	service	NOUN
cana-3949	74	32	irrespective	irrespective	ADV
cana-3949	74	33	of	of	ADP
cana-3949	74	34	the	the	DET
cana-3949	74	35	value	value	NOUN
cana-3949	74	36	of	of	ADP
cana-3949	74	37	𝑥	𝑥	PROPN
cana-3949	74	38	.	.	PUNCT
cana-3949	75	1	•	•	NUM
cana-3949	75	2	𝑃𝑛	𝑃𝑛	PROPN
cana-3949	75	3	(	(	PUNCT
cana-3949	75	4	2	2	NUM
cana-3949	75	5	)	)	PUNCT
cana-3949	75	6	(	(	PUNCT
cana-3949	75	7	𝑥	𝑥	NOUN
cana-3949	75	8	,	,	PUNCT
cana-3949	75	9	𝑡	𝑡	PROPN
cana-3949	75	10	)	)	PUNCT
cana-3949	75	11	:	:	PUNCT
cana-3949	75	12	probability	probability	NOUN
cana-3949	75	13	that	that	SCONJ
cana-3949	75	14	at	at	ADP
cana-3949	75	15	time	time	NOUN
cana-3949	75	16	𝑡	𝑡	PROPN
cana-3949	75	17	,	,	PUNCT
cana-3949	75	18	there	there	PRON
cana-3949	75	19	are	be	VERB
cana-3949	75	20	𝑛	𝑛	DET
cana-3949	75	21	≥	≥	NUM
cana-3949	75	22	0	0	NUM
cana-3949	75	23	customers	customer	NOUN
cana-3949	75	24	in	in	ADP
cana-3949	75	25	the	the	DET
cana-3949	75	26	queue	queue	NOUN
cana-3949	75	27	excluding	exclude	VERB
cana-3949	75	28	one	one	NUM
cana-3949	75	29	customer	customer	NOUN
cana-3949	75	30	in	in	ADP
cana-3949	75	31	second	second	ADJ
cana-3949	75	32	stage	stage	NOUN
cana-3949	75	33	of	of	ADP
cana-3949	75	34	service	service	NOUN
cana-3949	75	35	and	and	CCONJ
cana-3949	75	36	the	the	DET
cana-3949	75	37	elapsed	elapse	VERB
cana-3949	75	38	served	serve	VERB
cana-3949	75	39	time	time	NOUN
cana-3949	75	40	of	of	ADP
cana-3949	75	41	this	this	DET
cana-3949	75	42	customer	customer	NOUN
cana-3949	75	43	is	be	AUX
cana-3949	75	44	𝑥.	𝑥.	VERB
cana-3949	75	45	consequently	consequently	ADV
cana-3949	75	46	𝑃𝑛	𝑃𝑛	PROPN
cana-3949	75	47	(	(	PUNCT
cana-3949	75	48	2)(𝑡	2)(𝑡	PROPN
cana-3949	75	49	)	)	PUNCT
cana-3949	75	50	=	=	SYM
cana-3949	76	1	∫	∫	PROPN
cana-3949	76	2	𝑃𝑛	𝑃𝑛	PROPN
cana-3949	76	3	(	(	PUNCT
cana-3949	76	4	2)(𝑥	2)(𝑥	NUM
cana-3949	76	5	,	,	PUNCT
cana-3949	76	6	𝑡)𝑑𝑥	𝑡)𝑑𝑥	PROPN
cana-3949	76	7	∞	∞	NUM
cana-3949	76	8	0	0	NUM
cana-3949	76	9	denotes	denote	VERB
cana-3949	76	10	the	the	DET
cana-3949	76	11	probability	probability	NOUN
cana-3949	76	12	that	that	SCONJ
cana-3949	76	13	at	at	ADP
cana-3949	76	14	time	time	NOUN
cana-3949	76	15	𝑡	𝑡	PROPN
cana-3949	76	16	,	,	PUNCT
cana-3949	76	17	there	there	PRON
cana-3949	76	18	are	be	VERB
cana-3949	76	19	𝑛	𝑛	DET
cana-3949	76	20	customers	customer	NOUN
cana-3949	76	21	in	in	ADP
cana-3949	76	22	the	the	DET
cana-3949	76	23	queue	queue	NOUN
cana-3949	76	24	excluding	exclude	VERB
cana-3949	76	25	the	the	DET
cana-3949	76	26	one	one	NUM
cana-3949	76	27	customer	customer	NOUN
cana-3949	76	28	in	in	ADP
cana-3949	76	29	second	second	ADJ
cana-3949	76	30	stage	stage	NOUN
cana-3949	76	31	of	of	ADP
cana-3949	76	32	service	service	NOUN
cana-3949	76	33	irrespective	irrespective	ADV
cana-3949	76	34	of	of	ADP
cana-3949	76	35	the	the	DET
cana-3949	76	36	value	value	NOUN
cana-3949	76	37	of	of	ADP
cana-3949	76	38	𝑥	𝑥	PROPN
cana-3949	76	39	.	.	PUNCT
cana-3949	77	1	•	•	NUM
cana-3949	77	2	𝑉𝑛(𝑡	𝑉𝑛(𝑡	NOUN
cana-3949	77	3	)	)	PUNCT
cana-3949	78	1	:	:	PUNCT
cana-3949	78	2	probability	probability	NOUN
cana-3949	78	3	that	that	SCONJ
cana-3949	78	4	at	at	ADP
cana-3949	78	5	time	time	NOUN
cana-3949	78	6	𝑡	𝑡	PROPN
cana-3949	78	7	,	,	PUNCT
cana-3949	78	8	there	there	PRON
cana-3949	78	9	are	be	VERB
cana-3949	78	10	𝑛	𝑛	DET
cana-3949	78	11	≥	≥	NUM
cana-3949	78	12	0	0	NUM
cana-3949	78	13	customers	customer	NOUN
cana-3949	78	14	in	in	ADP
cana-3949	78	15	the	the	DET
cana-3949	78	16	queue	queue	NOUN
cana-3949	78	17	and	and	CCONJ
cana-3949	78	18	the	the	DET
cana-3949	78	19	server	server	NOUN
cana-3949	78	20	is	be	AUX
cana-3949	78	21	under	under	ADP
cana-3949	78	22	vacation	vacation	NOUN
cana-3949	78	23	.	.	PUNCT
cana-3949	79	1	•	•	NUM
cana-3949	79	2	𝑄(𝑡	𝑄(𝑡	PRON
cana-3949	79	3	)	)	PUNCT
cana-3949	80	1	:	:	PUNCT
cana-3949	80	2	probability	probability	NOUN
cana-3949	80	3	that	that	SCONJ
cana-3949	80	4	at	at	ADP
cana-3949	80	5	time	time	NOUN
cana-3949	80	6	𝑡	𝑡	NOUN
cana-3949	80	7	,	,	PUNCT
cana-3949	80	8	there	there	PRON
cana-3949	80	9	is	be	VERB
cana-3949	80	10	no	no	DET
cana-3949	80	11	customer	customer	NOUN
cana-3949	80	12	in	in	ADP
cana-3949	80	13	the	the	DET
cana-3949	80	14	system	system	NOUN
cana-3949	80	15	and	and	CCONJ
cana-3949	80	16	the	the	DET
cana-3949	80	17	server	server	NOUN
cana-3949	80	18	is	be	AUX
cana-3949	80	19	idle	idle	ADJ
cana-3949	80	20	but	but	CCONJ
cana-3949	80	21	available	available	ADJ
cana-3949	80	22	in	in	ADP
cana-3949	80	23	the	the	DET
cana-3949	80	24	system	system	NOUN
cana-3949	80	25	.	.	PUNCT
cana-3949	81	1	•	•	INTJ
cana-3949	81	2	we	we	PRON
cana-3949	81	3	assume	assume	VERB
cana-3949	81	4	that	that	SCONJ
cana-3949	81	5	𝑘𝑟	𝑘𝑟	PROPN
cana-3949	81	6	is	be	AUX
cana-3949	81	7	the	the	DET
cana-3949	81	8	probability	probability	NOUN
cana-3949	81	9	of	of	ADP
cana-3949	81	10	𝑟	𝑟	NOUN
cana-3949	81	11	arrivals	arrival	NOUN
cana-3949	81	12	during	during	ADP
cana-3949	81	13	a	a	DET
cana-3949	81	14	vacation	vacation	NOUN
cana-3949	81	15	period	period	NOUN
cana-3949	81	16	of	of	ADP
cana-3949	81	17	duration	duration	NOUN
cana-3949	81	18	𝑑	𝑑	NOUN
cana-3949	81	19	so	so	SCONJ
cana-3949	81	20	that	that	SCONJ
cana-3949	81	21	𝑘𝑟	𝑘𝑟	ADV
cana-3949	81	22	=	=	SYM
cana-3949	81	23	𝑒−𝜆𝑑(𝜆𝑑)𝑟	𝑒−𝜆𝑑(𝜆𝑑)𝑟	PROPN
cana-3949	81	24	𝑟	𝑟	NOUN
cana-3949	81	25	!	!	NOUN
cana-3949	81	26	,	,	PUNCT
cana-3949	81	27	𝑟	𝑟	X
cana-3949	81	28	=	=	SYM
cana-3949	81	29	0,1	0,1	NUM
cana-3949	81	30	,	,	PUNCT
cana-3949	81	31	…	…	PUNCT
cana-3949	81	32	.	.	PUNCT
cana-3949	82	1	(	(	PUNCT
cana-3949	82	2	3	3	X
cana-3949	82	3	)	)	PUNCT
cana-3949	82	4	the	the	DET
cana-3949	82	5	system	system	NOUN
cana-3949	82	6	is	be	AUX
cana-3949	82	7	then	then	ADV
cana-3949	82	8	governed	govern	VERB
cana-3949	82	9	by	by	ADP
cana-3949	82	10	the	the	DET
cana-3949	82	11	following	follow	VERB
cana-3949	82	12	set	set	NOUN
cana-3949	82	13	of	of	ADP
cana-3949	82	14	differential	differential	ADJ
cana-3949	82	15	–	–	PUNCT
cana-3949	82	16	difference	difference	NOUN
cana-3949	82	17	equations	equation	NOUN
cana-3949	82	18	communications	communication	NOUN
cana-3949	82	19	on	on	ADP
cana-3949	82	20	applied	apply	VERB
cana-3949	82	21	nonlinear	nonlinear	ADJ
cana-3949	82	22	analysis	analysis	NOUN
cana-3949	82	23	issn	issn	NOUN
cana-3949	82	24	:	:	PUNCT
cana-3949	82	25	1074	1074	NUM
cana-3949	82	26	-	-	PUNCT
cana-3949	82	27	133x	133x	NUM
cana-3949	82	28	vol	vol	NOUN
cana-3949	82	29	32	32	NUM
cana-3949	82	30	no	no	NOUN
cana-3949	82	31	.	.	PUNCT
cana-3949	83	1	9s	9s	NUM
cana-3949	83	2	(	(	PUNCT
cana-3949	83	3	2025	2025	NUM
cana-3949	83	4	)	)	PUNCT
cana-3949	83	5	380	380	NUM
cana-3949	83	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3949	83	7	𝜕	𝜕	NOUN
cana-3949	83	8	𝜕𝑥	𝜕𝑥	PUNCT
cana-3949	83	9	𝑃𝑛	𝑃𝑛	PROPN
cana-3949	83	10	(	(	PUNCT
cana-3949	83	11	1)(𝑥	1)(𝑥	NUM
cana-3949	83	12	,	,	PUNCT
cana-3949	83	13	𝑡	𝑡	NOUN
cana-3949	83	14	)	)	PUNCT
cana-3949	83	15	+	+	CCONJ
cana-3949	83	16	𝜕	𝜕	NOUN
cana-3949	83	17	𝜕𝑡	𝜕𝑡	NOUN
cana-3949	83	18	𝑃𝑛	𝑃𝑛	PROPN
cana-3949	83	19	(	(	PUNCT
cana-3949	83	20	1)(𝑥	1)(𝑥	NUM
cana-3949	83	21	,	,	PUNCT
cana-3949	83	22	𝑡	𝑡	X
cana-3949	83	23	)	)	PUNCT
cana-3949	83	24	+	+	CCONJ
cana-3949	83	25	(	(	PUNCT
cana-3949	83	26	𝜆	𝜆	X
cana-3949	83	27	+	+	X
cana-3949	83	28	𝜇1(𝑥))𝑃𝑛	𝜇1(𝑥))𝑃𝑛	PROPN
cana-3949	83	29	(	(	PUNCT
cana-3949	83	30	1)(𝑥	1)(𝑥	NUM
cana-3949	83	31	,	,	PUNCT
cana-3949	83	32	𝑡	𝑡	X
cana-3949	83	33	)	)	PUNCT
cana-3949	83	34	=	=	SYM
cana-3949	83	35	𝜆𝑃𝑛−1	𝜆𝑃𝑛−1	NOUN
cana-3949	83	36	(	(	PUNCT
cana-3949	83	37	1	1	NUM
cana-3949	83	38	)	)	PUNCT
cana-3949	83	39	(	(	PUNCT
cana-3949	83	40	𝑥	𝑥	NOUN
cana-3949	83	41	,	,	PUNCT
cana-3949	83	42	𝑡	𝑡	NOUN
cana-3949	83	43	)	)	PUNCT
cana-3949	83	44	,	,	PUNCT
cana-3949	83	45	𝑛	𝑛	NOUN
cana-3949	83	46	=	=	SYM
cana-3949	83	47	1,2	1,2	NUM
cana-3949	83	48	,	,	PUNCT
cana-3949	83	49	…	…	PUNCT
cana-3949	83	50	,	,	PUNCT
cana-3949	83	51	(	(	PUNCT
cana-3949	83	52	4	4	X
cana-3949	83	53	)	)	PUNCT
cana-3949	83	54	𝜕	𝜕	PROPN
cana-3949	83	55	𝜕𝑥	𝜕𝑥	X
cana-3949	83	56	𝑃0	𝑃0	NOUN
cana-3949	83	57	(	(	PUNCT
cana-3949	83	58	1)(𝑥	1)(𝑥	NUM
cana-3949	83	59	,	,	PUNCT
cana-3949	83	60	𝑡	𝑡	NOUN
cana-3949	83	61	)	)	PUNCT
cana-3949	83	62	+	+	CCONJ
cana-3949	83	63	𝜕	𝜕	PROPN
cana-3949	83	64	𝜕𝑡	𝜕𝑡	PROPN
cana-3949	83	65	𝑃0	𝑃0	NOUN
cana-3949	83	66	(	(	PUNCT
cana-3949	83	67	1)(𝑥	1)(𝑥	NUM
cana-3949	83	68	,	,	PUNCT
cana-3949	83	69	𝑡	𝑡	X
cana-3949	83	70	)	)	PUNCT
cana-3949	83	71	+	+	CCONJ
cana-3949	83	72	(	(	PUNCT
cana-3949	83	73	𝜆	𝜆	X
cana-3949	83	74	+	+	X
cana-3949	83	75	𝜇1(𝑥))𝑃0	𝜇1(𝑥))𝑃0	ADJ
cana-3949	83	76	(	(	PUNCT
cana-3949	83	77	1)(𝑥	1)(𝑥	NUM
cana-3949	83	78	,	,	PUNCT
cana-3949	83	79	𝑡	𝑡	X
cana-3949	83	80	)	)	PUNCT
cana-3949	83	81	=	=	SYM
cana-3949	83	82	0	0	NUM
cana-3949	83	83	,	,	PUNCT
cana-3949	83	84	(	(	PUNCT
cana-3949	83	85	5	5	X
cana-3949	83	86	)	)	PUNCT
cana-3949	84	1	𝜕	𝜕	NOUN
cana-3949	84	2	𝜕𝑥	𝜕𝑥	NOUN
cana-3949	84	3	𝑃𝑛	𝑃𝑛	PROPN
cana-3949	84	4	(	(	PUNCT
cana-3949	84	5	2)(𝑥	2)(𝑥	NUM
cana-3949	84	6	,	,	PUNCT
cana-3949	84	7	𝑡	𝑡	NOUN
cana-3949	84	8	)	)	PUNCT
cana-3949	84	9	+	+	CCONJ
cana-3949	84	10	𝜕	𝜕	NOUN
cana-3949	84	11	𝜕𝑡	𝜕𝑡	NOUN
cana-3949	84	12	𝑃𝑛	𝑃𝑛	PROPN
cana-3949	84	13	(	(	PUNCT
cana-3949	84	14	2)(𝑥	2)(𝑥	NUM
cana-3949	84	15	,	,	PUNCT
cana-3949	84	16	𝑡	𝑡	X
cana-3949	84	17	)	)	PUNCT
cana-3949	84	18	+	+	CCONJ
cana-3949	84	19	(	(	PUNCT
cana-3949	84	20	𝜆	𝜆	PROPN
cana-3949	84	21	+	+	X
cana-3949	84	22	𝜇2(𝑥))𝑃𝑛	𝜇2(𝑥))𝑃𝑛	PROPN
cana-3949	84	23	(	(	PUNCT
cana-3949	84	24	2)(𝑥	2)(𝑥	NUM
cana-3949	84	25	,	,	PUNCT
cana-3949	84	26	𝑡	𝑡	NOUN
cana-3949	84	27	)	)	PUNCT
cana-3949	85	1	+	+	CCONJ
cana-3949	85	2	𝜆𝑃𝑛−1	𝜆𝑃𝑛−1	NOUN
cana-3949	85	3	(	(	PUNCT
cana-3949	85	4	1	1	NUM
cana-3949	85	5	)	)	PUNCT
cana-3949	85	6	(	(	PUNCT
cana-3949	85	7	𝑥	𝑥	NOUN
cana-3949	85	8	,	,	PUNCT
cana-3949	85	9	𝑡	𝑡	NOUN
cana-3949	85	10	)	)	PUNCT
cana-3949	85	11	,	,	PUNCT
cana-3949	85	12	𝑛	𝑛	NOUN
cana-3949	85	13	=	=	SYM
cana-3949	85	14	1,2	1,2	NUM
cana-3949	85	15	,	,	PUNCT
cana-3949	85	16	…	…	PUNCT
cana-3949	85	17	,	,	PUNCT
cana-3949	85	18	(	(	PUNCT
cana-3949	85	19	6	6	NUM
cana-3949	85	20	)	)	PUNCT
cana-3949	85	21	𝜕	𝜕	PROPN
cana-3949	85	22	𝜕𝑥	𝜕𝑥	X
cana-3949	85	23	𝑃0	𝑃0	NOUN
cana-3949	85	24	(	(	PUNCT
cana-3949	85	25	2)(𝑥	2)(𝑥	NUM
cana-3949	85	26	,	,	PUNCT
cana-3949	85	27	𝑡	𝑡	NOUN
cana-3949	85	28	)	)	PUNCT
cana-3949	85	29	+	+	CCONJ
cana-3949	85	30	𝜕	𝜕	PROPN
cana-3949	85	31	𝜕𝑡	𝜕𝑡	PROPN
cana-3949	85	32	𝑃0	𝑃0	NOUN
cana-3949	85	33	(	(	PUNCT
cana-3949	85	34	2)(𝑥	2)(𝑥	NUM
cana-3949	85	35	,	,	PUNCT
cana-3949	85	36	𝑡	𝑡	X
cana-3949	85	37	)	)	PUNCT
cana-3949	85	38	+	+	CCONJ
cana-3949	85	39	(	(	PUNCT
cana-3949	85	40	𝜆	𝜆	ADP
cana-3949	85	41	+	+	X
cana-3949	85	42	𝜇2(𝑥))𝑃0	𝜇2(𝑥))𝑃0	X
cana-3949	85	43	(	(	PUNCT
cana-3949	85	44	2)(𝑥	2)(𝑥	NUM
cana-3949	85	45	,	,	PUNCT
cana-3949	85	46	𝑡	𝑡	X
cana-3949	85	47	)	)	PUNCT
cana-3949	85	48	=	=	SYM
cana-3949	85	49	0	0	NUM
cana-3949	85	50	,	,	PUNCT
cana-3949	85	51	(	(	PUNCT
cana-3949	85	52	7	7	X
cana-3949	85	53	)	)	PUNCT
cana-3949	85	54	𝑑	𝑑	VERB
cana-3949	85	55	𝑑𝑡	𝑑𝑡	ADP
cana-3949	85	56	𝑉0(𝑡	𝑉0(𝑡	ADJ
cana-3949	85	57	)	)	PUNCT
cana-3949	85	58	=	=	SYM
cana-3949	85	59	∫	∫	PROPN
cana-3949	85	60	𝑃0	𝑃0	NOUN
cana-3949	85	61	(	(	PUNCT
cana-3949	85	62	2)(𝑥	2)(𝑥	NUM
cana-3949	85	63	,	,	PUNCT
cana-3949	85	64	𝑡)𝜇2(𝑥)𝑑𝑥	𝑡)𝜇2(𝑥)𝑑𝑥	VERB
cana-3949	85	65	∞	∞	NUM
cana-3949	85	66	0	0	PUNCT
cana-3949	86	1	+	+	CCONJ
cana-3949	86	2	𝑉0(𝑡)[−𝐾0	𝑉0(𝑡)[−𝐾0	NUM
cana-3949	86	3	−	−	NOUN
cana-3949	86	4	𝐾1	𝐾1	NOUN
cana-3949	86	5	−⋯	−⋯	PROPN
cana-3949	86	6	]	]	PUNCT
cana-3949	86	7	,	,	PUNCT
cana-3949	86	8	(	(	PUNCT
cana-3949	86	9	8)	8)	NUM
cana-3949	86	10	𝑑	𝑑	NOUN
cana-3949	86	11	𝑑𝑡	𝑑𝑡	ADP
cana-3949	86	12	𝑉𝑛(𝑡	𝑉𝑛(𝑡	NOUN
cana-3949	86	13	)	)	PUNCT
cana-3949	86	14	=	=	SYM
cana-3949	87	1	∫	∫	PROPN
cana-3949	87	2	𝑃𝑛	𝑃𝑛	PROPN
cana-3949	87	3	(	(	PUNCT
cana-3949	87	4	2)(𝑥	2)(𝑥	NUM
cana-3949	87	5	,	,	PUNCT
cana-3949	87	6	𝑡)𝜇2(𝑥)𝑑𝑥	𝑡)𝜇2(𝑥)𝑑𝑥	VERB
cana-3949	87	7	∞	∞	NOUN
cana-3949	87	8	0	0	NUM
cana-3949	88	1	+	+	CCONJ
cana-3949	88	2	𝑉𝑛(𝑡)[−𝐾0	𝑉𝑛(𝑡)[−𝐾0	VERB
cana-3949	88	3	−	−	ADP
cana-3949	88	4	𝐾1	𝐾1	NOUN
cana-3949	89	1	−⋯	−⋯	NUM
cana-3949	89	2	]	]	PUNCT
cana-3949	89	3	,	,	PUNCT
cana-3949	89	4	𝑛	𝑛	PROPN
cana-3949	89	5	=	=	SYM
cana-3949	89	6	1,2	1,2	NUM
cana-3949	89	7	,	,	PUNCT
cana-3949	89	8	…	…	PUNCT
cana-3949	89	9	,	,	PUNCT
cana-3949	89	10	(	(	PUNCT
cana-3949	89	11	9	9	X
cana-3949	89	12	)	)	PUNCT
cana-3949	89	13	𝑑	𝑑	NOUN
cana-3949	89	14	𝑑𝑡	𝑑𝑡	ADP
cana-3949	89	15	𝑄(𝑡	𝑄(𝑡	PRON
cana-3949	89	16	)	)	PUNCT
cana-3949	89	17	=	=	SYM
cana-3949	89	18	−𝜆𝑄(𝑡	−𝜆𝑄(𝑡	X
cana-3949	89	19	)	)	PUNCT
cana-3949	89	20	+	+	CCONJ
cana-3949	89	21	𝑉0(𝑡)𝐾0	𝑉0(𝑡)𝐾0	PROPN
cana-3949	89	22	.	.	PUNCT
cana-3949	90	1	(	(	PUNCT
cana-3949	90	2	10	10	NUM
cana-3949	90	3	)	)	PUNCT
cana-3949	90	4	equations	equation	NOUN
cana-3949	90	5	(	(	PUNCT
cana-3949	90	6	4	4	NUM
cana-3949	90	7	)	)	PUNCT
cana-3949	90	8	−	−	PROPN
cana-3949	90	9	(	(	PUNCT
cana-3949	90	10	10	10	NUM
cana-3949	90	11	)	)	PUNCT
cana-3949	90	12	are	be	AUX
cana-3949	90	13	to	to	PART
cana-3949	90	14	be	be	AUX
cana-3949	90	15	solved	solve	VERB
cana-3949	90	16	subject	subject	ADJ
cana-3949	90	17	to	to	ADP
cana-3949	90	18	following	follow	VERB
cana-3949	90	19	boundary	boundary	ADJ
cana-3949	90	20	conditions	condition	NOUN
cana-3949	90	21	𝑃0	𝑃0	NOUN
cana-3949	90	22	(	(	PUNCT
cana-3949	90	23	1)(0	1)(0	NUM
cana-3949	90	24	,	,	PUNCT
cana-3949	90	25	𝑡	𝑡	NOUN
cana-3949	90	26	)	)	PUNCT
cana-3949	91	1	=	=	SYM
cana-3949	91	2	𝜆𝑄(𝑡)+𝑉0(𝑡)𝑘1+𝑉1(𝑡)𝑘0	𝜆𝑄(𝑡)+𝑉0(𝑡)𝑘1+𝑉1(𝑡)𝑘0	X
cana-3949	91	3	(	(	PUNCT
cana-3949	91	4	11	11	NUM
cana-3949	91	5	)	)	PUNCT
cana-3949	91	6	𝑃𝑛	𝑃𝑛	NOUN
cana-3949	91	7	(	(	PUNCT
cana-3949	91	8	1)(0	1)(0	NUM
cana-3949	91	9	,	,	PUNCT
cana-3949	91	10	𝑡	𝑡	NOUN
cana-3949	91	11	)	)	PUNCT
cana-3949	91	12	=	=	SYM
cana-3949	91	13	𝑉0(𝑡)𝑘𝑛+1	𝑉0(𝑡)𝑘𝑛+1	NOUN
cana-3949	91	14	+	+	CCONJ
cana-3949	91	15	𝑉1(𝑡)𝑘𝑛	𝑉1(𝑡)𝑘𝑛	VERB
cana-3949	91	16	+	+	NOUN
cana-3949	91	17	⋯+	⋯+	NOUN
cana-3949	91	18	𝑉𝑛(𝑡)𝑘1	𝑉𝑛(𝑡)𝑘1	X
cana-3949	91	19	+	+	CCONJ
cana-3949	91	20	𝑉𝑛+1(𝑡)𝑘0	𝑉𝑛+1(𝑡)𝑘0	NUM
cana-3949	91	21	,	,	PUNCT
cana-3949	91	22	𝑛	𝑛	PRON
cana-3949	91	23	=	=	SYM
cana-3949	91	24	1,2	1,2	NUM
cana-3949	91	25	,	,	PUNCT
cana-3949	91	26	…	…	PUNCT
cana-3949	91	27	,	,	PUNCT
cana-3949	91	28	(	(	PUNCT
cana-3949	91	29	12	12	NUM
cana-3949	91	30	)	)	PUNCT
cana-3949	91	31	𝑃𝑛	𝑃𝑛	NOUN
cana-3949	91	32	(	(	PUNCT
cana-3949	91	33	2)(0	2)(0	NUM
cana-3949	91	34	,	,	PUNCT
cana-3949	91	35	𝑡	𝑡	X
cana-3949	91	36	)	)	PUNCT
cana-3949	91	37	=	=	SYM
cana-3949	91	38	∫	∫	PROPN
cana-3949	92	1	𝑃𝑛	𝑃𝑛	PROPN
cana-3949	92	2	(	(	PUNCT
cana-3949	92	3	1)(𝑥	1)(𝑥	NUM
cana-3949	92	4	,	,	PUNCT
cana-3949	92	5	𝑡)𝜇1(𝑥)𝑑𝑥	𝑡)𝜇1(𝑥)𝑑𝑥	NOUN
cana-3949	92	6	,	,	PUNCT
cana-3949	92	7	𝑛	𝑛	PROPN
cana-3949	92	8	=	=	SYM
cana-3949	92	9	0,1	0,1	NUM
cana-3949	92	10	,	,	PUNCT
cana-3949	92	11	…	…	PUNCT
cana-3949	92	12	∞	∞	NUM
cana-3949	92	13	0	0	NUM
cana-3949	92	14	(	(	PUNCT
cana-3949	92	15	13	13	NUM
cana-3949	92	16	)	)	PUNCT
cana-3949	92	17	we	we	PRON
cana-3949	92	18	assume	assume	VERB
cana-3949	92	19	that	that	SCONJ
cana-3949	92	20	initially	initially	ADV
cana-3949	92	21	there	there	PRON
cana-3949	92	22	is	be	VERB
cana-3949	92	23	no	no	DET
cana-3949	92	24	customer	customer	NOUN
cana-3949	92	25	in	in	ADP
cana-3949	92	26	the	the	DET
cana-3949	92	27	system	system	NOUN
cana-3949	92	28	and	and	CCONJ
cana-3949	92	29	the	the	DET
cana-3949	92	30	server	server	NOUN
cana-3949	92	31	is	be	AUX
cana-3949	92	32	idle	idle	ADJ
cana-3949	92	33	so	so	SCONJ
cana-3949	92	34	that	that	SCONJ
cana-3949	92	35	initial	initial	ADJ
cana-3949	92	36	conditions	condition	NOUN
cana-3949	92	37	are	be	AUX
cana-3949	92	38	𝑄(0	𝑄(0	NOUN
cana-3949	92	39	)	)	PUNCT
cana-3949	93	1	=	=	SYM
cana-3949	93	2	1	1	NUM
cana-3949	93	3	,	,	PUNCT
cana-3949	93	4	𝑃𝑛	𝑃𝑛	PROPN
cana-3949	93	5	(	(	PUNCT
cana-3949	93	6	𝑗)(0	𝑗)(0	NUM
cana-3949	93	7	)	)	PUNCT
cana-3949	94	1	=	=	SYM
cana-3949	94	2	0	0	NUM
cana-3949	94	3	,	,	PUNCT
cana-3949	94	4	𝑗	𝑗	NOUN
cana-3949	94	5	=	=	SYM
cana-3949	94	6	1,2	1,2	NUM
cana-3949	94	7	,	,	PUNCT
cana-3949	94	8	𝑉𝑛(0	𝑉𝑛(0	ADJ
cana-3949	94	9	)	)	PUNCT
cana-3949	94	10	=	=	SYM
cana-3949	94	11	0	0	NUM
cana-3949	94	12	,	,	PUNCT
cana-3949	94	13	𝑉0(0	𝑉0(0	NOUN
cana-3949	94	14	)	)	PUNCT
cana-3949	94	15	=	=	SYM
cana-3949	94	16	0	0	NUM
cana-3949	94	17	,	,	PUNCT
cana-3949	94	18	𝑛	𝑛	DET
cana-3949	94	19	≥	≥	NOUN
cana-3949	94	20	0	0	NUM
cana-3949	94	21	.	.	PUNCT
cana-3949	95	1	(	(	PUNCT
cana-3949	95	2	14	14	NUM
cana-3949	95	3	)	)	SYM
cana-3949	95	4	4	4	NUM
cana-3949	95	5	.	.	PUNCT
cana-3949	95	6	generating	generating	NOUN
cana-3949	95	7	functions	function	NOUN
cana-3949	95	8	of	of	ADP
cana-3949	95	9	the	the	DET
cana-3949	95	10	queue	queue	NOUN
cana-3949	95	11	length	length	NOUN
cana-3949	95	12	:	:	PUNCT
cana-3949	95	13	the	the	DET
cana-3949	95	14	time	time	NOUN
cana-3949	95	15	dependent	dependent	ADJ
cana-3949	95	16	solution	solution	NOUN
cana-3949	95	17	in	in	ADP
cana-3949	95	18	this	this	DET
cana-3949	95	19	section	section	NOUN
cana-3949	95	20	we	we	PRON
cana-3949	95	21	define	define	VERB
cana-3949	95	22	the	the	DET
cana-3949	95	23	transient	transient	ADJ
cana-3949	95	24	solution	solution	NOUN
cana-3949	95	25	for	for	ADP
cana-3949	95	26	the	the	DET
cana-3949	95	27	above	above	ADJ
cana-3949	95	28	set	set	NOUN
cana-3949	95	29	of	of	ADP
cana-3949	95	30	differential	differential	ADJ
cana-3949	95	31	-	-	PUNCT
cana-3949	95	32	difference	difference	NOUN
cana-3949	95	33	equations	equation	NOUN
cana-3949	95	34	.	.	PUNCT
cana-3949	96	1	we	we	PRON
cana-3949	96	2	define	define	VERB
cana-3949	96	3	probability	probability	NOUN
cana-3949	96	4	generating	generating	NOUN
cana-3949	96	5	functions	function	NOUN
cana-3949	96	6	𝑃(1)(𝑥	𝑃(1)(𝑥	PROPN
cana-3949	96	7	,	,	PUNCT
cana-3949	96	8	𝑧	𝑧	PROPN
cana-3949	96	9	,	,	PUNCT
cana-3949	96	10	𝑡	𝑡	NOUN
cana-3949	96	11	)	)	PUNCT
cana-3949	96	12	=	=	PUNCT
cana-3949	97	1	∑	∑	PUNCT
cana-3949	97	2	𝑧𝑛∞	𝑧𝑛∞	PROPN
cana-3949	97	3	𝑛=0	𝑛=0	PROPN
cana-3949	97	4	𝑃𝑛	𝑃𝑛	PROPN
cana-3949	97	5	(	(	PUNCT
cana-3949	97	6	1)(𝑥	1)(𝑥	NUM
cana-3949	97	7	,	,	PUNCT
cana-3949	97	8	𝑡	𝑡	NOUN
cana-3949	97	9	)	)	PUNCT
cana-3949	97	10	,	,	PUNCT
cana-3949	97	11	𝑃(1)(𝑧	𝑃(1)(𝑧	PROPN
cana-3949	97	12	,	,	PUNCT
cana-3949	97	13	𝑡	𝑡	X
cana-3949	97	14	)	)	PUNCT
cana-3949	97	15	=	=	PUNCT
cana-3949	97	16	∑	∑	PUNCT
cana-3949	97	17	𝑧𝑛∞	𝑧𝑛∞	PROPN
cana-3949	97	18	𝑛=0	𝑛=0	PROPN
cana-3949	97	19	𝑃𝑛	𝑃𝑛	PROPN
cana-3949	97	20	(	(	PUNCT
cana-3949	97	21	1)(𝑡	1)(𝑡	PROPN
cana-3949	97	22	)	)	PUNCT
cana-3949	97	23	𝑃(2)(𝑥	𝑃(2)(𝑥	PROPN
cana-3949	97	24	,	,	PUNCT
cana-3949	97	25	𝑧	𝑧	NOUN
cana-3949	97	26	,	,	PUNCT
cana-3949	97	27	𝑡	𝑡	NOUN
cana-3949	97	28	)	)	PUNCT
cana-3949	97	29	=	=	PUNCT
cana-3949	97	30	∑	∑	PUNCT
cana-3949	97	31	𝑧𝑛∞	𝑧𝑛∞	PROPN
cana-3949	97	32	𝑛=0	𝑛=0	PROPN
cana-3949	97	33	𝑃𝑛	𝑃𝑛	PROPN
cana-3949	97	34	(	(	PUNCT
cana-3949	97	35	2)(𝑥	2)(𝑥	NUM
cana-3949	97	36	,	,	PUNCT
cana-3949	97	37	𝑡	𝑡	NOUN
cana-3949	97	38	)	)	PUNCT
cana-3949	97	39	,	,	PUNCT
cana-3949	97	40	𝑃(2)(𝑧	𝑃(2)(𝑧	PROPN
cana-3949	97	41	,	,	PUNCT
cana-3949	97	42	𝑡	𝑡	PROPN
cana-3949	97	43	)	)	PUNCT
cana-3949	97	44	=	=	PUNCT
cana-3949	97	45	∑	∑	PUNCT
cana-3949	97	46	𝑧𝑛∞	𝑧𝑛∞	PROPN
cana-3949	97	47	𝑛=0	𝑛=0	PROPN
cana-3949	98	1	𝑃𝑛	𝑃𝑛	PROPN
cana-3949	98	2	(	(	PUNCT
cana-3949	98	3	2)(𝑡	2)(𝑡	PROPN
cana-3949	98	4	)	)	PUNCT
cana-3949	98	5	𝑉(𝑧	𝑉(𝑧	X
cana-3949	98	6	,	,	PUNCT
cana-3949	98	7	𝑡	𝑡	X
cana-3949	98	8	)	)	PUNCT
cana-3949	98	9	=	=	PUNCT
cana-3949	98	10	∑	∑	PROPN
cana-3949	98	11	𝑧𝑛∞	𝑧𝑛∞	PROPN
cana-3949	98	12	𝑛=0	𝑛=0	PROPN
cana-3949	98	13	𝑉(𝑡	𝑉(𝑡	ADV
cana-3949	98	14	)	)	PUNCT
cana-3949	98	15	.	.	PUNCT
cana-3949	98	16	}	}	PUNCT
cana-3949	98	17	(	(	PUNCT
cana-3949	98	18	15	15	NUM
cana-3949	98	19	)	)	PUNCT
cana-3949	98	20	which	which	PRON
cana-3949	98	21	are	be	AUX
cana-3949	98	22	convergent	convergent	ADJ
cana-3949	98	23	inside	inside	ADP
cana-3949	98	24	the	the	DET
cana-3949	98	25	circle	circle	NOUN
cana-3949	98	26	given	give	VERB
cana-3949	98	27	by	by	ADP
cana-3949	98	28	|𝑧|	|𝑧|	PROPN
cana-3949	98	29	≤	≤	NUM
cana-3949	98	30	1	1	NUM
cana-3949	98	31	and	and	CCONJ
cana-3949	98	32	define	define	VERB
cana-3949	98	33	the	the	DET
cana-3949	98	34	laplace	laplace	NOUN
cana-3949	98	35	transform	transform	NOUN
cana-3949	98	36	of	of	ADP
cana-3949	98	37	a	a	DET
cana-3949	98	38	function	function	NOUN
cana-3949	98	39	𝑓(𝑡	𝑓(𝑡	NOUN
cana-3949	98	40	)	)	PUNCT
cana-3949	98	41	as	as	ADP
cana-3949	98	42	𝑓(𝑠	𝑓(𝑠	NOUN
cana-3949	98	43	)	)	PUNCT
cana-3949	98	44	=	=	SYM
cana-3949	98	45	∫	∫	PROPN
cana-3949	98	46	𝑒−𝑠𝑡	𝑒−𝑠𝑡	NUM
cana-3949	98	47	∞	∞	PROPN
cana-3949	98	48	0	0	NUM
cana-3949	98	49	𝑓(𝑡)𝑑𝑡,ℜ(𝑠	𝑓(𝑡)𝑑𝑡,ℜ(𝑠	NOUN
cana-3949	98	50	)	)	PUNCT
cana-3949	98	51	>	>	X
cana-3949	98	52	0	0	PUNCT
cana-3949	98	53	.	.	PUNCT
cana-3949	99	1	(	(	PUNCT
cana-3949	99	2	16	16	X
cana-3949	99	3	)	)	PUNCT
cana-3949	99	4	taking	take	VERB
cana-3949	99	5	laplace	laplace	NOUN
cana-3949	99	6	transforms	transform	NOUN
cana-3949	99	7	of	of	ADP
cana-3949	99	8	equations	equation	NOUN
cana-3949	99	9	(	(	PUNCT
cana-3949	99	10	4	4	NUM
cana-3949	99	11	)	)	PUNCT
cana-3949	99	12	–	–	PUNCT
cana-3949	99	13	(	(	PUNCT
cana-3949	99	14	13	13	NUM
cana-3949	99	15	)	)	PUNCT
cana-3949	99	16	and	and	CCONJ
cana-3949	99	17	using	use	VERB
cana-3949	99	18	initial	initial	ADJ
cana-3949	99	19	conditions	condition	NOUN
cana-3949	99	20	(	(	PUNCT
cana-3949	99	21	14	14	NUM
cana-3949	99	22	)	)	PUNCT
cana-3949	99	23	,	,	PUNCT
cana-3949	99	24	we	we	PRON
cana-3949	99	25	obtain	obtain	VERB
cana-3949	99	26	𝜕	𝜕	NOUN
cana-3949	99	27	𝜕𝑥	𝜕𝑥	NOUN
cana-3949	99	28	𝑃𝑛	𝑃𝑛	PROPN
cana-3949	99	29	(	(	PUNCT
cana-3949	99	30	1	1	NUM
cana-3949	99	31	)	)	PUNCT
cana-3949	99	32	(	(	PUNCT
cana-3949	99	33	𝑥	𝑥	NOUN
cana-3949	99	34	,	,	PUNCT
cana-3949	99	35	𝑠	𝑠	PROPN
cana-3949	99	36	)	)	PUNCT
cana-3949	100	1	+	+	CCONJ
cana-3949	100	2	(	(	PUNCT
cana-3949	100	3	𝑠	𝑠	PROPN
cana-3949	100	4	+	+	CCONJ
cana-3949	100	5	𝜆	𝜆	PROPN
cana-3949	100	6	+	+	X
cana-3949	100	7	𝜇1(𝑥))𝑃𝑛	𝜇1(𝑥))𝑃𝑛	PROPN
cana-3949	100	8	(	(	PUNCT
cana-3949	100	9	1	1	NUM
cana-3949	100	10	)	)	PUNCT
cana-3949	100	11	(	(	PUNCT
cana-3949	100	12	𝑥	𝑥	NOUN
cana-3949	100	13	,	,	PUNCT
cana-3949	100	14	𝑠	𝑠	NOUN
cana-3949	100	15	)	)	PUNCT
cana-3949	100	16	=	=	SYM
cana-3949	100	17	𝜆𝑃𝑛−1	𝜆𝑃𝑛−1	NOUN
cana-3949	100	18	(	(	PUNCT
cana-3949	100	19	1	1	NUM
cana-3949	100	20	)	)	PUNCT
cana-3949	100	21	(	(	PUNCT
cana-3949	100	22	𝑥	𝑥	NOUN
cana-3949	100	23	,	,	PUNCT
cana-3949	100	24	𝑠	𝑠	PROPN
cana-3949	100	25	)	)	PUNCT
cana-3949	100	26	,	,	PUNCT
cana-3949	100	27	𝑛	𝑛	PROPN
cana-3949	100	28	=	=	SYM
cana-3949	100	29	1,2	1,2	NUM
cana-3949	100	30	,	,	PUNCT
cana-3949	100	31	…	…	PUNCT
cana-3949	100	32	,	,	PUNCT
cana-3949	100	33	(	(	PUNCT
cana-3949	100	34	17	17	NUM
cana-3949	100	35	)	)	PUNCT
cana-3949	100	36	𝜕	𝜕	PROPN
cana-3949	100	37	𝜕𝑥	𝜕𝑥	X
cana-3949	100	38	𝑃0	𝑃0	NOUN
cana-3949	100	39	(	(	PUNCT
cana-3949	100	40	1	1	NUM
cana-3949	100	41	)	)	PUNCT
cana-3949	100	42	(	(	PUNCT
cana-3949	100	43	𝑥	𝑥	NOUN
cana-3949	100	44	,	,	PUNCT
cana-3949	100	45	𝑠	𝑠	PROPN
cana-3949	100	46	)	)	PUNCT
cana-3949	101	1	+	+	CCONJ
cana-3949	101	2	(	(	PUNCT
cana-3949	101	3	𝑠	𝑠	PROPN
cana-3949	101	4	+	+	CCONJ
cana-3949	101	5	𝜆	𝜆	PROPN
cana-3949	101	6	+	+	X
cana-3949	101	7	𝜇1(𝑥))𝑃0	𝜇1(𝑥))𝑃0	ADJ
cana-3949	101	8	(	(	PUNCT
cana-3949	101	9	1	1	NUM
cana-3949	101	10	)	)	PUNCT
cana-3949	101	11	(	(	PUNCT
cana-3949	101	12	𝑥	𝑥	NOUN
cana-3949	101	13	,	,	PUNCT
cana-3949	101	14	𝑠	𝑠	NOUN
cana-3949	101	15	)	)	PUNCT
cana-3949	101	16	=	=	SYM
cana-3949	101	17	0	0	NUM
cana-3949	101	18	,	,	PUNCT
cana-3949	101	19	(	(	PUNCT
cana-3949	101	20	18	18	NUM
cana-3949	101	21	)	)	PUNCT
cana-3949	101	22	𝜕	𝜕	NOUN
cana-3949	101	23	𝜕𝑥	𝜕𝑥	NOUN
cana-3949	101	24	𝑃𝑛	𝑃𝑛	PROPN
cana-3949	101	25	(	(	PUNCT
cana-3949	101	26	2	2	NUM
cana-3949	101	27	)	)	PUNCT
cana-3949	101	28	(	(	PUNCT
cana-3949	101	29	𝑥	𝑥	NOUN
cana-3949	101	30	,	,	PUNCT
cana-3949	101	31	𝑠	𝑠	PROPN
cana-3949	101	32	)	)	PUNCT
cana-3949	102	1	+	+	CCONJ
cana-3949	102	2	(	(	PUNCT
cana-3949	102	3	𝑠	𝑠	PROPN
cana-3949	102	4	+	+	NUM
cana-3949	102	5	𝜆	𝜆	PROPN
cana-3949	103	1	+	+	X
cana-3949	103	2	𝜇2(𝑥))𝑃𝑛	𝜇2(𝑥))𝑃𝑛	PROPN
cana-3949	103	3	(	(	PUNCT
cana-3949	103	4	2	2	NUM
cana-3949	103	5	)	)	PUNCT
cana-3949	103	6	(	(	PUNCT
cana-3949	103	7	𝑥	𝑥	NOUN
cana-3949	103	8	,	,	PUNCT
cana-3949	103	9	𝑠	𝑠	NOUN
cana-3949	103	10	)	)	PUNCT
cana-3949	103	11	=	=	SYM
cana-3949	103	12	𝜆𝑃𝑛−1	𝜆𝑃𝑛−1	NOUN
cana-3949	103	13	(	(	PUNCT
cana-3949	103	14	2	2	NUM
cana-3949	103	15	)	)	PUNCT
cana-3949	103	16	(	(	PUNCT
cana-3949	103	17	𝑥	𝑥	NOUN
cana-3949	103	18	,	,	PUNCT
cana-3949	103	19	𝑠	𝑠	PROPN
cana-3949	103	20	)	)	PUNCT
cana-3949	103	21	,	,	PUNCT
cana-3949	103	22	𝑛	𝑛	PROPN
cana-3949	103	23	=	=	SYM
cana-3949	103	24	1,2	1,2	NUM
cana-3949	103	25	,	,	PUNCT
cana-3949	103	26	…	…	PUNCT
cana-3949	103	27	,	,	PUNCT
cana-3949	103	28	(	(	PUNCT
cana-3949	103	29	19	19	NUM
cana-3949	103	30	)	)	PUNCT
cana-3949	103	31	communications	communication	NOUN
cana-3949	103	32	on	on	ADP
cana-3949	103	33	applied	apply	VERB
cana-3949	103	34	nonlinear	nonlinear	ADJ
cana-3949	103	35	analysis	analysis	NOUN
cana-3949	103	36	issn	issn	NOUN
cana-3949	103	37	:	:	PUNCT
cana-3949	103	38	1074	1074	NUM
cana-3949	103	39	-	-	PUNCT
cana-3949	103	40	133x	133x	NUM
cana-3949	103	41	vol	vol	NOUN
cana-3949	103	42	32	32	NUM
cana-3949	103	43	no	no	NOUN
cana-3949	103	44	.	.	PUNCT
cana-3949	104	1	9s	9s	NUM
cana-3949	104	2	(	(	PUNCT
cana-3949	104	3	2025	2025	NUM
cana-3949	104	4	)	)	PUNCT
cana-3949	104	5	381	381	NUM
cana-3949	105	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-3949	105	2	𝜕	𝜕	PROPN
cana-3949	105	3	𝜕𝑥	𝜕𝑥	X
cana-3949	105	4	𝑃0	𝑃0	NOUN
cana-3949	105	5	(	(	PUNCT
cana-3949	105	6	2	2	NUM
cana-3949	105	7	)	)	PUNCT
cana-3949	105	8	(	(	PUNCT
cana-3949	105	9	𝑥	𝑥	NOUN
cana-3949	105	10	,	,	PUNCT
cana-3949	105	11	𝑠	𝑠	PROPN
cana-3949	105	12	)	)	PUNCT
cana-3949	105	13	+	+	CCONJ
cana-3949	105	14	(	(	PUNCT
cana-3949	105	15	𝑠	𝑠	PROPN
cana-3949	105	16	+	+	CCONJ
cana-3949	105	17	𝜆	𝜆	PROPN
cana-3949	105	18	+	+	X
cana-3949	105	19	𝜇2(𝑥))𝑃0	𝜇2(𝑥))𝑃0	ADJ
cana-3949	105	20	(	(	PUNCT
cana-3949	105	21	2	2	NUM
cana-3949	105	22	)	)	PUNCT
cana-3949	105	23	(	(	PUNCT
cana-3949	105	24	𝑥	𝑥	NOUN
cana-3949	105	25	,	,	PUNCT
cana-3949	105	26	𝑠	𝑠	NOUN
cana-3949	105	27	)	)	PUNCT
cana-3949	105	28	=	=	SYM
cana-3949	105	29	0	0	NUM
cana-3949	105	30	,	,	PUNCT
cana-3949	105	31	(	(	PUNCT
cana-3949	105	32	20	20	NUM
cana-3949	105	33	)	)	PUNCT
cana-3949	105	34	𝑠𝑉0(𝑠	𝑠𝑉0(𝑠	NOUN
cana-3949	105	35	)	)	PUNCT
cana-3949	106	1	=	=	SYM
cana-3949	106	2	𝑉0(𝑠)[−𝑘0	𝑉0(𝑠)[−𝑘0	NOUN
cana-3949	106	3	−	−	PROPN
cana-3949	106	4	𝑘1	𝑘1	NOUN
cana-3949	106	5	−⋯	−⋯	PROPN
cana-3949	106	6	]	]	PUNCT
cana-3949	107	1	+	+	NUM
cana-3949	107	2	∫	∫	PROPN
cana-3949	107	3	𝑃0	𝑃0	NOUN
cana-3949	107	4	(	(	PUNCT
cana-3949	107	5	2	2	NUM
cana-3949	107	6	)	)	PUNCT
cana-3949	107	7	(	(	PUNCT
cana-3949	107	8	𝑥	𝑥	NOUN
cana-3949	107	9	,	,	PUNCT
cana-3949	107	10	𝑠)𝜇2(𝑥)𝑑𝑥	𝑠)𝜇2(𝑥)𝑑𝑥	ADJ
cana-3949	107	11	,	,	PUNCT
cana-3949	107	12	∞	∞	PROPN
cana-3949	107	13	0	0	NUM
cana-3949	107	14	(	(	PUNCT
cana-3949	107	15	21	21	NUM
cana-3949	107	16	)	)	PUNCT
cana-3949	107	17	𝑠𝑉𝑛(𝑠	𝑠𝑉𝑛(𝑠	PROPN
cana-3949	107	18	)	)	PUNCT
cana-3949	107	19	=	=	SYM
cana-3949	107	20	𝑉𝑛(𝑠)[−𝑘0	𝑉𝑛(𝑠)[−𝑘0	NOUN
cana-3949	107	21	−	−	PROPN
cana-3949	107	22	𝑘1	𝑘1	NOUN
cana-3949	107	23	−⋯	−⋯	PROPN
cana-3949	107	24	]	]	PUNCT
cana-3949	108	1	+	+	NUM
cana-3949	108	2	∫	∫	X
cana-3949	108	3	𝑃𝑛	𝑃𝑛	PROPN
cana-3949	108	4	(	(	PUNCT
cana-3949	108	5	2	2	NUM
cana-3949	108	6	)	)	PUNCT
cana-3949	108	7	(	(	PUNCT
cana-3949	108	8	𝑥	𝑥	NOUN
cana-3949	108	9	,	,	PUNCT
cana-3949	108	10	𝑠)𝜇2(𝑥)𝑑𝑥	𝑠)𝜇2(𝑥)𝑑𝑥	ADJ
cana-3949	108	11	,	,	PUNCT
cana-3949	108	12	∞	∞	PROPN
cana-3949	108	13	0	0	NUM
cana-3949	108	14	𝑛	𝑛	NOUN
cana-3949	108	15	=	=	SYM
cana-3949	108	16	1,2	1,2	NUM
cana-3949	108	17	,	,	PUNCT
cana-3949	108	18	…	…	PUNCT
cana-3949	108	19	(	(	PUNCT
cana-3949	108	20	22	22	NUM
cana-3949	108	21	)	)	PUNCT
cana-3949	108	22	(	(	PUNCT
cana-3949	108	23	𝑠	𝑠	X
cana-3949	108	24	+	+	CCONJ
cana-3949	108	25	𝜆)	𝜆)	PROPN
cana-3949	108	26	�	�	NOUN
cana-3949	108	27	̅	̅	NOUN
cana-3949	108	28	�	�	NOUN
cana-3949	108	29	(𝑠	(𝑠	NOUN
cana-3949	108	30	)	)	PUNCT
cana-3949	108	31	=	=	SYM
cana-3949	108	32	1	1	NUM
cana-3949	108	33	+	+	NUM
cana-3949	108	34	𝑉0(𝑠)𝑘0	𝑉0(𝑠)𝑘0	ADJ
cana-3949	108	35	,	,	PUNCT
cana-3949	108	36	(	(	PUNCT
cana-3949	108	37	23	23	NUM
cana-3949	108	38	)	)	PUNCT
cana-3949	108	39	𝑃0	𝑃0	NOUN
cana-3949	108	40	(	(	PUNCT
cana-3949	108	41	1	1	NUM
cana-3949	108	42	)	)	PUNCT
cana-3949	108	43	(	(	PUNCT
cana-3949	108	44	0	0	NUM
cana-3949	108	45	,	,	PUNCT
cana-3949	108	46	𝑠	𝑠	NOUN
cana-3949	108	47	)	)	PUNCT
cana-3949	108	48	=	=	SYM
cana-3949	108	49	𝜆𝑄(𝑠	𝜆𝑄(𝑠	PROPN
cana-3949	108	50	)	)	PUNCT
cana-3949	108	51	+	+	CCONJ
cana-3949	108	52	𝑉0(𝑠)𝑘1+𝑉1(𝑠)𝑘0	𝑉0(𝑠)𝑘1+𝑉1(𝑠)𝑘0	NOUN
cana-3949	108	53	,	,	PUNCT
cana-3949	108	54	(	(	PUNCT
cana-3949	108	55	24	24	NUM
cana-3949	108	56	)	)	PUNCT
cana-3949	108	57	𝑃𝑛	𝑃𝑛	NOUN
cana-3949	108	58	(	(	PUNCT
cana-3949	108	59	1	1	NUM
cana-3949	108	60	)	)	PUNCT
cana-3949	108	61	(	(	PUNCT
cana-3949	108	62	0	0	NUM
cana-3949	108	63	,	,	PUNCT
cana-3949	108	64	𝑠	𝑠	NOUN
cana-3949	108	65	)	)	PUNCT
cana-3949	108	66	=	=	PUNCT
cana-3949	108	67	𝑉0(𝑠)𝑘𝑛+1+𝑉1(𝑠)𝑘𝑛	𝑉0(𝑠)𝑘𝑛+1+𝑉1(𝑠)𝑘𝑛	PROPN
cana-3949	108	68	+	+	NOUN
cana-3949	108	69	⋯+	⋯+	NOUN
cana-3949	108	70	𝑉𝑛(𝑠)𝑘1	𝑉𝑛(𝑠)𝑘1	X
cana-3949	108	71	+	+	CCONJ
cana-3949	108	72	𝑉𝑛+1(𝑠)𝑘0	𝑉𝑛+1(𝑠)𝑘0	ADJ
cana-3949	108	73	,	,	PUNCT
cana-3949	108	74	𝑛	𝑛	NOUN
cana-3949	108	75	=	=	SYM
cana-3949	108	76	1,2	1,2	NUM
cana-3949	108	77	,	,	PUNCT
cana-3949	108	78	…	…	PUNCT
cana-3949	108	79	,	,	PUNCT
cana-3949	108	80	(	(	PUNCT
cana-3949	108	81	25	25	NUM
cana-3949	108	82	)	)	PUNCT
cana-3949	108	83	𝑃𝑛	𝑃𝑛	NOUN
cana-3949	108	84	(	(	PUNCT
cana-3949	108	85	2	2	NUM
cana-3949	108	86	)	)	PUNCT
cana-3949	108	87	(	(	PUNCT
cana-3949	108	88	0	0	NUM
cana-3949	108	89	,	,	PUNCT
cana-3949	108	90	𝑠	𝑠	NOUN
cana-3949	108	91	)	)	PUNCT
cana-3949	108	92	=	=	SYM
cana-3949	108	93	∫	∫	PROPN
cana-3949	109	1	𝑃𝑛	𝑃𝑛	NOUN
cana-3949	109	2	(	(	PUNCT
cana-3949	109	3	1	1	NUM
cana-3949	109	4	)	)	PUNCT
cana-3949	109	5	(	(	PUNCT
cana-3949	109	6	𝑥	𝑥	NOUN
cana-3949	109	7	,	,	PUNCT
cana-3949	109	8	𝑠)𝜇1(𝑥)𝑑𝑥	𝑠)𝜇1(𝑥)𝑑𝑥	ADJ
cana-3949	109	9	,	,	PUNCT
cana-3949	109	10	𝑛	𝑛	PROPN
cana-3949	109	11	=	=	SYM
cana-3949	109	12	0,1	0,1	NUM
cana-3949	109	13	,	,	PUNCT
cana-3949	109	14	∞	∞	PROPN
cana-3949	109	15	0	0	NUM
cana-3949	109	16	…	…	PUNCT
cana-3949	109	17	(	(	PUNCT
cana-3949	109	18	26	26	NUM
cana-3949	109	19	)	)	PUNCT
cana-3949	109	20	now	now	ADV
cana-3949	109	21	multiplying	multiply	VERB
cana-3949	109	22	equation	equation	NOUN
cana-3949	109	23	(	(	PUNCT
cana-3949	109	24	17	17	NUM
cana-3949	109	25	)	)	PUNCT
cana-3949	109	26	by	by	ADP
cana-3949	109	27	𝑧𝑛and	𝑧𝑛and	NOUN
cana-3949	109	28	summing	sum	VERB
cana-3949	109	29	over	over	ADP
cana-3949	109	30	𝑛	𝑛	PROPN
cana-3949	109	31	from	from	ADP
cana-3949	109	32	1	1	NUM
cana-3949	109	33	𝑡𝑜	𝑡𝑜	NUM
cana-3949	109	34	∞	∞	NUM
cana-3949	109	35	,	,	PUNCT
cana-3949	109	36	adding	add	VERB
cana-3949	109	37	to	to	ADP
cana-3949	109	38	equation	equation	NOUN
cana-3949	109	39	(	(	PUNCT
cana-3949	109	40	18	18	NUM
cana-3949	109	41	)	)	PUNCT
cana-3949	109	42	and	and	CCONJ
cana-3949	109	43	using	use	VERB
cana-3949	109	44	equation	equation	NOUN
cana-3949	109	45	(	(	PUNCT
cana-3949	109	46	15	15	NUM
cana-3949	109	47	)	)	PUNCT
cana-3949	109	48	,	,	PUNCT
cana-3949	109	49	we	we	PRON
cana-3949	109	50	obtain	obtain	VERB
cana-3949	109	51	𝜕	𝜕	NOUN
cana-3949	109	52	𝜕𝑥	𝜕𝑥	X
cana-3949	109	53	𝑃	𝑃	NOUN
cana-3949	109	54	(	(	PUNCT
cana-3949	109	55	1	1	NUM
cana-3949	109	56	)	)	PUNCT
cana-3949	109	57	(	(	PUNCT
cana-3949	109	58	𝑥	𝑥	NOUN
cana-3949	109	59	,	,	PUNCT
cana-3949	109	60	𝑧	𝑧	PROPN
cana-3949	109	61	,	,	PUNCT
cana-3949	109	62	𝑠	𝑠	PROPN
cana-3949	109	63	)	)	PUNCT
cana-3949	109	64	+	+	CCONJ
cana-3949	110	1	(	(	PUNCT
cana-3949	110	2	𝑠	𝑠	PROPN
cana-3949	110	3	+	+	NOUN
cana-3949	110	4	𝜆	𝜆	DET
cana-3949	110	5	−	−	PROPN
cana-3949	110	6	𝜆𝑧	𝜆𝑧	NOUN
cana-3949	110	7	+	+	NOUN
cana-3949	110	8	𝜇1(𝑥))𝑃	𝜇1(𝑥))𝑃	NOUN
cana-3949	110	9	(	(	PUNCT
cana-3949	110	10	1	1	NUM
cana-3949	110	11	)	)	PUNCT
cana-3949	110	12	(	(	PUNCT
cana-3949	110	13	𝑥	𝑥	NOUN
cana-3949	110	14	,	,	PUNCT
cana-3949	110	15	𝑧	𝑧	PROPN
cana-3949	110	16	,	,	PUNCT
cana-3949	110	17	𝑠	𝑠	NOUN
cana-3949	110	18	)	)	PUNCT
cana-3949	110	19	=	=	SYM
cana-3949	110	20	0	0	NUM
cana-3949	110	21	,	,	PUNCT
cana-3949	110	22	(	(	PUNCT
cana-3949	110	23	27	27	NUM
cana-3949	110	24	)	)	PUNCT
cana-3949	110	25	performing	perform	VERB
cana-3949	110	26	similar	similar	ADJ
cana-3949	110	27	operations	operation	NOUN
cana-3949	110	28	on	on	ADP
cana-3949	110	29	equations	equation	NOUN
cana-3949	110	30	(	(	PUNCT
cana-3949	110	31	19	19	NUM
cana-3949	110	32	)	)	PUNCT
cana-3949	110	33	–	–	PUNCT
cana-3949	110	34	(	(	PUNCT
cana-3949	110	35	22	22	NUM
cana-3949	110	36	)	)	PUNCT
cana-3949	110	37	,	,	PUNCT
cana-3949	110	38	we	we	PRON
cana-3949	110	39	get	get	VERB
cana-3949	110	40	𝜕	𝜕	NOUN
cana-3949	110	41	𝜕𝑥	𝜕𝑥	X
cana-3949	110	42	𝑃	𝑃	NOUN
cana-3949	110	43	(	(	PUNCT
cana-3949	110	44	2	2	NUM
cana-3949	110	45	)	)	PUNCT
cana-3949	110	46	(	(	PUNCT
cana-3949	110	47	𝑥	𝑥	NOUN
cana-3949	110	48	,	,	PUNCT
cana-3949	110	49	𝑧	𝑧	PROPN
cana-3949	110	50	,	,	PUNCT
cana-3949	110	51	𝑠	𝑠	PROPN
cana-3949	110	52	)	)	PUNCT
cana-3949	111	1	+	+	CCONJ
cana-3949	111	2	(	(	PUNCT
cana-3949	111	3	𝑠	𝑠	PROPN
cana-3949	111	4	+	+	NOUN
cana-3949	111	5	𝜆	𝜆	DET
cana-3949	111	6	−	−	PROPN
cana-3949	111	7	𝜆𝑧	𝜆𝑧	NOUN
cana-3949	111	8	+	+	NOUN
cana-3949	111	9	𝜇2(𝑥))𝑃	𝜇2(𝑥))𝑃	NOUN
cana-3949	111	10	(	(	PUNCT
cana-3949	111	11	2	2	NUM
cana-3949	111	12	)	)	PUNCT
cana-3949	111	13	(	(	PUNCT
cana-3949	111	14	𝑥	𝑥	NOUN
cana-3949	111	15	,	,	PUNCT
cana-3949	111	16	𝑧	𝑧	PROPN
cana-3949	111	17	,	,	PUNCT
cana-3949	111	18	𝑠	𝑠	NOUN
cana-3949	111	19	)	)	PUNCT
cana-3949	111	20	=	=	SYM
cana-3949	111	21	0	0	NUM
cana-3949	111	22	,	,	PUNCT
cana-3949	111	23	(	(	PUNCT
cana-3949	111	24	28	28	NUM
cana-3949	111	25	)	)	PUNCT
cana-3949	111	26	(	(	PUNCT
cana-3949	111	27	𝑠	𝑠	PROPN
cana-3949	111	28	+	+	SYM
cana-3949	111	29	1)𝑉(𝑧	1)𝑉(𝑧	PROPN
cana-3949	111	30	,	,	PUNCT
cana-3949	111	31	𝑠	𝑠	NOUN
cana-3949	111	32	)	)	PUNCT
cana-3949	112	1	=	=	SYM
cana-3949	112	2	∫	∫	PROPN
cana-3949	112	3	𝑃	𝑃	NOUN
cana-3949	112	4	(	(	PUNCT
cana-3949	112	5	2	2	NUM
cana-3949	112	6	)	)	PUNCT
cana-3949	112	7	(	(	PUNCT
cana-3949	112	8	𝑥	𝑥	NOUN
cana-3949	112	9	,	,	PUNCT
cana-3949	112	10	𝑧	𝑧	PROPN
cana-3949	112	11	,	,	PUNCT
cana-3949	112	12	𝑠)𝜇2(𝑥)𝑑𝑥	𝑠)𝜇2(𝑥)𝑑𝑥	ADJ
cana-3949	112	13	∞	∞	NOUN
cana-3949	112	14	0	0	NUM
cana-3949	112	15	.	.	PUNCT
cana-3949	113	1	(	(	PUNCT
cana-3949	113	2	29	29	NUM
cana-3949	113	3	)	)	PUNCT
cana-3949	113	4	for	for	ADP
cana-3949	113	5	boundary	boundary	ADJ
cana-3949	113	6	conditions	condition	NOUN
cana-3949	113	7	,	,	PUNCT
cana-3949	113	8	we	we	PRON
cana-3949	113	9	multiply	multiply	VERB
cana-3949	113	10	both	both	DET
cana-3949	113	11	sides	side	NOUN
cana-3949	113	12	of	of	ADP
cana-3949	113	13	equation	equation	NOUN
cana-3949	113	14	(	(	PUNCT
cana-3949	113	15	24	24	NUM
cana-3949	113	16	)	)	PUNCT
cana-3949	113	17	by	by	ADP
cana-3949	113	18	𝑧	𝑧	PROPN
cana-3949	113	19	,	,	PUNCT
cana-3949	113	20	multiply	multiply	VERB
cana-3949	113	21	both	both	DET
cana-3949	113	22	sides	side	NOUN
cana-3949	113	23	of	of	ADP
cana-3949	113	24	equation	equation	NOUN
cana-3949	113	25	(	(	PUNCT
cana-3949	113	26	25	25	NUM
cana-3949	113	27	)	)	PUNCT
cana-3949	113	28	by	by	ADP
cana-3949	113	29	𝑧𝑛+1	𝑧𝑛+1	NUM
cana-3949	113	30	,	,	PUNCT
cana-3949	113	31	sum	sum	VERB
cana-3949	113	32	over	over	ADP
cana-3949	113	33	n	n	ADV
cana-3949	113	34	from	from	ADP
cana-3949	113	35	1	1	NUM
cana-3949	113	36	to	to	ADP
cana-3949	113	37	∞	∞	NUM
cana-3949	113	38	,	,	PUNCT
cana-3949	113	39	add	add	VERB
cana-3949	113	40	two	two	NUM
cana-3949	113	41	results	result	NOUN
cana-3949	113	42	and	and	CCONJ
cana-3949	113	43	use	use	VERB
cana-3949	113	44	equation	equation	NOUN
cana-3949	113	45	(	(	PUNCT
cana-3949	113	46	15	15	NUM
cana-3949	113	47	)	)	PUNCT
cana-3949	113	48	to	to	PART
cana-3949	113	49	get	get	VERB
cana-3949	113	50	𝑧𝑃	𝑧𝑃	PROPN
cana-3949	113	51	(	(	PUNCT
cana-3949	113	52	1	1	NUM
cana-3949	113	53	)	)	PUNCT
cana-3949	113	54	(	(	PUNCT
cana-3949	113	55	0	0	NUM
cana-3949	113	56	,	,	PUNCT
cana-3949	113	57	𝑧	𝑧	NOUN
cana-3949	113	58	,	,	PUNCT
cana-3949	113	59	𝑠	𝑠	NOUN
cana-3949	113	60	)	)	PUNCT
cana-3949	113	61	=	=	SYM
cana-3949	113	62	𝜆𝑧𝑄(𝑠	𝜆𝑧𝑄(𝑠	PROPN
cana-3949	113	63	)	)	PUNCT
cana-3949	113	64	+	+	NUM
cana-3949	113	65	𝑉(𝑧	𝑉(𝑧	X
cana-3949	113	66	,	,	PUNCT
cana-3949	113	67	𝑠)𝑒−𝜆𝑑(1−𝑧	𝑠)𝑒−𝜆𝑑(1−𝑧	NUM
cana-3949	113	68	)	)	PUNCT
cana-3949	114	1	−	−	PROPN
cana-3949	114	2	𝑉0(𝑠)𝑘0	𝑉0(𝑠)𝑘0	ADJ
cana-3949	114	3	(	(	PUNCT
cana-3949	114	4	30	30	NUM
cana-3949	114	5	)	)	PUNCT
cana-3949	114	6	performing	perform	VERB
cana-3949	114	7	similar	similar	ADJ
cana-3949	114	8	operations	operation	NOUN
cana-3949	114	9	on	on	ADP
cana-3949	114	10	equation	equation	NOUN
cana-3949	114	11	(	(	PUNCT
cana-3949	114	12	26	26	NUM
cana-3949	114	13	)	)	PUNCT
cana-3949	114	14	to	to	PART
cana-3949	114	15	obtain	obtain	VERB
cana-3949	114	16	,	,	PUNCT
cana-3949	114	17	𝑃	𝑃	PROPN
cana-3949	114	18	(	(	PUNCT
cana-3949	114	19	2	2	NUM
cana-3949	114	20	)	)	PUNCT
cana-3949	114	21	(	(	PUNCT
cana-3949	114	22	0	0	NUM
cana-3949	114	23	,	,	PUNCT
cana-3949	114	24	𝑧	𝑧	NOUN
cana-3949	114	25	,	,	PUNCT
cana-3949	114	26	𝑠	𝑠	NOUN
cana-3949	114	27	)	)	PUNCT
cana-3949	114	28	=	=	SYM
cana-3949	115	1	∫	∫	PROPN
cana-3949	115	2	𝑃	𝑃	NOUN
cana-3949	115	3	(	(	PUNCT
cana-3949	115	4	1	1	NUM
cana-3949	115	5	)	)	PUNCT
cana-3949	115	6	(	(	PUNCT
cana-3949	115	7	𝑥	𝑥	NOUN
cana-3949	115	8	,	,	PUNCT
cana-3949	115	9	𝑧	𝑧	ADJ
cana-3949	115	10	,	,	PUNCT
cana-3949	115	11	𝑠)𝜇1(𝑥)𝑑𝑥	𝑠)𝜇1(𝑥)𝑑𝑥	ADJ
cana-3949	115	12	∞	∞	NOUN
cana-3949	115	13	0	0	NUM
cana-3949	115	14	.	.	PUNCT
cana-3949	116	1	(	(	PUNCT
cana-3949	116	2	31	31	NUM
cana-3949	116	3	)	)	PUNCT
cana-3949	116	4	using	use	VERB
cana-3949	116	5	equation	equation	NOUN
cana-3949	116	6	(	(	PUNCT
cana-3949	116	7	23	23	NUM
cana-3949	116	8	)	)	PUNCT
cana-3949	116	9	,	,	PUNCT
cana-3949	116	10	equation	equation	NOUN
cana-3949	116	11	(	(	PUNCT
cana-3949	116	12	30	30	NUM
cana-3949	116	13	)	)	PUNCT
cana-3949	116	14	becomes	become	VERB
cana-3949	116	15	𝑧𝑃	𝑧𝑃	PROPN
cana-3949	116	16	(	(	PUNCT
cana-3949	116	17	1	1	NUM
cana-3949	116	18	)	)	PUNCT
cana-3949	116	19	(	(	PUNCT
cana-3949	116	20	0	0	NUM
cana-3949	116	21	,	,	PUNCT
cana-3949	116	22	𝑧	𝑧	NOUN
cana-3949	116	23	,	,	PUNCT
cana-3949	116	24	𝑠	𝑠	NOUN
cana-3949	116	25	)	)	PUNCT
cana-3949	116	26	=	=	SYM
cana-3949	116	27	𝜆𝑧𝑄(𝑠	𝜆𝑧𝑄(𝑠	PROPN
cana-3949	116	28	)	)	PUNCT
cana-3949	116	29	+	+	NUM
cana-3949	116	30	𝑉(𝑧	𝑉(𝑧	X
cana-3949	116	31	,	,	PUNCT
cana-3949	116	32	𝑠)𝑒−𝜆𝑑(1−𝑧	𝑠)𝑒−𝜆𝑑(1−𝑧	NUM
cana-3949	116	33	)	)	PUNCT
cana-3949	117	1	+1	+1	PRON
cana-3949	117	2	−	−	PROPN
cana-3949	118	1	(	(	PUNCT
cana-3949	118	2	𝑠	𝑠	PROPN
cana-3949	118	3	+	+	CCONJ
cana-3949	118	4	𝜆)𝑄(𝑠	𝜆)𝑄(𝑠	PROPN
cana-3949	118	5	)	)	PUNCT
cana-3949	118	6	(	(	PUNCT
cana-3949	118	7	32	32	X
cana-3949	118	8	)	)	PUNCT
cana-3949	118	9	integrating	integrate	VERB
cana-3949	118	10	equation	equation	NOUN
cana-3949	118	11	(	(	PUNCT
cana-3949	118	12	27	27	NUM
cana-3949	118	13	)	)	PUNCT
cana-3949	118	14	from	from	ADP
cana-3949	118	15	0	0	NUM
cana-3949	118	16	to	to	ADP
cana-3949	118	17	𝑥	𝑥	PROPN
cana-3949	118	18	yields	yield	NOUN
cana-3949	118	19	𝑃	𝑃	NOUN
cana-3949	118	20	(	(	PUNCT
cana-3949	118	21	1	1	NUM
cana-3949	118	22	)	)	PUNCT
cana-3949	118	23	(	(	PUNCT
cana-3949	118	24	𝑥	𝑥	NOUN
cana-3949	118	25	,	,	PUNCT
cana-3949	118	26	𝑧	𝑧	PROPN
cana-3949	118	27	,	,	PUNCT
cana-3949	118	28	𝑠	𝑠	NOUN
cana-3949	118	29	)	)	PUNCT
cana-3949	118	30	=	=	PUNCT
cana-3949	118	31	𝑃	𝑃	NOUN
cana-3949	118	32	(	(	PUNCT
cana-3949	118	33	1	1	NUM
cana-3949	118	34	)	)	PUNCT
cana-3949	118	35	(	(	PUNCT
cana-3949	118	36	0	0	NUM
cana-3949	118	37	,	,	PUNCT
cana-3949	118	38	𝑧	𝑧	PROPN
cana-3949	118	39	,	,	PUNCT
cana-3949	118	40	𝑠)𝑒−(𝑠+𝜆−𝜆𝑧)𝑥−∫	𝑠)𝑒−(𝑠+𝜆−𝜆𝑧)𝑥−∫	PROPN
cana-3949	118	41	𝜇1(𝑡)𝑑𝑡	𝜇1(𝑡)𝑑𝑡	NOUN
cana-3949	118	42	∞	∞	NUM
cana-3949	118	43	0	0	NUM
cana-3949	118	44	.	.	PUNCT
cana-3949	119	1	(	(	PUNCT
cana-3949	119	2	33	33	NUM
cana-3949	119	3	)	)	PUNCT
cana-3949	119	4	where	where	SCONJ
cana-3949	119	5	𝑃	𝑃	NOUN
cana-3949	119	6	(	(	PUNCT
cana-3949	119	7	1	1	NUM
cana-3949	119	8	)	)	PUNCT
cana-3949	119	9	(	(	PUNCT
cana-3949	119	10	0	0	NUM
cana-3949	119	11	,	,	PUNCT
cana-3949	119	12	𝑧	𝑧	PROPN
cana-3949	119	13	,	,	PUNCT
cana-3949	119	14	𝑠	𝑠	X
cana-3949	119	15	)	)	PUNCT
cana-3949	119	16	is	be	AUX
cana-3949	119	17	given	give	VERB
cana-3949	119	18	by	by	ADP
cana-3949	119	19	equation	equation	NOUN
cana-3949	119	20	(	(	PUNCT
cana-3949	119	21	32	32	NUM
cana-3949	119	22	)	)	PUNCT
cana-3949	119	23	.	.	PUNCT
cana-3949	120	1	again	again	ADV
cana-3949	120	2	,	,	PUNCT
cana-3949	120	3	integrating	integrate	VERB
cana-3949	120	4	equation	equation	NOUN
cana-3949	120	5	(	(	PUNCT
cana-3949	120	6	33	33	NUM
cana-3949	120	7	)	)	PUNCT
cana-3949	120	8	by	by	ADP
cana-3949	120	9	parts	part	NOUN
cana-3949	120	10	with	with	ADP
cana-3949	120	11	respect	respect	NOUN
cana-3949	120	12	to	to	ADP
cana-3949	120	13	𝑥	𝑥	PROPN
cana-3949	120	14	yields	yield	NOUN
cana-3949	120	15	𝑃	𝑃	NOUN
cana-3949	120	16	(	(	PUNCT
cana-3949	120	17	1	1	NUM
cana-3949	120	18	)	)	PUNCT
cana-3949	120	19	(	(	PUNCT
cana-3949	120	20	𝑧	𝑧	PROPN
cana-3949	120	21	,	,	PUNCT
cana-3949	120	22	𝑠	𝑠	NOUN
cana-3949	120	23	)	)	PUNCT
cana-3949	121	1	=	=	PUNCT
cana-3949	121	2	𝑃	𝑃	NOUN
cana-3949	121	3	(	(	PUNCT
cana-3949	121	4	1	1	NUM
cana-3949	121	5	)	)	PUNCT
cana-3949	121	6	(	(	PUNCT
cana-3949	121	7	0	0	NUM
cana-3949	121	8	,	,	PUNCT
cana-3949	121	9	𝑧	𝑧	NOUN
cana-3949	121	10	,	,	PUNCT
cana-3949	121	11	𝑠	𝑠	NOUN
cana-3949	121	12	)	)	PUNCT
cana-3949	121	13	[	[	PUNCT
cana-3949	121	14	1−	1−	NUM
cana-3949	121	15	𝐵1(𝑠+𝜆−𝜆𝑧	𝐵1(𝑠+𝜆−𝜆𝑧	NOUN
cana-3949	121	16	)	)	PUNCT
cana-3949	121	17	𝑠+𝜆−𝜆𝑧	𝑠+𝜆−𝜆𝑧	PROPN
cana-3949	121	18	]	]	PUNCT
cana-3949	121	19	,	,	PUNCT
cana-3949	121	20	(	(	PUNCT
cana-3949	121	21	34	34	NUM
cana-3949	121	22	)	)	PUNCT
cana-3949	121	23	where	where	SCONJ
cana-3949	121	24	𝐵1(𝑠	𝐵1(𝑠	PROPN
cana-3949	122	1	+	+	CCONJ
cana-3949	122	2	𝜆	𝜆	DET
cana-3949	122	3	−	−	PROPN
cana-3949	122	4	𝜆𝑧	𝜆𝑧	NOUN
cana-3949	122	5	)	)	PUNCT
cana-3949	122	6	=	=	VERB
cana-3949	123	1	∫	∫	PROPN
cana-3949	123	2	𝑒	𝑒	PROPN
cana-3949	123	3	∞	∞	NUM
cana-3949	123	4	0	0	NUM
cana-3949	123	5	−(𝑠+𝜆−𝜆𝑧)𝑥	−(𝑠+𝜆−𝜆𝑧)𝑥	PROPN
cana-3949	123	6	db1(x	db1(x	NOUN
cana-3949	123	7	)	)	PUNCT
cana-3949	123	8	(	(	PUNCT
cana-3949	123	9	35	35	NUM
cana-3949	123	10	)	)	PUNCT
cana-3949	123	11	communications	communication	NOUN
cana-3949	123	12	on	on	ADP
cana-3949	123	13	applied	apply	VERB
cana-3949	123	14	nonlinear	nonlinear	ADJ
cana-3949	123	15	analysis	analysis	NOUN
cana-3949	123	16	issn	issn	NOUN
cana-3949	123	17	:	:	PUNCT
cana-3949	123	18	1074	1074	NUM
cana-3949	123	19	-	-	PUNCT
cana-3949	123	20	133x	133x	NUM
cana-3949	123	21	vol	vol	NOUN
cana-3949	123	22	32	32	NUM
cana-3949	123	23	no	no	NOUN
cana-3949	123	24	.	.	PUNCT
cana-3949	124	1	9s	9s	NUM
cana-3949	124	2	(	(	PUNCT
cana-3949	124	3	2025	2025	NUM
cana-3949	124	4	)	)	PUNCT
cana-3949	124	5	382	382	NUM
cana-3949	125	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-3949	125	2	is	be	AUX
cana-3949	125	3	the	the	DET
cana-3949	125	4	laplace	laplace	NOUN
cana-3949	125	5	steiltjes	steiltjes	ADP
cana-3949	125	6	transform	transform	NOUN
cana-3949	125	7	of	of	ADP
cana-3949	125	8	the	the	DET
cana-3949	125	9	first	first	ADJ
cana-3949	125	10	stage	stage	NOUN
cana-3949	125	11	of	of	ADP
cana-3949	125	12	service	service	NOUN
cana-3949	125	13	time	time	NOUN
cana-3949	125	14	𝐵1(𝑥	𝐵1(𝑥	NUM
cana-3949	125	15	)	)	PUNCT
cana-3949	125	16	.	.	PUNCT
cana-3949	126	1	now	now	ADV
cana-3949	126	2	multiplying	multiply	VERB
cana-3949	126	3	both	both	DET
cana-3949	126	4	sides	side	NOUN
cana-3949	126	5	of	of	ADP
cana-3949	126	6	equation	equation	NOUN
cana-3949	126	7	of	of	ADP
cana-3949	126	8	(	(	PUNCT
cana-3949	126	9	33	33	NUM
cana-3949	126	10	)	)	PUNCT
cana-3949	126	11	by	by	ADP
cana-3949	126	12	𝜇1(𝑥	𝜇1(𝑥	NOUN
cana-3949	126	13	)	)	PUNCT
cana-3949	126	14	and	and	CCONJ
cana-3949	126	15	integrating	integrate	VERB
cana-3949	126	16	over	over	ADP
cana-3949	126	17	𝑥	𝑥	PROPN
cana-3949	126	18	,	,	PUNCT
cana-3949	126	19	we	we	PRON
cana-3949	126	20	obtain	obtain	VERB
cana-3949	126	21	,	,	PUNCT
cana-3949	126	22	∫	∫	PROPN
cana-3949	126	23	𝑃	𝑃	PROPN
cana-3949	126	24	(	(	PUNCT
cana-3949	126	25	1	1	NUM
cana-3949	126	26	)	)	PUNCT
cana-3949	126	27	(	(	PUNCT
cana-3949	126	28	𝑥	𝑥	NOUN
cana-3949	126	29	,	,	PUNCT
cana-3949	126	30	𝑧	𝑧	ADJ
cana-3949	126	31	,	,	PUNCT
cana-3949	126	32	𝑠)𝜇1(𝑥)𝑑𝑥	𝑠)𝜇1(𝑥)𝑑𝑥	ADJ
cana-3949	126	33	=	=	PUNCT
cana-3949	126	34	𝑃	𝑃	NOUN
cana-3949	126	35	(	(	PUNCT
cana-3949	126	36	1	1	NUM
cana-3949	126	37	)	)	PUNCT
cana-3949	126	38	(	(	PUNCT
cana-3949	126	39	0	0	NUM
cana-3949	126	40	,	,	PUNCT
cana-3949	126	41	𝑧	𝑧	PROPN
cana-3949	126	42	,	,	PUNCT
cana-3949	126	43	𝑠)𝐵1(𝑠	𝑠)𝐵1(𝑠	PROPN
cana-3949	127	1	+	+	CCONJ
cana-3949	127	2	𝜆	𝜆	PROPN
cana-3949	127	3	−	−	PROPN
cana-3949	127	4	𝜆𝑧	𝜆𝑧	NUM
cana-3949	127	5	)	)	PUNCT
cana-3949	127	6	∞	∞	NOUN
cana-3949	127	7	0	0	NUM
cana-3949	127	8	(	(	PUNCT
cana-3949	127	9	36	36	NUM
cana-3949	127	10	)	)	PUNCT
cana-3949	127	11	similarly	similarly	ADV
cana-3949	127	12	,	,	PUNCT
cana-3949	127	13	on	on	ADP
cana-3949	127	14	integrating	integrate	VERB
cana-3949	127	15	equation	equation	NOUN
cana-3949	127	16	(	(	PUNCT
cana-3949	127	17	28	28	NUM
cana-3949	127	18	)	)	PUNCT
cana-3949	127	19	from	from	ADP
cana-3949	127	20	0	0	NUM
cana-3949	127	21	to	to	PART
cana-3949	127	22	𝑥	𝑥	PRON
cana-3949	127	23	,	,	PUNCT
cana-3949	127	24	we	we	PRON
cana-3949	127	25	get	get	VERB
cana-3949	127	26	𝑃	𝑃	NOUN
cana-3949	127	27	(	(	PUNCT
cana-3949	127	28	2	2	NUM
cana-3949	127	29	)	)	PUNCT
cana-3949	127	30	(	(	PUNCT
cana-3949	127	31	𝑥	𝑥	NOUN
cana-3949	127	32	,	,	PUNCT
cana-3949	127	33	𝑧	𝑧	PROPN
cana-3949	127	34	,	,	PUNCT
cana-3949	127	35	𝑠	𝑠	NOUN
cana-3949	127	36	)	)	PUNCT
cana-3949	127	37	=	=	PUNCT
cana-3949	127	38	𝑃	𝑃	NOUN
cana-3949	127	39	(	(	PUNCT
cana-3949	127	40	2	2	NUM
cana-3949	127	41	)	)	PUNCT
cana-3949	127	42	(	(	PUNCT
cana-3949	127	43	0	0	NUM
cana-3949	127	44	,	,	PUNCT
cana-3949	127	45	𝑧	𝑧	X
cana-3949	127	46	,	,	PUNCT
cana-3949	127	47	𝑠)𝑒−(𝑠+𝜆−𝜆𝑧)𝑥−∫	𝑠)𝑒−(𝑠+𝜆−𝜆𝑧)𝑥−∫	PROPN
cana-3949	127	48	𝜇2(𝑡)𝑑𝑡	𝜇2(𝑡)𝑑𝑡	NOUN
cana-3949	127	49	∞	∞	NUM
cana-3949	127	50	0	0	NUM
cana-3949	127	51	,	,	PUNCT
cana-3949	127	52	(	(	PUNCT
cana-3949	127	53	37	37	NUM
cana-3949	127	54	)	)	PUNCT
cana-3949	127	55	where	where	SCONJ
cana-3949	127	56	𝑃	𝑃	NOUN
cana-3949	127	57	(	(	PUNCT
cana-3949	127	58	2	2	NUM
cana-3949	127	59	)	)	PUNCT
cana-3949	127	60	(	(	PUNCT
cana-3949	127	61	0	0	NUM
cana-3949	127	62	,	,	PUNCT
cana-3949	127	63	𝑧	𝑧	PROPN
cana-3949	127	64	,	,	PUNCT
cana-3949	127	65	𝑠	𝑠	X
cana-3949	127	66	)	)	PUNCT
cana-3949	127	67	is	be	AUX
cana-3949	127	68	given	give	VERB
cana-3949	127	69	by	by	ADP
cana-3949	127	70	equation	equation	NOUN
cana-3949	127	71	(	(	PUNCT
cana-3949	127	72	31	31	NUM
cana-3949	127	73	)	)	PUNCT
cana-3949	127	74	.	.	PUNCT
cana-3949	128	1	again	again	ADV
cana-3949	128	2	,	,	PUNCT
cana-3949	128	3	integrating	integrate	VERB
cana-3949	128	4	equation	equation	NOUN
cana-3949	128	5	(	(	PUNCT
cana-3949	128	6	37	37	NUM
cana-3949	128	7	)	)	PUNCT
cana-3949	128	8	by	by	ADP
cana-3949	128	9	parts	part	NOUN
cana-3949	128	10	with	with	ADP
cana-3949	128	11	respect	respect	NOUN
cana-3949	128	12	to	to	ADP
cana-3949	128	13	𝑥	𝑥	PROPN
cana-3949	128	14	yields	yield	NOUN
cana-3949	128	15	𝑃	𝑃	NOUN
cana-3949	128	16	(	(	PUNCT
cana-3949	128	17	2	2	NUM
cana-3949	128	18	)	)	PUNCT
cana-3949	128	19	(	(	PUNCT
cana-3949	128	20	𝑧	𝑧	PROPN
cana-3949	128	21	,	,	PUNCT
cana-3949	128	22	𝑠	𝑠	NOUN
cana-3949	128	23	)	)	PUNCT
cana-3949	128	24	=	=	PUNCT
cana-3949	128	25	𝑃	𝑃	NOUN
cana-3949	128	26	(	(	PUNCT
cana-3949	128	27	2	2	NUM
cana-3949	128	28	)	)	PUNCT
cana-3949	128	29	(	(	PUNCT
cana-3949	128	30	0	0	NUM
cana-3949	128	31	,	,	PUNCT
cana-3949	128	32	𝑧	𝑧	NOUN
cana-3949	128	33	,	,	PUNCT
cana-3949	128	34	𝑠	𝑠	NOUN
cana-3949	128	35	)	)	PUNCT
cana-3949	128	36	[	[	PUNCT
cana-3949	128	37	1−	1−	NUM
cana-3949	128	38	𝐵2(𝑠+𝜆−𝜆𝑧	𝐵2(𝑠+𝜆−𝜆𝑧	NOUN
cana-3949	128	39	)	)	PUNCT
cana-3949	128	40	𝑠+𝜆−𝜆𝑧	𝑠+𝜆−𝜆𝑧	PROPN
cana-3949	128	41	]	]	PUNCT
cana-3949	128	42	,	,	PUNCT
cana-3949	128	43	(	(	PUNCT
cana-3949	128	44	38	38	NUM
cana-3949	128	45	)	)	PUNCT
cana-3949	128	46	where	where	SCONJ
cana-3949	128	47	𝐵2(𝑠	𝐵2(𝑠	PUNCT
cana-3949	128	48	+	+	CCONJ
cana-3949	128	49	𝜆	𝜆	DET
cana-3949	128	50	−	−	PROPN
cana-3949	128	51	𝜆𝑧	𝜆𝑧	NOUN
cana-3949	128	52	)	)	PUNCT
cana-3949	128	53	=	=	VERB
cana-3949	129	1	∫	∫	PROPN
cana-3949	129	2	𝑒	𝑒	PROPN
cana-3949	129	3	∞	∞	PROPN
cana-3949	129	4	0	0	NUM
cana-3949	129	5	−(𝑠+𝜆−𝜆𝑧)𝑥	−(𝑠+𝜆−𝜆𝑧)𝑥	PROPN
cana-3949	129	6	db2(x	db2(x	PROPN
cana-3949	129	7	)	)	PUNCT
cana-3949	129	8	,	,	PUNCT
cana-3949	129	9	(	(	PUNCT
cana-3949	129	10	39	39	NUM
cana-3949	129	11	)	)	PUNCT
cana-3949	129	12	is	be	AUX
cana-3949	129	13	the	the	DET
cana-3949	129	14	laplace	laplace	NOUN
cana-3949	129	15	steiltjes	steiltjes	ADP
cana-3949	129	16	transform	transform	NOUN
cana-3949	129	17	of	of	ADP
cana-3949	129	18	second	second	ADJ
cana-3949	129	19	stage	stage	NOUN
cana-3949	129	20	of	of	ADP
cana-3949	129	21	service	service	NOUN
cana-3949	129	22	time	time	NOUN
cana-3949	129	23	𝐵2(𝑥	𝐵2(𝑥	NUM
cana-3949	129	24	)	)	PUNCT
cana-3949	129	25	.	.	PUNCT
cana-3949	130	1	we	we	PRON
cana-3949	130	2	see	see	VERB
cana-3949	130	3	that	that	SCONJ
cana-3949	130	4	by	by	ADP
cana-3949	130	5	virtue	virtue	NOUN
cana-3949	130	6	of	of	ADP
cana-3949	130	7	equation	equation	NOUN
cana-3949	130	8	(	(	PUNCT
cana-3949	130	9	37	37	NUM
cana-3949	130	10	)	)	PUNCT
cana-3949	130	11	,	,	PUNCT
cana-3949	130	12	we	we	PRON
cana-3949	130	13	have	have	VERB
cana-3949	130	14	∫	∫	PROPN
cana-3949	130	15	𝑃	𝑃	PROPN
cana-3949	130	16	(	(	PUNCT
cana-3949	130	17	2	2	NUM
cana-3949	130	18	)	)	PUNCT
cana-3949	130	19	(	(	PUNCT
cana-3949	130	20	𝑥	𝑥	NOUN
cana-3949	130	21	,	,	PUNCT
cana-3949	130	22	𝑧	𝑧	ADJ
cana-3949	130	23	,	,	PUNCT
cana-3949	130	24	𝑠)𝜇2(𝑥)𝑑𝑥	𝑠)𝜇2(𝑥)𝑑𝑥	ADJ
cana-3949	130	25	=	=	PUNCT
cana-3949	130	26	𝑃	𝑃	NOUN
cana-3949	130	27	(	(	PUNCT
cana-3949	130	28	2	2	NUM
cana-3949	130	29	)	)	PUNCT
cana-3949	130	30	(	(	PUNCT
cana-3949	130	31	0	0	NUM
cana-3949	130	32	,	,	PUNCT
cana-3949	130	33	𝑧	𝑧	ADJ
cana-3949	130	34	,	,	PUNCT
cana-3949	130	35	𝑠)𝐵2(𝑠	𝑠)𝐵2(𝑠	PROPN
cana-3949	130	36	+	+	PUNCT
cana-3949	130	37	𝜆	𝜆	DET
cana-3949	130	38	−	−	PROPN
cana-3949	130	39	𝜆𝑧	𝜆𝑧	NUM
cana-3949	130	40	)	)	PUNCT
cana-3949	130	41	∞	∞	NOUN
cana-3949	130	42	0	0	NUM
cana-3949	130	43	.	.	PUNCT
cana-3949	131	1	(	(	PUNCT
cana-3949	131	2	40	40	NUM
cana-3949	131	3	)	)	PUNCT
cana-3949	131	4	now	now	ADV
cana-3949	131	5	by	by	ADP
cana-3949	131	6	using	use	VERB
cana-3949	131	7	equations	equation	NOUN
cana-3949	131	8	(	(	PUNCT
cana-3949	131	9	31	31	NUM
cana-3949	131	10	)	)	PUNCT
cana-3949	131	11	and	and	CCONJ
cana-3949	131	12	(	(	PUNCT
cana-3949	131	13	36	36	NUM
cana-3949	131	14	)	)	PUNCT
cana-3949	131	15	,	,	PUNCT
cana-3949	131	16	equation	equation	NOUN
cana-3949	131	17	(	(	PUNCT
cana-3949	131	18	40	40	NUM
cana-3949	131	19	)	)	PUNCT
cana-3949	131	20	becomes	become	VERB
cana-3949	131	21	∫	∫	PROPN
cana-3949	131	22	𝑃	𝑃	PROPN
cana-3949	131	23	(	(	PUNCT
cana-3949	131	24	2	2	NUM
cana-3949	131	25	)	)	PUNCT
cana-3949	131	26	(	(	PUNCT
cana-3949	131	27	𝑥	𝑥	NOUN
cana-3949	131	28	,	,	PUNCT
cana-3949	131	29	𝑧	𝑧	ADJ
cana-3949	131	30	,	,	PUNCT
cana-3949	131	31	𝑠)𝜇2(𝑥)𝑑𝑥	𝑠)𝜇2(𝑥)𝑑𝑥	ADJ
cana-3949	131	32	=	=	PUNCT
cana-3949	131	33	𝑃	𝑃	NOUN
cana-3949	131	34	(	(	PUNCT
cana-3949	131	35	1	1	NUM
cana-3949	131	36	)	)	PUNCT
cana-3949	131	37	(	(	PUNCT
cana-3949	131	38	0	0	NUM
cana-3949	131	39	,	,	PUNCT
cana-3949	131	40	𝑧	𝑧	PROPN
cana-3949	131	41	,	,	PUNCT
cana-3949	131	42	𝑠)𝐵1(𝑠	𝑠)𝐵1(𝑠	PROPN
cana-3949	132	1	+	+	CCONJ
cana-3949	132	2	𝜆	𝜆	PROPN
cana-3949	132	3	−	−	PROPN
cana-3949	132	4	𝜆𝑧	𝜆𝑧	NUM
cana-3949	132	5	)	)	PUNCT
cana-3949	132	6	∞	∞	NOUN
cana-3949	132	7	0	0	NUM
cana-3949	133	1	𝐵2(𝑠	𝐵2(𝑠	PROPN
cana-3949	134	1	+	+	CCONJ
cana-3949	134	2	𝜆	𝜆	DET
cana-3949	134	3	−	−	PROPN
cana-3949	134	4	𝜆𝑧	𝜆𝑧	NUM
cana-3949	134	5	)	)	PUNCT
cana-3949	134	6	.	.	PUNCT
cana-3949	135	1	(	(	PUNCT
cana-3949	135	2	41	41	NUM
cana-3949	135	3	)	)	PUNCT
cana-3949	135	4	from	from	ADP
cana-3949	135	5	equation	equation	NOUN
cana-3949	135	6	(	(	PUNCT
cana-3949	135	7	32	32	NUM
cana-3949	135	8	)	)	PUNCT
cana-3949	135	9	,	,	PUNCT
cana-3949	135	10	we	we	PRON
cana-3949	135	11	obtain	obtain	VERB
cana-3949	135	12	𝑃	𝑃	NOUN
cana-3949	135	13	(	(	PUNCT
cana-3949	135	14	1	1	NUM
cana-3949	135	15	)	)	PUNCT
cana-3949	135	16	(	(	PUNCT
cana-3949	135	17	0	0	NUM
cana-3949	135	18	,	,	PUNCT
cana-3949	135	19	𝑧	𝑧	NOUN
cana-3949	135	20	,	,	PUNCT
cana-3949	135	21	𝑠	𝑠	NOUN
cana-3949	135	22	)	)	PUNCT
cana-3949	135	23	=	=	PUNCT
cana-3949	136	1	[	[	PUNCT
cana-3949	136	2	𝑉(𝑧,𝑠)𝑒−𝜆𝑑(1−𝑧)+[1−𝑠𝑄(𝑠)]+𝜆𝑄(𝑠)[𝑧−1	𝑉(𝑧,𝑠)𝑒−𝜆𝑑(1−𝑧)+[1−𝑠𝑄(𝑠)]+𝜆𝑄(𝑠)[𝑧−1	X
cana-3949	136	3	]	]	X
cana-3949	136	4	𝑧	𝑧	X
cana-3949	136	5	]	]	X
cana-3949	136	6	.	.	PUNCT
cana-3949	137	1	(	(	PUNCT
cana-3949	137	2	42	42	X
cana-3949	137	3	)	)	PUNCT
cana-3949	137	4	substituting	substitute	VERB
cana-3949	137	5	the	the	DET
cana-3949	137	6	value	value	NOUN
cana-3949	137	7	of	of	ADP
cana-3949	137	8	𝑃	𝑃	NOUN
cana-3949	137	9	(	(	PUNCT
cana-3949	137	10	1	1	NUM
cana-3949	137	11	)	)	PUNCT
cana-3949	137	12	(	(	PUNCT
cana-3949	137	13	0	0	NUM
cana-3949	137	14	,	,	PUNCT
cana-3949	137	15	𝑧	𝑧	NOUN
cana-3949	137	16	,	,	PUNCT
cana-3949	137	17	𝑠	𝑠	NOUN
cana-3949	137	18	)	)	PUNCT
cana-3949	137	19	into	into	ADP
cana-3949	137	20	equation	equation	NOUN
cana-3949	137	21	(	(	PUNCT
cana-3949	137	22	34	34	NUM
cana-3949	137	23	)	)	PUNCT
cana-3949	137	24	,	,	PUNCT
cana-3949	137	25	we	we	PRON
cana-3949	137	26	get	get	VERB
cana-3949	137	27	𝑃	𝑃	NOUN
cana-3949	137	28	(	(	PUNCT
cana-3949	137	29	1	1	NUM
cana-3949	137	30	)	)	PUNCT
cana-3949	137	31	(	(	PUNCT
cana-3949	137	32	𝑧	𝑧	PROPN
cana-3949	137	33	,	,	PUNCT
cana-3949	137	34	𝑠	𝑠	NOUN
cana-3949	137	35	)	)	PUNCT
cana-3949	137	36	=	=	NOUN
cana-3949	137	37	[	[	PUNCT
cana-3949	137	38	1−𝐵1(𝑠+𝜆−𝜆𝑧	1−𝐵1(𝑠+𝜆−𝜆𝑧	NUM
cana-3949	137	39	)	)	PUNCT
cana-3949	137	40	(	(	PUNCT
cana-3949	137	41	𝑠+𝜆−𝜆𝑧	𝑠+𝜆−𝜆𝑧	PROPN
cana-3949	137	42	)	)	PUNCT
cana-3949	137	43	]	]	PUNCT
cana-3949	138	1	[	[	PUNCT
cana-3949	138	2	𝑉(𝑧,𝑠)𝑒−𝜆𝑑(1−𝑧)+[1−𝑠𝑄(𝑠)]+𝜆𝑄(𝑠)[𝑧−1	𝑉(𝑧,𝑠)𝑒−𝜆𝑑(1−𝑧)+[1−𝑠𝑄(𝑠)]+𝜆𝑄(𝑠)[𝑧−1	X
cana-3949	138	3	]	]	X
cana-3949	138	4	𝑧	𝑧	X
cana-3949	138	5	]	]	X
cana-3949	138	6	(	(	PUNCT
cana-3949	138	7	43	43	NUM
cana-3949	138	8	)	)	PUNCT
cana-3949	138	9	now	now	ADV
cana-3949	138	10	using	use	VERB
cana-3949	138	11	equations	equation	NOUN
cana-3949	138	12	(	(	PUNCT
cana-3949	138	13	31	31	NUM
cana-3949	138	14	)	)	PUNCT
cana-3949	138	15	,	,	PUNCT
cana-3949	138	16	(	(	PUNCT
cana-3949	138	17	32	32	NUM
cana-3949	138	18	)	)	PUNCT
cana-3949	138	19	and	and	CCONJ
cana-3949	138	20	(	(	PUNCT
cana-3949	138	21	36	36	NUM
cana-3949	138	22	)	)	PUNCT
cana-3949	138	23	,	,	PUNCT
cana-3949	138	24	equation	equation	NOUN
cana-3949	138	25	(	(	PUNCT
cana-3949	138	26	38	38	NUM
cana-3949	138	27	)	)	PUNCT
cana-3949	138	28	become	become	VERB
cana-3949	138	29	𝑃	𝑃	NOUN
cana-3949	138	30	(	(	PUNCT
cana-3949	138	31	2	2	NUM
cana-3949	138	32	)	)	PUNCT
cana-3949	138	33	(	(	PUNCT
cana-3949	138	34	𝑧	𝑧	PROPN
cana-3949	138	35	,	,	PUNCT
cana-3949	138	36	𝑠	𝑠	NOUN
cana-3949	138	37	)	)	PUNCT
cana-3949	138	38	=	=	PUNCT
cana-3949	139	1	[	[	PUNCT
cana-3949	139	2	𝑉(𝑧,𝑠)𝑒−𝜆𝑑(1−𝑧)+[1−𝑠𝑄(𝑠)]+𝜆𝑄(𝑠)[𝑧−1	𝑉(𝑧,𝑠)𝑒−𝜆𝑑(1−𝑧)+[1−𝑠𝑄(𝑠)]+𝜆𝑄(𝑠)[𝑧−1	X
cana-3949	139	3	]	]	X
cana-3949	139	4	𝑧	𝑧	X
cana-3949	139	5	]	]	PUNCT
cana-3949	139	6	𝐵1(𝑠	𝐵1(𝑠	PROPN
cana-3949	140	1	+	+	CCONJ
cana-3949	140	2	𝜆	𝜆	DET
cana-3949	140	3	−	−	PROPN
cana-3949	140	4	𝜆𝑧	𝜆𝑧	NOUN
cana-3949	140	5	)	)	PUNCT
cana-3949	140	6	[	[	PUNCT
cana-3949	140	7	1−𝐵2(𝑠+𝜆−𝜆𝑧	1−𝐵2(𝑠+𝜆−𝜆𝑧	NUM
cana-3949	140	8	)	)	PUNCT
cana-3949	140	9	(	(	PUNCT
cana-3949	140	10	𝑠+𝜆−𝜆𝑧	𝑠+𝜆−𝜆𝑧	PROPN
cana-3949	140	11	)	)	PUNCT
cana-3949	140	12	]	]	PUNCT
cana-3949	140	13	.	.	PUNCT
cana-3949	141	1	(	(	PUNCT
cana-3949	141	2	44	44	NUM
cana-3949	141	3	)	)	PUNCT
cana-3949	141	4	from	from	ADP
cana-3949	141	5	equation	equation	NOUN
cana-3949	141	6	(	(	PUNCT
cana-3949	141	7	29	29	NUM
cana-3949	141	8	)	)	PUNCT
cana-3949	141	9	(	(	PUNCT
cana-3949	141	10	𝑠	𝑠	X
cana-3949	141	11	+	+	NOUN
cana-3949	141	12	1)	1)	NUM
cana-3949	141	13	�	�	NOUN
cana-3949	141	14	̅	̅	NOUN
cana-3949	141	15	�	�	NOUN
cana-3949	142	1	(𝑧	(𝑧	NOUN
cana-3949	142	2	,	,	PUNCT
cana-3949	142	3	𝑠	𝑠	PROPN
cana-3949	142	4	)	)	PUNCT
cana-3949	142	5	=	=	PUNCT
cana-3949	143	1	[	[	PUNCT
cana-3949	143	2	𝑉(𝑧,𝑠)𝑒−𝜆𝑑(1−𝑧)+[1−𝑠𝑄(𝑠)]+𝜆𝑄(𝑠)[𝑧−1	𝑉(𝑧,𝑠)𝑒−𝜆𝑑(1−𝑧)+[1−𝑠𝑄(𝑠)]+𝜆𝑄(𝑠)[𝑧−1	X
cana-3949	143	3	]	]	X
cana-3949	143	4	𝑧	𝑧	X
cana-3949	143	5	]	]	X
cana-3949	143	6	𝐵1(𝑠	𝐵1(𝑠	PROPN
cana-3949	144	1	+	+	CCONJ
cana-3949	144	2	𝜆	𝜆	ADV
cana-3949	144	3	−	−	NOUN
cana-3949	144	4	𝜆𝑧)𝐵2(𝑠	𝜆𝑧)𝐵2(𝑠	NUM
cana-3949	145	1	+	+	CCONJ
cana-3949	145	2	𝜆	𝜆	DET
cana-3949	145	3	−	−	PROPN
cana-3949	145	4	𝜆𝑧	𝜆𝑧	NUM
cana-3949	145	5	)	)	PUNCT
cana-3949	145	6	.	.	PUNCT
cana-3949	146	1	(	(	PUNCT
cana-3949	146	2	45	45	NUM
cana-3949	146	3	)	)	PUNCT
cana-3949	146	4	which	which	PRON
cana-3949	146	5	further	far	ADV
cana-3949	146	6	reduces	reduce	VERB
cana-3949	146	7	to	to	ADP
cana-3949	146	8	�	�	NOUN
cana-3949	146	9	̅	̅	NOUN
cana-3949	146	10	�	�	NOUN
cana-3949	147	1	(𝑧	(𝑧	NOUN
cana-3949	147	2	,	,	PUNCT
cana-3949	147	3	𝑠	𝑠	PROPN
cana-3949	147	4	)	)	PUNCT
cana-3949	148	1	=	=	NOUN
cana-3949	149	1	[	[	PUNCT
cana-3949	149	2	[	[	X
cana-3949	149	3	1−𝑠𝑄(𝑠)]+𝜆𝑄(𝑠)[𝑧−1	1−𝑠𝑄(𝑠)]+𝜆𝑄(𝑠)[𝑧−1	X
cana-3949	149	4	]	]	X
cana-3949	149	5	(	(	PUNCT
cana-3949	149	6	𝑠+1)[𝑍−𝐵1(𝑠+𝜆−𝜆𝑧)𝐵2(𝑠+𝜆−𝜆𝑧)+𝐵1(𝑠+𝜆−𝜆𝑧)𝐵2(𝑠+𝜆−𝜆𝑧)[1−𝑒	𝑠+1)[𝑍−𝐵1(𝑠+𝜆−𝜆𝑧)𝐵2(𝑠+𝜆−𝜆𝑧)+𝐵1(𝑠+𝜆−𝜆𝑧)𝐵2(𝑠+𝜆−𝜆𝑧)[1−𝑒	NUM
cana-3949	149	7	−𝜆𝑑(1−𝑧	−𝜆𝑑(1−𝑧	PROPN
cana-3949	149	8	)	)	PUNCT
cana-3949	149	9	]	]	PUNCT
cana-3949	149	10	]	]	X
cana-3949	149	11	]	]	PUNCT
cana-3949	149	12	communications	communication	NOUN
cana-3949	149	13	on	on	ADP
cana-3949	149	14	applied	apply	VERB
cana-3949	149	15	nonlinear	nonlinear	ADJ
cana-3949	149	16	analysis	analysis	NOUN
cana-3949	149	17	issn	issn	NOUN
cana-3949	149	18	:	:	PUNCT
cana-3949	149	19	1074	1074	NUM
cana-3949	149	20	-	-	PUNCT
cana-3949	149	21	133x	133x	NUM
cana-3949	149	22	vol	vol	NOUN
cana-3949	149	23	32	32	NUM
cana-3949	149	24	no	no	NOUN
cana-3949	149	25	.	.	PUNCT
cana-3949	150	1	9s	9s	NUM
cana-3949	150	2	(	(	PUNCT
cana-3949	150	3	2025	2025	NUM
cana-3949	150	4	)	)	PUNCT
cana-3949	150	5	383	383	NUM
cana-3949	150	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3949	150	7	𝐵1(𝑠	𝐵1(𝑠	PROPN
cana-3949	151	1	+	+	CCONJ
cana-3949	151	2	𝜆	𝜆	ADV
cana-3949	151	3	−	−	NOUN
cana-3949	151	4	𝜆𝑧)𝐵2(𝑠	𝜆𝑧)𝐵2(𝑠	NUM
cana-3949	152	1	+	+	CCONJ
cana-3949	152	2	𝜆	𝜆	DET
cana-3949	152	3	−	−	PROPN
cana-3949	152	4	𝜆𝑧	𝜆𝑧	NUM
cana-3949	152	5	)	)	PUNCT
cana-3949	152	6	.	.	PUNCT
cana-3949	153	1	(	(	PUNCT
cana-3949	153	2	46	46	X
cana-3949	153	3	)	)	PUNCT
cana-3949	153	4	let	let	VERB
cana-3949	153	5	𝑃(𝑧	𝑃(𝑧	SYM
cana-3949	153	6	,	,	PUNCT
cana-3949	153	7	𝑠	𝑠	NOUN
cana-3949	153	8	)	)	PUNCT
cana-3949	153	9	=	=	PUNCT
cana-3949	153	10	𝑃	𝑃	NOUN
cana-3949	153	11	(	(	PUNCT
cana-3949	153	12	1	1	NUM
cana-3949	153	13	)	)	PUNCT
cana-3949	153	14	(	(	PUNCT
cana-3949	153	15	𝑧	𝑧	PROPN
cana-3949	153	16	,	,	PUNCT
cana-3949	153	17	𝑠	𝑠	NOUN
cana-3949	153	18	)	)	PUNCT
cana-3949	154	1	+	+	CCONJ
cana-3949	154	2	𝑃	𝑃	NOUN
cana-3949	154	3	(	(	PUNCT
cana-3949	154	4	2	2	NUM
cana-3949	154	5	)	)	PUNCT
cana-3949	154	6	(	(	PUNCT
cana-3949	154	7	𝑧	𝑧	PROPN
cana-3949	154	8	,	,	PUNCT
cana-3949	154	9	𝑠	𝑠	NOUN
cana-3949	154	10	)	)	PUNCT
cana-3949	154	11	denote	denote	VERB
cana-3949	154	12	the	the	DET
cana-3949	154	13	probability	probability	NOUN
cana-3949	154	14	generating	generating	NOUN
cana-3949	154	15	function	function	NOUN
cana-3949	154	16	of	of	ADP
cana-3949	154	17	the	the	DET
cana-3949	154	18	number	number	NOUN
cana-3949	154	19	in	in	ADP
cana-3949	154	20	the	the	DET
cana-3949	154	21	queue	queue	NOUN
cana-3949	154	22	irrespective	irrespective	ADV
cana-3949	154	23	of	of	ADP
cana-3949	154	24	the	the	DET
cana-3949	154	25	type	type	NOUN
cana-3949	154	26	of	of	ADP
cana-3949	154	27	service	service	NOUN
cana-3949	154	28	being	be	AUX
cana-3949	154	29	provided	provide	VERB
cana-3949	154	30	.	.	PUNCT
cana-3949	155	1	then	then	ADV
cana-3949	155	2	adding	add	VERB
cana-3949	155	3	equations	equation	NOUN
cana-3949	155	4	(	(	PUNCT
cana-3949	155	5	43	43	NUM
cana-3949	155	6	)	)	PUNCT
cana-3949	155	7	and	and	CCONJ
cana-3949	155	8	(	(	PUNCT
cana-3949	155	9	44	44	NUM
cana-3949	155	10	)	)	PUNCT
cana-3949	155	11	,	,	PUNCT
cana-3949	155	12	we	we	PRON
cana-3949	155	13	have	have	VERB
cana-3949	155	14	𝑃(𝑧	𝑃(𝑧	NUM
cana-3949	155	15	,	,	PUNCT
cana-3949	155	16	𝑠	𝑠	NOUN
cana-3949	155	17	)	)	PUNCT
cana-3949	155	18	=	=	PUNCT
cana-3949	156	1	[	[	PUNCT
cana-3949	156	2	𝑉(𝑧,𝑠)𝑒−𝜆𝑑(1−𝑧)+[1−𝑠𝑄(𝑠)]+𝜆𝑄(𝑠)[𝑧−1	𝑉(𝑧,𝑠)𝑒−𝜆𝑑(1−𝑧)+[1−𝑠𝑄(𝑠)]+𝜆𝑄(𝑠)[𝑧−1	X
cana-3949	156	3	]	]	X
cana-3949	156	4	𝑧	𝑧	X
cana-3949	156	5	]	]	X
cana-3949	156	6	[	[	PUNCT
cana-3949	156	7	1−𝐵1(𝑠+𝜆−𝜆𝑧)𝐵2(𝑠+𝜆−𝜆𝑧	1−𝐵1(𝑠+𝜆−𝜆𝑧)𝐵2(𝑠+𝜆−𝜆𝑧	NUM
cana-3949	156	8	)	)	PUNCT
cana-3949	156	9	(	(	PUNCT
cana-3949	156	10	𝑠+𝜆−𝜆𝑧	𝑠+𝜆−𝜆𝑧	PROPN
cana-3949	156	11	)	)	PUNCT
cana-3949	156	12	]	]	PUNCT
cana-3949	156	13	.	.	PUNCT
cana-3949	157	1	(	(	PUNCT
cana-3949	157	2	47	47	NUM
cana-3949	157	3	)	)	PUNCT
cana-3949	157	4	thus	thus	ADV
cana-3949	157	5	substituting	substitute	VERB
cana-3949	157	6	the	the	DET
cana-3949	157	7	value	value	NOUN
cana-3949	157	8	of	of	ADP
cana-3949	157	9	�	�	PROPN
cana-3949	157	10	̅	̅	NOUN
cana-3949	157	11	�	�	NOUN
cana-3949	157	12	(𝑧	(𝑧	NOUN
cana-3949	157	13	,	,	PUNCT
cana-3949	157	14	𝑠	𝑠	PROPN
cana-3949	157	15	)	)	PUNCT
cana-3949	157	16	from	from	ADP
cana-3949	157	17	equation	equation	NOUN
cana-3949	157	18	(	(	PUNCT
cana-3949	157	19	46	46	NUM
cana-3949	157	20	)	)	PUNCT
cana-3949	157	21	into	into	ADP
cana-3949	157	22	equation	equation	NOUN
cana-3949	157	23	(	(	PUNCT
cana-3949	157	24	47	47	NUM
cana-3949	157	25	)	)	PUNCT
cana-3949	157	26	,	,	PUNCT
cana-3949	157	27	we	we	PRON
cana-3949	157	28	get	get	VERB
cana-3949	157	29	𝑃(𝑧	𝑃(𝑧	SYM
cana-3949	157	30	,	,	PUNCT
cana-3949	157	31	𝑠	𝑠	NOUN
cana-3949	157	32	)	)	PUNCT
cana-3949	157	33	=	=	SYM
cana-3949	157	34	𝑁(𝑧,𝑠	𝑁(𝑧,𝑠	PROPN
cana-3949	157	35	)	)	PUNCT
cana-3949	157	36	𝐷(𝑧,𝑠	𝐷(𝑧,𝑠	NOUN
cana-3949	157	37	)	)	PUNCT
cana-3949	158	1	(	(	PUNCT
cana-3949	158	2	48	48	NUM
cana-3949	158	3	)	)	PUNCT
cana-3949	158	4	𝑁(𝑧	𝑁(𝑧	NUM
cana-3949	158	5	,	,	PUNCT
cana-3949	158	6	𝑠	𝑠	NOUN
cana-3949	158	7	)	)	PUNCT
cana-3949	158	8	=	=	SYM
cana-3949	158	9	(	(	PUNCT
cana-3949	158	10	(	(	PUNCT
cana-3949	158	11	𝑠	𝑠	X
cana-3949	158	12	+	+	NOUN
cana-3949	158	13	1	1	NUM
cana-3949	158	14	)	)	PUNCT
cana-3949	158	15	[	[	PUNCT
cana-3949	158	16	𝑧	𝑧	NOUN
cana-3949	158	17	−	−	PROPN
cana-3949	158	18	𝐵1(𝑠	𝐵1(𝑠	PROPN
cana-3949	159	1	+	+	CCONJ
cana-3949	159	2	𝜆	𝜆	ADV
cana-3949	159	3	−	−	NOUN
cana-3949	159	4	𝜆𝑧)𝐵2(𝑠	𝜆𝑧)𝐵2(𝑠	NUM
cana-3949	160	1	+	+	CCONJ
cana-3949	160	2	𝜆	𝜆	DET
cana-3949	160	3	−	−	PROPN
cana-3949	160	4	𝜆𝑧	𝜆𝑧	NUM
cana-3949	160	5	)	)	PUNCT
cana-3949	161	1	+	+	NUM
cana-3949	161	2	𝐵1(𝑠	𝐵1(𝑠	PROPN
cana-3949	162	1	+	+	CCONJ
cana-3949	162	2	𝜆	𝜆	DET
cana-3949	162	3	−	−	PROPN
cana-3949	162	4	𝜆𝑧	𝜆𝑧	NUM
cana-3949	162	5	)	)	PUNCT
cana-3949	162	6	𝐵2(𝑠	𝐵2(𝑠	PROPN
cana-3949	163	1	+	+	CCONJ
cana-3949	163	2	𝜆	𝜆	PRON
cana-3949	163	3	−	−	X
cana-3949	163	4	𝜆𝑧)[1	𝜆𝑧)[1	PROPN
cana-3949	163	5	−	−	PROPN
cana-3949	163	6	𝑒	𝑒	PROPN
cana-3949	163	7	−𝜆𝑑(1−𝑧	−𝜆𝑑(1−𝑧	NOUN
cana-3949	163	8	)	)	PUNCT
cana-3949	163	9	]	]	PUNCT
cana-3949	164	1	[	[	X
cana-3949	164	2	1	1	NUM
cana-3949	164	3	−	−	PROPN
cana-3949	164	4	𝑠𝑄(𝑠	𝑠𝑄(𝑠	PROPN
cana-3949	164	5	)	)	PUNCT
cana-3949	164	6	+	+	CCONJ
cana-3949	164	7	𝜆𝑄(𝑠)[𝑧	𝜆𝑄(𝑠)[𝑧	VERB
cana-3949	164	8	−	−	PROPN
cana-3949	164	9	1	1	NUM
cana-3949	164	10	]	]	PUNCT
cana-3949	164	11	]	]	PUNCT
cana-3949	164	12	]	]	PUNCT
cana-3949	165	1	+	+	PUNCT
cana-3949	165	2	𝐵1(𝑠	𝐵1(𝑠	PROPN
cana-3949	165	3	+	+	CCONJ
cana-3949	165	4	𝜆	𝜆	ADP
cana-3949	165	5	−	−	NOUN
cana-3949	165	6	𝜆𝑧)𝐵2(𝑠	𝜆𝑧)𝐵2(𝑠	NUM
cana-3949	166	1	+	+	CCONJ
cana-3949	166	2	𝜆	𝜆	DET
cana-3949	166	3	−	−	PROPN
cana-3949	166	4	𝜆𝑧)𝑒	𝜆𝑧)𝑒	NOUN
cana-3949	166	5	−𝜆𝑑(1−𝑧	−𝜆𝑑(1−𝑧	NOUN
cana-3949	166	6	)	)	PUNCT
cana-3949	167	1	[	[	X
cana-3949	167	2	1	1	NUM
cana-3949	167	3	−	−	PROPN
cana-3949	167	4	𝑠𝑄(𝑠	𝑠𝑄(𝑠	PROPN
cana-3949	167	5	)	)	PUNCT
cana-3949	167	6	+	+	CCONJ
cana-3949	167	7	𝜆𝑄(𝑠)[𝑧	𝜆𝑄(𝑠)[𝑧	VERB
cana-3949	167	8	−	−	PROPN
cana-3949	167	9	1	1	NUM
cana-3949	167	10	]	]	X
cana-3949	167	11	]	]	PUNCT
cana-3949	167	12	)	)	PUNCT
cana-3949	168	1	[	[	X
cana-3949	168	2	1	1	NUM
cana-3949	168	3	−	−	PROPN
cana-3949	168	4	𝐵1(𝑠	𝐵1(𝑠	PROPN
cana-3949	169	1	+	+	CCONJ
cana-3949	169	2	𝜆	𝜆	ADV
cana-3949	169	3	−	−	NOUN
cana-3949	169	4	𝜆𝑧)𝐵2(𝑠	𝜆𝑧)𝐵2(𝑠	NUM
cana-3949	170	1	+	+	CCONJ
cana-3949	170	2	𝜆	𝜆	DET
cana-3949	170	3	−	−	PROPN
cana-3949	170	4	𝜆𝑧	𝜆𝑧	NOUN
cana-3949	170	5	)	)	PUNCT
cana-3949	170	6	]	]	PUNCT
cana-3949	171	1	(	(	PUNCT
cana-3949	171	2	49	49	NUM
cana-3949	171	3	)	)	PUNCT
cana-3949	171	4	𝐷(𝑧	𝐷(𝑧	PROPN
cana-3949	171	5	,	,	PUNCT
cana-3949	171	6	𝑠	𝑠	NOUN
cana-3949	171	7	)	)	PUNCT
cana-3949	171	8	=	=	SYM
cana-3949	172	1	(	(	PUNCT
cana-3949	172	2	𝑠	𝑠	PROPN
cana-3949	172	3	+	+	CCONJ
cana-3949	172	4	𝜆	𝜆	DET
cana-3949	172	5	−	−	PROPN
cana-3949	172	6	𝜆𝑧	𝜆𝑧	NOUN
cana-3949	172	7	)	)	PUNCT
cana-3949	173	1	[	[	X
cana-3949	173	2	(	(	PUNCT
cana-3949	173	3	𝑠	𝑠	X
cana-3949	173	4	+	+	NUM
cana-3949	173	5	1)𝑧	1)𝑧	NUM
cana-3949	173	6	[	[	PUNCT
cana-3949	173	7	𝑧	𝑧	NOUN
cana-3949	173	8	−	−	PROPN
cana-3949	173	9	𝐵1(𝑠	𝐵1(𝑠	PROPN
cana-3949	174	1	+	+	CCONJ
cana-3949	174	2	𝜆	𝜆	ADV
cana-3949	174	3	−	−	NOUN
cana-3949	174	4	𝜆𝑧)𝐵2(𝑠	𝜆𝑧)𝐵2(𝑠	NUM
cana-3949	175	1	+	+	CCONJ
cana-3949	175	2	𝜆	𝜆	DET
cana-3949	175	3	−	−	PROPN
cana-3949	175	4	𝜆𝑧	𝜆𝑧	NOUN
cana-3949	175	5	)	)	PUNCT
cana-3949	176	1	+	+	NOUN
cana-3949	176	2	𝐵1(𝑠	𝐵1(𝑠	PROPN
cana-3949	177	1	+	+	CCONJ
cana-3949	177	2	𝜆	𝜆	ADV
cana-3949	177	3	−	−	NOUN
cana-3949	177	4	𝜆𝑧)𝐵2(𝑠	𝜆𝑧)𝐵2(𝑠	NUM
cana-3949	178	1	+	+	CCONJ
cana-3949	178	2	𝜆	𝜆	PRON
cana-3949	178	3	−	−	X
cana-3949	178	4	𝜆𝑧)[1	𝜆𝑧)[1	PROPN
cana-3949	178	5	−	−	PROPN
cana-3949	178	6	𝑒	𝑒	PROPN
cana-3949	178	7	−𝜆𝑑(1−𝑧	−𝜆𝑑(1−𝑧	PROPN
cana-3949	178	8	)	)	PUNCT
cana-3949	178	9	]	]	PUNCT
cana-3949	179	1	]	]	X
cana-3949	179	2	]	]	X
cana-3949	179	3	(	(	PUNCT
cana-3949	179	4	50	50	NUM
cana-3949	179	5	)	)	PUNCT
cana-3949	179	6	if	if	SCONJ
cana-3949	179	7	we	we	PRON
cana-3949	179	8	let	let	VERB
cana-3949	179	9	𝑧	𝑧	VERB
cana-3949	179	10	=	=	SYM
cana-3949	179	11	1	1	NUM
cana-3949	179	12	in	in	ADP
cana-3949	179	13	equation	equation	NOUN
cana-3949	179	14	(	(	PUNCT
cana-3949	179	15	48	48	NUM
cana-3949	179	16	)	)	PUNCT
cana-3949	179	17	,	,	PUNCT
cana-3949	179	18	we	we	PRON
cana-3949	179	19	can	can	AUX
cana-3949	179	20	easily	easily	ADV
cana-3949	179	21	verify	verify	VERB
cana-3949	179	22	that	that	SCONJ
cana-3949	179	23	𝑄(𝑠	𝑄(𝑠	NUM
cana-3949	179	24	)	)	PUNCT
cana-3949	179	25	+	+	CCONJ
cana-3949	179	26	�	�	NOUN
cana-3949	179	27	̅	̅	NOUN
cana-3949	179	28	�	�	NOUN
cana-3949	179	29	(𝑧	(𝑧	NOUN
cana-3949	179	30	,	,	PUNCT
cana-3949	179	31	𝑠	𝑠	PROPN
cana-3949	179	32	)	)	PUNCT
cana-3949	179	33	+	+	CCONJ
cana-3949	179	34	𝑃(𝑧	𝑃(𝑧	X
cana-3949	179	35	,	,	PUNCT
cana-3949	179	36	𝑠	𝑠	NOUN
cana-3949	179	37	)	)	PUNCT
cana-3949	179	38	=	=	SYM
cana-3949	179	39	1	1	NUM
cana-3949	179	40	𝑠	𝑠	INTJ
cana-3949	179	41	,	,	PUNCT
cana-3949	179	42	(	(	PUNCT
cana-3949	179	43	51	51	NUM
cana-3949	179	44	)	)	PUNCT
cana-3949	179	45	as	as	SCONJ
cana-3949	179	46	it	it	PRON
cana-3949	179	47	should	should	AUX
cana-3949	179	48	be	be	AUX
cana-3949	179	49	.	.	PUNCT
cana-3949	180	1	thus	thus	ADV
cana-3949	180	2	𝑃	𝑃	VERB
cana-3949	180	3	(	(	PUNCT
cana-3949	180	4	1	1	NUM
cana-3949	180	5	)	)	PUNCT
cana-3949	180	6	(	(	PUNCT
cana-3949	180	7	𝑧	𝑧	PROPN
cana-3949	180	8	,	,	PUNCT
cana-3949	180	9	𝑠	𝑠	NOUN
cana-3949	180	10	)	)	PUNCT
cana-3949	180	11	,	,	PUNCT
cana-3949	180	12	𝑃	𝑃	PROPN
cana-3949	180	13	(	(	PUNCT
cana-3949	180	14	2	2	NUM
cana-3949	180	15	)	)	PUNCT
cana-3949	180	16	(	(	PUNCT
cana-3949	180	17	𝑧	𝑧	PROPN
cana-3949	180	18	,	,	PUNCT
cana-3949	180	19	𝑠	𝑠	NOUN
cana-3949	180	20	)	)	PUNCT
cana-3949	180	21	and	and	CCONJ
cana-3949	180	22	�	�	PROPN
cana-3949	180	23	̅	̅	NOUN
cana-3949	180	24	�	�	NOUN
cana-3949	180	25	(𝑧	(𝑧	NOUN
cana-3949	180	26	,	,	PUNCT
cana-3949	180	27	𝑠	𝑠	PROPN
cana-3949	180	28	)	)	PUNCT
cana-3949	180	29	,	,	PUNCT
cana-3949	180	30	are	be	AUX
cana-3949	180	31	completely	completely	ADV
cana-3949	180	32	determined	determine	VERB
cana-3949	180	33	from	from	ADP
cana-3949	180	34	equations	equation	NOUN
cana-3949	180	35	(	(	PUNCT
cana-3949	180	36	43	43	NUM
cana-3949	180	37	)	)	PUNCT
cana-3949	180	38	,	,	PUNCT
cana-3949	180	39	(	(	PUNCT
cana-3949	180	40	44	44	NUM
cana-3949	180	41	)	)	PUNCT
cana-3949	180	42	and	and	CCONJ
cana-3949	180	43	(	(	PUNCT
cana-3949	180	44	46	46	NUM
cana-3949	180	45	)	)	PUNCT
cana-3949	180	46	respectively	respectively	ADV
cana-3949	180	47	.	.	PUNCT
cana-3949	181	1	5	5	X
cana-3949	181	2	.	.	PUNCT
cana-3949	181	3	the	the	DET
cana-3949	181	4	steady	steady	ADJ
cana-3949	181	5	state	state	NOUN
cana-3949	181	6	results	result	NOUN
cana-3949	181	7	in	in	ADP
cana-3949	181	8	this	this	DET
cana-3949	181	9	section	section	NOUN
cana-3949	181	10	,	,	PUNCT
cana-3949	181	11	we	we	PRON
cana-3949	181	12	shall	shall	AUX
cana-3949	181	13	derive	derive	VERB
cana-3949	181	14	the	the	DET
cana-3949	181	15	steady	steady	ADJ
cana-3949	181	16	state	state	NOUN
cana-3949	181	17	probability	probability	NOUN
cana-3949	181	18	distribution	distribution	NOUN
cana-3949	181	19	for	for	ADP
cana-3949	181	20	our	our	PRON
cana-3949	181	21	queueing	queue	VERB
cana-3949	181	22	model	model	NOUN
cana-3949	181	23	.	.	PUNCT
cana-3949	182	1	to	to	PART
cana-3949	182	2	define	define	VERB
cana-3949	182	3	the	the	DET
cana-3949	182	4	steady	steady	ADJ
cana-3949	182	5	state	state	NOUN
cana-3949	182	6	probabilities	probability	NOUN
cana-3949	182	7	,	,	PUNCT
cana-3949	182	8	we	we	PRON
cana-3949	182	9	suppress	suppress	VERB
cana-3949	182	10	the	the	DET
cana-3949	182	11	argument	argument	NOUN
cana-3949	182	12	𝑡	𝑡	ADP
cana-3949	182	13	wherever	wherever	SCONJ
cana-3949	182	14	it	it	PRON
cana-3949	182	15	appears	appear	VERB
cana-3949	182	16	in	in	ADP
cana-3949	182	17	the	the	DET
cana-3949	182	18	timedependent	timedependent	NOUN
cana-3949	182	19	analysis	analysis	NOUN
cana-3949	182	20	.	.	PUNCT
cana-3949	183	1	this	this	PRON
cana-3949	183	2	can	can	AUX
cana-3949	183	3	be	be	AUX
cana-3949	183	4	obtained	obtain	VERB
cana-3949	183	5	by	by	ADP
cana-3949	183	6	applying	apply	VERB
cana-3949	183	7	the	the	DET
cana-3949	183	8	well	well	ADV
cana-3949	183	9	-	-	PUNCT
cana-3949	183	10	known	know	VERB
cana-3949	183	11	tauberian	tauberian	ADJ
cana-3949	183	12	property	property	NOUN
cana-3949	183	13	,	,	PUNCT
cana-3949	183	14	lim	lim	PROPN
cana-3949	183	15	𝑠→0	𝑠→0	PROPN
cana-3949	184	1	𝑠	𝑠	PROPN
cana-3949	184	2	𝑓	𝑓	PROPN
cana-3949	184	3	(	(	PUNCT
cana-3949	184	4	𝑠	𝑠	NOUN
cana-3949	184	5	)	)	PUNCT
cana-3949	184	6	=	=	PROPN
cana-3949	184	7	lim	lim	PROPN
cana-3949	184	8	𝑡→∞	𝑡→∞	NUM
cana-3949	184	9	𝑓(𝑡	𝑓(𝑡	PROPN
cana-3949	184	10	)	)	PUNCT
cana-3949	184	11	,	,	PUNCT
cana-3949	184	12	(	(	PUNCT
cana-3949	184	13	52	52	NUM
cana-3949	184	14	)	)	PUNCT
cana-3949	184	15	in	in	ADP
cana-3949	184	16	order	order	NOUN
cana-3949	184	17	to	to	PART
cana-3949	184	18	determine	determine	VERB
cana-3949	184	19	𝑃	𝑃	PROPN
cana-3949	184	20	(	(	PUNCT
cana-3949	184	21	1	1	NUM
cana-3949	184	22	)	)	PUNCT
cana-3949	184	23	(	(	PUNCT
cana-3949	184	24	𝑧	𝑧	PROPN
cana-3949	184	25	,	,	PUNCT
cana-3949	184	26	𝑠	𝑠	NOUN
cana-3949	184	27	)	)	PUNCT
cana-3949	184	28	,	,	PUNCT
cana-3949	184	29	𝑃	𝑃	PROPN
cana-3949	184	30	(	(	PUNCT
cana-3949	184	31	2	2	NUM
cana-3949	184	32	)	)	PUNCT
cana-3949	184	33	(	(	PUNCT
cana-3949	184	34	𝑧	𝑧	PROPN
cana-3949	184	35	,	,	PUNCT
cana-3949	184	36	𝑠	𝑠	PROPN
cana-3949	184	37	)	)	PUNCT
cana-3949	184	38	and	and	CCONJ
cana-3949	184	39	𝑉(𝑧	𝑉(𝑧	PROPN
cana-3949	184	40	,	,	PUNCT
cana-3949	184	41	𝑠	𝑠	NOUN
cana-3949	184	42	)	)	PUNCT
cana-3949	184	43	completely	completely	ADV
cana-3949	184	44	,	,	PUNCT
cana-3949	184	45	we	we	PRON
cana-3949	184	46	have	have	VERB
cana-3949	184	47	yet	yet	ADV
cana-3949	184	48	to	to	PART
cana-3949	184	49	determine	determine	VERB
cana-3949	184	50	the	the	DET
cana-3949	184	51	unknown	unknown	ADJ
cana-3949	184	52	𝑄.	𝑄.	NOUN
cana-3949	184	53	for	for	ADP
cana-3949	184	54	that	that	DET
cana-3949	184	55	purpose	purpose	NOUN
cana-3949	184	56	,	,	PUNCT
cana-3949	184	57	we	we	PRON
cana-3949	184	58	shall	shall	AUX
cana-3949	184	59	use	use	VERB
cana-3949	184	60	the	the	DET
cana-3949	184	61	normalizing	normalizing	ADJ
cana-3949	184	62	condition	condition	NOUN
cana-3949	184	63	.	.	PUNCT
cana-3949	185	1	𝑃(1)(1	𝑃(1)(1	NOUN
cana-3949	185	2	)	)	PUNCT
cana-3949	186	1	+	+	NUM
cana-3949	186	2	𝑃(2)(1	𝑃(2)(1	NOUN
cana-3949	186	3	)	)	PUNCT
cana-3949	187	1	+	+	CCONJ
cana-3949	187	2	𝑉(1	𝑉(1	X
cana-3949	187	3	)	)	PUNCT
cana-3949	187	4	=	=	SYM
cana-3949	187	5	1	1	X
cana-3949	187	6	.	.	PUNCT
cana-3949	187	7	(	(	PUNCT
cana-3949	187	8	53	53	NUM
cana-3949	187	9	)	)	PUNCT
cana-3949	187	10	thus	thus	ADV
cana-3949	187	11	,	,	PUNCT
cana-3949	187	12	multiplying	multiply	VERB
cana-3949	187	13	both	both	DET
cana-3949	187	14	sides	side	NOUN
cana-3949	187	15	of	of	ADP
cana-3949	187	16	equations	equation	NOUN
cana-3949	187	17	(	(	PUNCT
cana-3949	187	18	43	43	NUM
cana-3949	187	19	)	)	PUNCT
cana-3949	187	20	,	,	PUNCT
cana-3949	187	21	(	(	PUNCT
cana-3949	187	22	44	44	NUM
cana-3949	187	23	)	)	PUNCT
cana-3949	187	24	and	and	CCONJ
cana-3949	187	25	(	(	PUNCT
cana-3949	187	26	46	46	NUM
cana-3949	187	27	)	)	PUNCT
cana-3949	187	28	by	by	ADP
cana-3949	187	29	𝑠	𝑠	PROPN
cana-3949	187	30	,	,	PUNCT
cana-3949	187	31	taking	take	VERB
cana-3949	187	32	limit	limit	NOUN
cana-3949	187	33	as	as	ADP
cana-3949	187	34	𝑠	𝑠	PROPN
cana-3949	187	35	→	→	SYM
cana-3949	187	36	0	0	NUM
cana-3949	187	37	,	,	PUNCT
cana-3949	187	38	applying	apply	VERB
cana-3949	187	39	property	property	NOUN
cana-3949	187	40	(	(	PUNCT
cana-3949	187	41	51	51	NUM
cana-3949	187	42	)	)	PUNCT
cana-3949	187	43	and	and	CCONJ
cana-3949	187	44	simplifying	simplify	VERB
cana-3949	187	45	we	we	PRON
cana-3949	187	46	have	have	VERB
cana-3949	187	47	𝑃(1)(𝑧	𝑃(1)(𝑧	NOUN
cana-3949	187	48	)	)	PUNCT
cana-3949	187	49	=	=	PUNCT
cana-3949	187	50	[	[	PUNCT
cana-3949	187	51	𝑉(𝑧)𝑒−𝜆𝑑(1−𝑧)+𝜆𝑄(𝑧−1	𝑉(𝑧)𝑒−𝜆𝑑(1−𝑧)+𝜆𝑄(𝑧−1	NOUN
cana-3949	187	52	)	)	PUNCT
cana-3949	187	53	𝑧	𝑧	NOUN
cana-3949	187	54	]	]	PUNCT
cana-3949	187	55	[	[	PUNCT
cana-3949	187	56	1−𝐵1(𝜆−𝜆𝑧	1−𝐵1(𝜆−𝜆𝑧	NUM
cana-3949	187	57	)	)	PUNCT
cana-3949	187	58	(	(	PUNCT
cana-3949	187	59	𝜆−𝜆𝑧	𝜆−𝜆𝑧	NOUN
cana-3949	187	60	)	)	PUNCT
cana-3949	187	61	]	]	PUNCT
cana-3949	187	62	,	,	PUNCT
cana-3949	187	63	(	(	PUNCT
cana-3949	187	64	54	54	NUM
cana-3949	187	65	)	)	PUNCT
cana-3949	187	66	communications	communication	NOUN
cana-3949	187	67	on	on	ADP
cana-3949	187	68	applied	apply	VERB
cana-3949	187	69	nonlinear	nonlinear	ADJ
cana-3949	187	70	analysis	analysis	NOUN
cana-3949	187	71	issn	issn	NOUN
cana-3949	187	72	:	:	PUNCT
cana-3949	187	73	1074	1074	NUM
cana-3949	187	74	-	-	PUNCT
cana-3949	187	75	133x	133x	NUM
cana-3949	187	76	vol	vol	NOUN
cana-3949	187	77	32	32	NUM
cana-3949	187	78	no	no	NOUN
cana-3949	187	79	.	.	PUNCT
cana-3949	188	1	9s	9s	NUM
cana-3949	188	2	(	(	PUNCT
cana-3949	188	3	2025	2025	NUM
cana-3949	188	4	)	)	PUNCT
cana-3949	188	5	384	384	NUM
cana-3949	188	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3949	188	7	𝑃(2)(𝑧	𝑃(2)(𝑧	PROPN
cana-3949	188	8	)	)	PUNCT
cana-3949	188	9	=	=	PROPN
cana-3949	188	10	[	[	PUNCT
cana-3949	188	11	𝑉(𝑧)𝑒−𝜆𝑑(1−𝑧)+𝜆𝑄(𝑧−1	𝑉(𝑧)𝑒−𝜆𝑑(1−𝑧)+𝜆𝑄(𝑧−1	NOUN
cana-3949	188	12	)	)	PUNCT
cana-3949	188	13	𝑧	𝑧	X
cana-3949	188	14	]	]	X
cana-3949	188	15	𝐵1(𝜆	𝐵1(𝜆	NUM
cana-3949	188	16	−	−	NUM
cana-3949	189	1	𝜆𝑧	𝜆𝑧	NOUN
cana-3949	189	2	)	)	PUNCT
cana-3949	189	3	[	[	PUNCT
cana-3949	189	4	1−𝐵2(𝜆−𝜆𝑧	1−𝐵2(𝜆−𝜆𝑧	NUM
cana-3949	189	5	)	)	PUNCT
cana-3949	189	6	(	(	PUNCT
cana-3949	189	7	𝜆−𝜆𝑧	𝜆−𝜆𝑧	NOUN
cana-3949	189	8	)	)	PUNCT
cana-3949	189	9	]	]	PUNCT
cana-3949	189	10	,	,	PUNCT
cana-3949	189	11	(	(	PUNCT
cana-3949	189	12	55	55	NUM
cana-3949	189	13	)	)	PUNCT
cana-3949	189	14	𝑉(𝑧	𝑉(𝑧	X
cana-3949	189	15	)	)	PUNCT
cana-3949	189	16	=	=	SYM
cana-3949	189	17	𝐵1(𝜆−𝜆𝑧)𝐵2(𝜆−𝜆𝑧)𝑄(𝑧−1	𝐵1(𝜆−𝜆𝑧)𝐵2(𝜆−𝜆𝑧)𝑄(𝑧−1	X
cana-3949	189	18	)	)	PUNCT
cana-3949	189	19	𝑧−𝐵1(𝜆−𝜆𝑧)𝐵2(𝜆−𝜆𝑧)+𝐵1(𝜆−𝜆𝑧)𝐵2(𝜆−𝜆𝑧)[1−𝑒	𝑧−𝐵1(𝜆−𝜆𝑧)𝐵2(𝜆−𝜆𝑧)+𝐵1(𝜆−𝜆𝑧)𝐵2(𝜆−𝜆𝑧)[1−𝑒	CCONJ
cana-3949	189	20	−𝜆𝑑(1−𝑧	−𝜆𝑑(1−𝑧	NOUN
cana-3949	189	21	)	)	PUNCT
cana-3949	189	22	]	]	PUNCT
cana-3949	190	1	(	(	PUNCT
cana-3949	190	2	56	56	NUM
cana-3949	190	3	)	)	PUNCT
cana-3949	190	4	where	where	SCONJ
cana-3949	190	5	𝑃(𝑧	𝑃(𝑧	X
cana-3949	190	6	)	)	PUNCT
cana-3949	190	7	=	=	SYM
cana-3949	190	8	𝑃(1)(𝑧	𝑃(1)(𝑧	NOUN
cana-3949	190	9	)	)	PUNCT
cana-3949	190	10	+	+	CCONJ
cana-3949	190	11	𝑃(2)(𝑧	𝑃(2)(𝑧	PROPN
cana-3949	190	12	)	)	PUNCT
cana-3949	190	13	(	(	PUNCT
cana-3949	190	14	57	57	NUM
cana-3949	190	15	)	)	PUNCT
cana-3949	190	16	=	=	NOUN
cana-3949	190	17	[	[	PUNCT
cana-3949	190	18	𝑉(𝑧)𝑒−𝜆𝑑(1−𝑧)+𝜆𝑄(𝑧−1	𝑉(𝑧)𝑒−𝜆𝑑(1−𝑧)+𝜆𝑄(𝑧−1	NOUN
cana-3949	190	19	)	)	PUNCT
cana-3949	190	20	𝑧−𝐵1(𝜆−𝜆𝑧)𝐵2(𝜆−𝜆𝑧	𝑧−𝐵1(𝜆−𝜆𝑧)𝐵2(𝜆−𝜆𝑧	PROPN
cana-3949	190	21	)	)	PUNCT
cana-3949	190	22	]	]	PUNCT
cana-3949	191	1	[	[	PUNCT
cana-3949	191	2	1−𝐵1(𝜆−𝜆𝑧)𝐵2(𝜆−𝜆𝑧	1−𝐵1(𝜆−𝜆𝑧)𝐵2(𝜆−𝜆𝑧	NUM
cana-3949	191	3	)	)	PUNCT
cana-3949	191	4	(	(	PUNCT
cana-3949	191	5	𝜆−𝜆𝑧	𝜆−𝜆𝑧	NOUN
cana-3949	191	6	)	)	PUNCT
cana-3949	191	7	]	]	PUNCT
cana-3949	192	1	(	(	PUNCT
cana-3949	192	2	58	58	NUM
cana-3949	192	3	)	)	PUNCT
cana-3949	192	4	now	now	ADV
cana-3949	192	5	using	use	VERB
cana-3949	192	6	equation	equation	NOUN
cana-3949	192	7	(	(	PUNCT
cana-3949	192	8	56	56	NUM
cana-3949	192	9	)	)	PUNCT
cana-3949	192	10	into	into	ADP
cana-3949	192	11	equation	equation	NOUN
cana-3949	192	12	(	(	PUNCT
cana-3949	192	13	58	58	NUM
cana-3949	192	14	)	)	PUNCT
cana-3949	192	15	,	,	PUNCT
cana-3949	192	16	we	we	PRON
cana-3949	192	17	get	get	VERB
cana-3949	192	18	𝑃(𝑧	𝑃(𝑧	PRON
cana-3949	192	19	)	)	PUNCT
cana-3949	192	20	=	=	SYM
cana-3949	193	1	[	[	PUNCT
cana-3949	193	2	{	{	PUNCT
cana-3949	193	3	𝐵1(𝜆−𝜆𝑧)𝐵2(𝜆−𝜆𝑧)−1}𝑄	𝐵1(𝜆−𝜆𝑧)𝐵2(𝜆−𝜆𝑧)−1}𝑄	X
cana-3949	193	4	𝑧−𝐵1(𝜆−𝜆𝑧)𝐵2(𝜆−𝜆𝑧)+𝐵1(𝜆−𝜆𝑧)𝐵2(𝜆−𝜆𝑧)[1−𝑒	𝑧−𝐵1(𝜆−𝜆𝑧)𝐵2(𝜆−𝜆𝑧)+𝐵1(𝜆−𝜆𝑧)𝐵2(𝜆−𝜆𝑧)[1−𝑒	NUM
cana-3949	193	5	−𝜆𝑑(1−𝑧	−𝜆𝑑(1−𝑧	NOUN
cana-3949	193	6	)	)	PUNCT
cana-3949	193	7	]	]	PUNCT
cana-3949	193	8	]	]	PUNCT
cana-3949	193	9	(	(	PUNCT
cana-3949	193	10	59	59	NUM
cana-3949	193	11	)	)	PUNCT
cana-3949	193	12	we	we	PRON
cana-3949	193	13	see	see	VERB
cana-3949	193	14	that	that	PRON
cana-3949	193	15	for	for	ADP
cana-3949	193	16	𝑧	𝑧	NOUN
cana-3949	193	17	=	=	SYM
cana-3949	193	18	1	1	NUM
cana-3949	193	19	,	,	PUNCT
cana-3949	193	20	the	the	DET
cana-3949	193	21	right	right	ADJ
cana-3949	193	22	side	side	NOUN
cana-3949	193	23	of	of	ADP
cana-3949	193	24	both	both	DET
cana-3949	193	25	equations	equation	NOUN
cana-3949	193	26	(	(	PUNCT
cana-3949	193	27	54	54	NUM
cana-3949	193	28	)	)	PUNCT
cana-3949	193	29	and	and	CCONJ
cana-3949	193	30	(	(	PUNCT
cana-3949	193	31	55	55	NUM
cana-3949	193	32	)	)	PUNCT
cana-3949	193	33	are	be	AUX
cana-3949	193	34	indeterminate	indeterminate	ADJ
cana-3949	193	35	of	of	ADP
cana-3949	193	36	the	the	DET
cana-3949	193	37	form	form	NOUN
cana-3949	193	38	0	0	NUM
cana-3949	193	39	0	0	NUM
cana-3949	193	40	.	.	PUNCT
cana-3949	194	1	therefore	therefore	ADV
cana-3949	194	2	applying	apply	VERB
cana-3949	194	3	lhopital	lhopital	PROPN
cana-3949	194	4	’s	’s	PART
cana-3949	194	5	rule	rule	NOUN
cana-3949	194	6	,	,	PUNCT
cana-3949	194	7	we	we	PRON
cana-3949	194	8	obtain	obtain	VERB
cana-3949	194	9	𝑉(1	𝑉(1	NOUN
cana-3949	194	10	)	)	PUNCT
cana-3949	194	11	=	=	SYM
cana-3949	195	1	𝜆𝑄𝜇1𝜇2	𝜆𝑄𝜇1𝜇2	PROPN
cana-3949	195	2	𝜇1𝜇2−𝜆(𝜇1+𝜇2)−𝜆𝜇1𝜇2𝑑	𝜇1𝜇2−𝜆(𝜇1+𝜇2)−𝜆𝜇1𝜇2𝑑	PROPN
cana-3949	195	3	,	,	PUNCT
cana-3949	195	4	(	(	PUNCT
cana-3949	195	5	60	60	NUM
cana-3949	195	6	)	)	PUNCT
cana-3949	195	7	𝑃(1	𝑃(1	NUM
cana-3949	195	8	)	)	PUNCT
cana-3949	195	9	=	=	SYM
cana-3949	195	10	𝜆(𝜇1+𝜇2)𝑄	𝜆(𝜇1+𝜇2)𝑄	ADJ
cana-3949	195	11	𝑞𝜇1𝜇2−𝜆(𝜇1+𝜇2)−𝜆𝜇1𝜇2𝑑	𝑞𝜇1𝜇2−𝜆(𝜇1+𝜇2)−𝜆𝜇1𝜇2𝑑	NOUN
cana-3949	195	12	.	.	PUNCT
cana-3949	196	1	(	(	PUNCT
cana-3949	196	2	61	61	NUM
cana-3949	196	3	)	)	PUNCT
cana-3949	196	4	wherein	wherein	SCONJ
cana-3949	196	5	we	we	PRON
cana-3949	196	6	have	have	AUX
cana-3949	196	7	used	use	VERB
cana-3949	196	8	facts	fact	NOUN
cana-3949	196	9	that	that	SCONJ
cana-3949	196	10	𝐵1(0	𝐵1(0	PRON
cana-3949	196	11	)	)	PUNCT
cana-3949	196	12	=	=	SYM
cana-3949	196	13	𝐵2(0	𝐵2(0	NOUN
cana-3949	196	14	)	)	PUNCT
cana-3949	196	15	=	=	SYM
cana-3949	197	1	1,−𝐵1	1,−𝐵1	NUM
cana-3949	197	2	′	′	NUM
cana-3949	197	3	(	(	PUNCT
cana-3949	197	4	0	0	NUM
cana-3949	197	5	)	)	PUNCT
cana-3949	197	6	=	=	SYM
cana-3949	197	7	1	1	NUM
cana-3949	197	8	𝜇1	𝜇1	NOUN
cana-3949	197	9	and	and	CCONJ
cana-3949	197	10	−𝐵2	−𝐵2	PROPN
cana-3949	197	11	′	′	NUM
cana-3949	197	12	(	(	PUNCT
cana-3949	197	13	0	0	NUM
cana-3949	197	14	)	)	PUNCT
cana-3949	197	15	=	=	SYM
cana-3949	197	16	1	1	NUM
cana-3949	197	17	𝜇2	𝜇2	NOUN
cana-3949	197	18	.	.	PUNCT
cana-3949	198	1	now	now	ADV
cana-3949	198	2	to	to	PART
cana-3949	198	3	determine	determine	VERB
cana-3949	198	4	the	the	DET
cana-3949	198	5	only	only	ADJ
cana-3949	198	6	unknown	unknown	ADJ
cana-3949	198	7	𝑄.	𝑄.	NOUN
cana-3949	198	8	we	we	PRON
cana-3949	198	9	see	see	VERB
cana-3949	198	10	(	(	PUNCT
cana-3949	198	11	60	60	NUM
cana-3949	198	12	)	)	PUNCT
cana-3949	198	13	and	and	CCONJ
cana-3949	198	14	(	(	PUNCT
cana-3949	198	15	61	61	NUM
cana-3949	198	16	)	)	PUNCT
cana-3949	198	17	in	in	ADP
cana-3949	198	18	the	the	DET
cana-3949	198	19	normalizing	normalizing	ADJ
cana-3949	198	20	condition	condition	NOUN
cana-3949	198	21	𝑄	𝑄	PRON
cana-3949	198	22	+	+	CCONJ
cana-3949	198	23	𝑃(1	𝑃(1	NUM
cana-3949	198	24	)	)	PUNCT
cana-3949	198	25	+	+	CCONJ
cana-3949	198	26	𝑉(1	𝑉(1	X
cana-3949	198	27	)	)	PUNCT
cana-3949	198	28	=	=	SYM
cana-3949	198	29	1	1	NUM
cana-3949	198	30	and	and	CCONJ
cana-3949	198	31	have	have	VERB
cana-3949	198	32	𝑄	𝑄	PROPN
cana-3949	198	33	=	=	SYM
cana-3949	198	34	𝜇1𝜇2−𝜆(𝜇1+𝜇2)−𝜆𝜇1𝜇2𝑑	𝜇1𝜇2−𝜆(𝜇1+𝜇2)−𝜆𝜇1𝜇2𝑑	PROPN
cana-3949	198	35	𝜇1𝜇2(1−𝜆𝑑)+𝜆𝜇1𝜇2	𝜇1𝜇2(1−𝜆𝑑)+𝜆𝜇1𝜇2	PROPN
cana-3949	198	36	(	(	PUNCT
cana-3949	198	37	62	62	NUM
cana-3949	198	38	)	)	PUNCT
cana-3949	198	39	=	=	SYM
cana-3949	199	1	1	1	NUM
cana-3949	199	2	−	−	NUM
cana-3949	199	3	2𝜆𝜇1𝜇2	2𝜆𝜇1𝜇2	NUM
cana-3949	199	4	𝜇1𝜇2(1−𝜆𝑑)+𝜆𝜇1𝜇2	𝜇1𝜇2(1−𝜆𝑑)+𝜆𝜇1𝜇2	PROPN
cana-3949	199	5	(	(	PUNCT
cana-3949	199	6	63	63	NUM
cana-3949	199	7	)	)	PUNCT
cana-3949	199	8	where	where	SCONJ
cana-3949	199	9	𝜆	𝜆	DET
cana-3949	199	10	<	<	X
cana-3949	199	11	𝜇1𝜇2[1	𝜇1𝜇2[1	NOUN
cana-3949	199	12	−	−	NOUN
cana-3949	199	13	𝜆𝑑	𝜆𝑑	NOUN
cana-3949	199	14	]	]	PUNCT
cana-3949	199	15	.	.	PUNCT
cana-3949	200	1	equation	equation	NOUN
cana-3949	200	2	(	(	PUNCT
cana-3949	200	3	62	62	NUM
cana-3949	200	4	)	)	PUNCT
cana-3949	200	5	gives	give	VERB
cana-3949	200	6	the	the	DET
cana-3949	200	7	steady	steady	ADJ
cana-3949	200	8	state	state	NOUN
cana-3949	200	9	probability	probability	NOUN
cana-3949	200	10	that	that	SCONJ
cana-3949	200	11	there	there	PRON
cana-3949	200	12	is	be	VERB
cana-3949	200	13	no	no	DET
cana-3949	200	14	customer	customer	NOUN
cana-3949	200	15	in	in	ADP
cana-3949	200	16	the	the	DET
cana-3949	200	17	system	system	NOUN
cana-3949	200	18	and	and	CCONJ
cana-3949	200	19	the	the	DET
cana-3949	200	20	server	server	NOUN
cana-3949	200	21	is	be	AUX
cana-3949	200	22	idle	idle	ADJ
cana-3949	200	23	.	.	PUNCT
cana-3949	201	1	also	also	ADV
cana-3949	201	2	,	,	PUNCT
cana-3949	201	3	from	from	ADP
cana-3949	201	4	equation	equation	NOUN
cana-3949	201	5	(	(	PUNCT
cana-3949	201	6	63	63	NUM
cana-3949	201	7	)	)	PUNCT
cana-3949	201	8	,	,	PUNCT
cana-3949	201	9	we	we	PRON
cana-3949	201	10	obtain	obtain	VERB
cana-3949	201	11	𝜌	𝜌	ADP
cana-3949	201	12	,	,	PUNCT
cana-3949	201	13	the	the	DET
cana-3949	201	14	utilization	utilization	NOUN
cana-3949	201	15	factor	factor	NOUN
cana-3949	201	16	of	of	ADP
cana-3949	201	17	the	the	DET
cana-3949	201	18	system	system	NOUN
cana-3949	201	19	as	as	ADP
cana-3949	201	20	𝜌	𝜌	ADP
cana-3949	201	21	=	=	SYM
cana-3949	201	22	1	1	NUM
cana-3949	201	23	−	−	PROPN
cana-3949	201	24	𝑄	𝑄	PROPN
cana-3949	201	25	=	=	SYM
cana-3949	201	26	2𝜆𝜇1𝜇2	2𝜆𝜇1𝜇2	NUM
cana-3949	201	27	𝜇1𝜇2(1−𝜆𝑑)+𝜆𝜇1𝜇2	𝜇1𝜇2(1−𝜆𝑑)+𝜆𝜇1𝜇2	PROPN
cana-3949	201	28	<	<	X
cana-3949	201	29	1	1	NUM
cana-3949	201	30	(	(	PUNCT
cana-3949	201	31	64	64	NUM
cana-3949	201	32	)	)	PUNCT
cana-3949	201	33	acknowledgement	acknowledgement	NOUN
cana-3949	201	34	the	the	DET
cana-3949	201	35	author	author	NOUN
cana-3949	201	36	thanks	thank	VERB
cana-3949	201	37	the	the	DET
cana-3949	201	38	management	management	NOUN
cana-3949	201	39	of	of	ADP
cana-3949	201	40	sri	sri	PROPN
cana-3949	201	41	sivasubramaniya	sivasubramaniya	PROPN
cana-3949	201	42	nadar	nadar	PROPN
cana-3949	201	43	college	college	PROPN
cana-3949	201	44	of	of	ADP
cana-3949	201	45	engineering	engineering	NOUN
cana-3949	201	46	for	for	ADP
cana-3949	201	47	providing	provide	VERB
cana-3949	201	48	the	the	DET
cana-3949	201	49	necessary	necessary	ADJ
cana-3949	201	50	requirements	requirement	NOUN
cana-3949	201	51	during	during	ADP
cana-3949	201	52	the	the	DET
cana-3949	201	53	preparation	preparation	NOUN
cana-3949	201	54	of	of	ADP
cana-3949	201	55	this	this	DET
cana-3949	201	56	paper	paper	NOUN
cana-3949	201	57	.	.	PUNCT
cana-3949	202	1	references	reference	NOUN
cana-3949	202	2	[	[	X
cana-3949	202	3	1	1	NUM
cana-3949	202	4	]	]	X
cana-3949	202	5	choudhury	choudhury	PROPN
cana-3949	202	6	,	,	PUNCT
cana-3949	202	7	g.	g.	PROPN
cana-3949	202	8	,	,	PUNCT
cana-3949	202	9	chandi	chandi	PROPN
cana-3949	202	10	ram	ram	PROPN
cana-3949	202	11	kalita	kalita	PROPN
cana-3949	202	12	.	.	PUNCT
cana-3949	203	1	(	(	PUNCT
cana-3949	203	2	2018	2018	NUM
cana-3949	203	3	)	)	PUNCT
cana-3949	203	4	,	,	PUNCT
cana-3949	203	5	an	an	DET
cana-3949	203	6	m	m	NOUN
cana-3949	203	7	/	/	SYM
cana-3949	203	8	g/1	g/1	NOUN
cana-3949	203	9	queue	queue	NOUN
cana-3949	203	10	with	with	ADP
cana-3949	203	11	two	two	NUM
cana-3949	203	12	types	type	NOUN
cana-3949	203	13	of	of	ADP
cana-3949	203	14	general	general	ADJ
cana-3949	203	15	heterogeneous	heterogeneous	ADJ
cana-3949	203	16	service	service	NOUN
cana-3949	203	17	and	and	CCONJ
cana-3949	203	18	optional	optional	ADJ
cana-3949	203	19	repeated	repeat	VERB
cana-3949	203	20	service	service	NOUN
cana-3949	203	21	subject	subject	NOUN
cana-3949	203	22	to	to	ADP
cana-3949	203	23	server	server	NOUN
cana-3949	203	24	’s	’s	PART
cana-3949	203	25	breakdown	breakdown	NOUN
cana-3949	203	26	and	and	CCONJ
cana-3949	203	27	delayed	delay	VERB
cana-3949	203	28	repair	repair	NOUN
cana-3949	203	29	,	,	PUNCT
cana-3949	203	30	quality	quality	NOUN
cana-3949	203	31	technology	technology	NOUN
cana-3949	203	32	and	and	CCONJ
cana-3949	203	33	quantitative	quantitative	ADJ
cana-3949	203	34	management	management	NOUN
cana-3949	203	35	,	,	PUNCT
cana-3949	203	36	15(5	15(5	NUM
cana-3949	203	37	)	)	PUNCT
cana-3949	203	38	,	,	PUNCT
cana-3949	203	39	662	662	NUM
cana-3949	203	40	–	–	PUNCT
cana-3949	203	41	654	654	NUM
cana-3949	203	42	.	.	PUNCT
cana-3949	204	1	[	[	X
cana-3949	204	2	2	2	NUM
cana-3949	204	3	]	]	X
cana-3949	204	4	cohen	cohen	PROPN
cana-3949	204	5	,	,	PUNCT
cana-3949	204	6	j	j	PROPN
cana-3949	204	7	,	,	PUNCT
cana-3949	204	8	w.	w.	PROPN
cana-3949	204	9	(	(	PUNCT
cana-3949	204	10	1982	1982	NUM
cana-3949	204	11	)	)	PUNCT
cana-3949	204	12	,	,	PUNCT
cana-3949	204	13	the	the	DET
cana-3949	204	14	single	single	ADJ
cana-3949	204	15	server	server	NOUN
cana-3949	204	16	queue	queue	NOUN
cana-3949	204	17	.	.	PUNCT
cana-3949	205	1	2	2	NUM
cana-3949	205	2	nd	nd	NUM
cana-3949	205	3	edn	edn	NOUN
cana-3949	205	4	.	.	PUNCT
cana-3949	206	1	north	north	NOUN
cana-3949	206	2	–	–	PUNCT
cana-3949	206	3	holland	holland	PROPN
cana-3949	206	4	,	,	PUNCT
cana-3949	206	5	amsterdam	amsterdam	PROPN
cana-3949	206	6	.	.	PUNCT
cana-3949	207	1	communications	communication	NOUN
cana-3949	207	2	on	on	ADP
cana-3949	207	3	applied	apply	VERB
cana-3949	207	4	nonlinear	nonlinear	ADJ
cana-3949	207	5	analysis	analysis	NOUN
cana-3949	207	6	issn	issn	NOUN
cana-3949	207	7	:	:	PUNCT
cana-3949	207	8	1074	1074	NUM
cana-3949	207	9	-	-	PUNCT
cana-3949	207	10	133x	133x	NUM
cana-3949	207	11	vol	vol	NOUN
cana-3949	207	12	32	32	NUM
cana-3949	207	13	no	no	NOUN
cana-3949	207	14	.	.	PUNCT
cana-3949	208	1	9s	9s	NUM
cana-3949	208	2	(	(	PUNCT
cana-3949	208	3	2025	2025	NUM
cana-3949	208	4	)	)	PUNCT
cana-3949	208	5	385	385	NUM
cana-3949	208	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3949	209	1	[	[	X
cana-3949	209	2	3	3	NUM
cana-3949	209	3	]	]	X
cana-3949	209	4	cohen	cohen	PROPN
cana-3949	209	5	,	,	PUNCT
cana-3949	209	6	j	j	PROPN
cana-3949	209	7	,	,	PUNCT
cana-3949	209	8	w.	w.	PROPN
cana-3949	209	9	(	(	PUNCT
cana-3949	209	10	1988	1988	NUM
cana-3949	209	11	)	)	PUNCT
cana-3949	209	12	,	,	PUNCT
cana-3949	209	13	queueing	queue	VERB
cana-3949	209	14	and	and	CCONJ
cana-3949	209	15	its	its	PRON
cana-3949	209	16	applications	application	NOUN
cana-3949	209	17	,	,	PUNCT
cana-3949	209	18	north	north	NOUN
cana-3949	209	19	–	–	PUNCT
cana-3949	209	20	holland	holland	PROPN
cana-3949	209	21	,	,	PUNCT
cana-3949	209	22	amsterdam	amsterdam	PROPN
cana-3949	209	23	.	.	PUNCT
cana-3949	210	1	[	[	X
cana-3949	210	2	4	4	NUM
cana-3949	210	3	]	]	X
cana-3949	210	4	doshi	doshi	PROPN
cana-3949	210	5	,	,	PUNCT
cana-3949	210	6	b.t	b.t	PROPN
cana-3949	210	7	.	.	PROPN
cana-3949	210	8	(	(	PUNCT
cana-3949	210	9	1985	1985	NUM
cana-3949	210	10	)	)	PUNCT
cana-3949	210	11	,	,	PUNCT
cana-3949	210	12	a	a	DET
cana-3949	210	13	note	note	NOUN
cana-3949	210	14	on	on	ADP
cana-3949	210	15	stochastic	stochastic	ADJ
cana-3949	210	16	decomposition	decomposition	NOUN
cana-3949	210	17	in	in	ADP
cana-3949	210	18	a	a	DET
cana-3949	210	19	gi	gi	NOUN
cana-3949	210	20	/	/	SYM
cana-3949	210	21	g/1	g/1	NOUN
cana-3949	210	22	queue	queue	NOUN
cana-3949	210	23	with	with	ADP
cana-3949	210	24	vacation	vacation	NOUN
cana-3949	210	25	or	or	CCONJ
cana-3949	210	26	setup	setup	NOUN
cana-3949	210	27	times	time	NOUN
cana-3949	210	28	,	,	PUNCT
cana-3949	210	29	journal	journal	NOUN
cana-3949	210	30	of	of	ADP
cana-3949	210	31	applied	apply	VERB
cana-3949	210	32	probability	probability	NOUN
cana-3949	210	33	,	,	PUNCT
cana-3949	210	34	22	22	NUM
cana-3949	210	35	,	,	PUNCT
cana-3949	210	36	419	419	NUM
cana-3949	210	37	–	–	PUNCT
cana-3949	210	38	428	428	NUM
cana-3949	210	39	.	.	PUNCT
cana-3949	211	1	[	[	X
cana-3949	211	2	5	5	NUM
cana-3949	211	3	]	]	X
cana-3949	211	4	doshi	doshi	PROPN
cana-3949	211	5	,	,	PUNCT
cana-3949	211	6	b.t	b.t	PROPN
cana-3949	211	7	.	.	PROPN
cana-3949	211	8	(	(	PUNCT
cana-3949	211	9	1986	1986	NUM
cana-3949	211	10	)	)	PUNCT
cana-3949	211	11	,	,	PUNCT
cana-3949	211	12	queueing	queue	VERB
cana-3949	211	13	system	system	NOUN
cana-3949	211	14	with	with	ADP
cana-3949	211	15	vacations	vacation	NOUN
cana-3949	211	16	a	a	DET
cana-3949	211	17	survey	survey	NOUN
cana-3949	211	18	,	,	PUNCT
cana-3949	211	19	queueing	queue	VERB
cana-3949	211	20	systems	system	NOUN
cana-3949	211	21	,	,	PUNCT
cana-3949	211	22	1	1	NUM
cana-3949	211	23	,	,	PUNCT
cana-3949	211	24	29–66	29–66	NUM
cana-3949	211	25	.	.	PUNCT
cana-3949	212	1	[	[	X
cana-3949	212	2	6	6	NUM
cana-3949	212	3	]	]	X
cana-3949	212	4	doshi	doshi	PROPN
cana-3949	212	5	,	,	PUNCT
cana-3949	212	6	b.t	b.t	PROPN
cana-3949	212	7	.	.	PROPN
cana-3949	212	8	(	(	PUNCT
cana-3949	212	9	1990	1990	NUM
cana-3949	212	10	):	):	PUNCT
cana-3949	212	11	single	single	ADJ
cana-3949	212	12	server	server	NOUN
cana-3949	212	13	queues	queue	NOUN
cana-3949	212	14	with	with	ADP
cana-3949	212	15	vacations	vacation	NOUN
cana-3949	212	16	,	,	PUNCT
cana-3949	212	17	stochastic	stochastic	ADJ
cana-3949	212	18	analysis	analysis	NOUN
cana-3949	212	19	of	of	ADP
cana-3949	212	20	computer	computer	NOUN
cana-3949	212	21	and	and	CCONJ
cana-3949	212	22	communication	communication	NOUN
cana-3949	212	23	systems	system	NOUN
cana-3949	212	24	,	,	PUNCT
cana-3949	212	25	takagi	takagi	NOUN
cana-3949	212	26	,	,	PUNCT
cana-3949	212	27	h.	h.	PROPN
cana-3949	212	28	(	(	PUNCT
cana-3949	212	29	ed	ed	NOUN
cana-3949	212	30	.	.	PUNCT
cana-3949	212	31	)	)	PUNCT
cana-3949	212	32	,	,	PUNCT
cana-3949	212	33	elsevier	elsevier	NOUN
cana-3949	212	34	,	,	PUNCT
cana-3949	212	35	amsterdam	amsterdam	PROPN
cana-3949	212	36	.	.	PUNCT
cana-3949	213	1	[	[	X
cana-3949	213	2	7	7	NUM
cana-3949	213	3	]	]	X
cana-3949	213	4	doshi	doshi	PROPN
cana-3949	213	5	,	,	PUNCT
cana-3949	213	6	b.t	b.t	PROPN
cana-3949	213	7	.	.	PROPN
cana-3949	213	8	(	(	PUNCT
cana-3949	213	9	1991	1991	NUM
cana-3949	213	10	)	)	PUNCT
cana-3949	213	11	,	,	PUNCT
cana-3949	213	12	analysis	analysis	NOUN
cana-3949	213	13	of	of	ADP
cana-3949	213	14	a	a	DET
cana-3949	213	15	two	two	NUM
cana-3949	213	16	phase	phase	NOUN
cana-3949	213	17	queueing	queue	VERB
cana-3949	213	18	system	system	NOUN
cana-3949	213	19	with	with	ADP
cana-3949	213	20	general	general	ADJ
cana-3949	213	21	service	service	PROPN
cana-3949	213	22	times	time	NOUN
cana-3949	213	23	,	,	PUNCT
cana-3949	213	24	operation	operation	NOUN
cana-3949	213	25	research	research	NOUN
cana-3949	213	26	letters	letter	NOUN
cana-3949	213	27	,	,	PUNCT
cana-3949	213	28	10	10	NUM
cana-3949	213	29	,	,	PUNCT
cana-3949	213	30	265	265	NUM
cana-3949	213	31	–	–	PUNCT
cana-3949	213	32	272	272	NUM
cana-3949	213	33	.	.	PUNCT
cana-3949	214	1	[	[	X
cana-3949	214	2	8	8	NUM
cana-3949	214	3	]	]	SYM
cana-3949	214	4	fuhrmann	fuhrmann	NOUN
cana-3949	214	5	.	.	PUNCT
cana-3949	214	6	,	,	PUNCT
cana-3949	214	7	s.w	s.w	PROPN
cana-3949	214	8	.	.	PROPN
cana-3949	214	9	and	and	CCONJ
cana-3949	214	10	cooper	cooper	PROPN
cana-3949	214	11	,	,	PUNCT
cana-3949	214	12	r.b	r.b	PROPN
cana-3949	214	13	.	.	PROPN
cana-3949	215	1	(	(	PUNCT
cana-3949	215	2	1985	1985	NUM
cana-3949	215	3	)	)	PUNCT
cana-3949	215	4	,	,	PUNCT
cana-3949	215	5	stochastic	stochastic	ADJ
cana-3949	215	6	decompositions	decomposition	NOUN
cana-3949	215	7	in	in	ADP
cana-3949	215	8	the	the	DET
cana-3949	215	9	m	m	NOUN
cana-3949	215	10	/	/	SYM
cana-3949	215	11	g/1	g/1	NOUN
cana-3949	215	12	queue	queue	NOUN
cana-3949	215	13	with	with	ADP
cana-3949	215	14	generalized	generalized	ADJ
cana-3949	215	15	vacations	vacation	NOUN
cana-3949	215	16	,	,	PUNCT
cana-3949	215	17	operation	operation	NOUN
cana-3949	215	18	research	research	NOUN
cana-3949	215	19	,	,	PUNCT
cana-3949	215	20	83	83	NUM
cana-3949	215	21	,	,	PUNCT
cana-3949	215	22	1117–1129	1117–1129	NUM
cana-3949	215	23	.	.	PUNCT
cana-3949	216	1	[	[	X
cana-3949	216	2	9	9	NUM
cana-3949	216	3	]	]	X
cana-3949	216	4	kailash	kailash	PROPN
cana-3949	216	5	c.	c.	PROPN
cana-3949	216	6	madan	madan	PROPN
cana-3949	216	7	.	.	PUNCT
cana-3949	217	1	(	(	PUNCT
cana-3949	217	2	2021	2021	NUM
cana-3949	217	3	)	)	PUNCT
cana-3949	217	4	,	,	PUNCT
cana-3949	217	5	on	on	ADP
cana-3949	217	6	a	a	DET
cana-3949	217	7	single	single	ADJ
cana-3949	217	8	server	server	NOUN
cana-3949	217	9	queue	queue	NOUN
cana-3949	217	10	with	with	ADP
cana-3949	217	11	two	two	NUM
cana-3949	217	12	stage	stage	NOUN
cana-3949	217	13	first	first	ADV
cana-3949	217	14	essential	essential	ADJ
cana-3949	217	15	service	service	NOUN
cana-3949	217	16	followed	follow	VERB
cana-3949	217	17	by	by	ADP
cana-3949	217	18	one	one	NUM
cana-3949	217	19	of	of	ADP
cana-3949	217	20	the	the	DET
cana-3949	217	21	two	two	NUM
cana-3949	217	22	types	type	NOUN
cana-3949	217	23	of	of	ADP
cana-3949	217	24	additional	additional	ADJ
cana-3949	217	25	optional	optional	ADJ
cana-3949	217	26	service	service	NOUN
cana-3949	217	27	and	and	CCONJ
cana-3949	217	28	optional	optional	ADJ
cana-3949	217	29	deterministic	deterministic	ADJ
cana-3949	217	30	server	server	NOUN
cana-3949	217	31	vacations	vacation	NOUN
cana-3949	217	32	,	,	PUNCT
cana-3949	217	33	international	international	ADJ
cana-3949	217	34	journal	journal	NOUN
cana-3949	217	35	of	of	ADP
cana-3949	217	36	circuits	circuit	NOUN
cana-3949	217	37	systems	system	NOUN
cana-3949	217	38	and	and	CCONJ
cana-3949	217	39	signal	signal	NOUN
cana-3949	217	40	processing	processing	NOUN
cana-3949	217	41	,	,	PUNCT
cana-3949	217	42	15	15	NUM
cana-3949	217	43	,	,	PUNCT
cana-3949	217	44	1730	1730	NUM
cana-3949	217	45	-	-	SYM
cana-3949	217	46	1736	1736	NUM
cana-3949	217	47	.	.	PUNCT
cana-3949	218	1	[	[	X
cana-3949	218	2	10	10	NUM
cana-3949	218	3	]	]	X
cana-3949	218	4	kailash	kailash	PROPN
cana-3949	218	5	c.	c.	PROPN
cana-3949	218	6	madan	madan	PROPN
cana-3949	218	7	.	.	PUNCT
cana-3949	219	1	(	(	PUNCT
cana-3949	219	2	2024	2024	NUM
cana-3949	219	3	)	)	PUNCT
cana-3949	219	4	,	,	PUNCT
cana-3949	219	5	on	on	ADP
cana-3949	219	6	a	a	DET
cana-3949	219	7	single	single	ADJ
cana-3949	219	8	server	server	NOUN
cana-3949	219	9	vacation	vacation	NOUN
cana-3949	219	10	queue	queue	NOUN
cana-3949	219	11	with	with	ADP
cana-3949	219	12	two	two	NUM
cana-3949	219	13	types	type	NOUN
cana-3949	219	14	of	of	ADP
cana-3949	219	15	service	service	NOUN
cana-3949	219	16	and	and	CCONJ
cana-3949	219	17	two	two	NUM
cana-3949	219	18	types	type	NOUN
cana-3949	219	19	of	of	ADP
cana-3949	219	20	vacation	vacation	NOUN
cana-3949	219	21	,	,	PUNCT
cana-3949	219	22	wseas	wseas	VERB
cana-3949	219	23	transactions	transaction	NOUN
cana-3949	219	24	on	on	ADP
cana-3949	219	25	systems	system	NOUN
cana-3949	219	26	,	,	PUNCT
cana-3949	219	27	23	23	NUM
cana-3949	219	28	,	,	PUNCT
cana-3949	219	29	98	98	NUM
cana-3949	219	30	–	–	SYM
cana-3949	219	31	104	104	NUM
cana-3949	219	32	.	.	PUNCT
cana-3949	220	1	[	[	X
cana-3949	220	2	11	11	NUM
cana-3949	220	3	]	]	X
cana-3949	220	4	kleinrock	kleinrock	PROPN
cana-3949	220	5	,	,	PUNCT
cana-3949	220	6	l.	l.	PROPN
cana-3949	220	7	(	(	PUNCT
cana-3949	220	8	1976	1976	NUM
cana-3949	220	9	)	)	PUNCT
cana-3949	220	10	,	,	PUNCT
cana-3949	220	11	queueing	queue	VERB
cana-3949	220	12	systems	system	NOUN
cana-3949	220	13	vol	vol	NOUN
cana-3949	220	14	.	.	PUNCT
cana-3949	221	1	i	i	PRON
cana-3949	221	2	,	,	PUNCT
cana-3949	221	3	theory	theory	NOUN
cana-3949	221	4	,	,	PUNCT
cana-3949	221	5	john	john	PROPN
cana-3949	221	6	wiley	wiley	PROPN
cana-3949	221	7	and	and	CCONJ
cana-3949	221	8	sons	son	NOUN
cana-3949	221	9	,	,	PUNCT
cana-3949	221	10	new	new	PROPN
cana-3949	221	11	york	york	PROPN
cana-3949	221	12	.	.	PUNCT
cana-3949	222	1	[	[	X
cana-3949	222	2	12	12	NUM
cana-3949	222	3	]	]	X
cana-3949	222	4	krishna	krishna	PROPN
cana-3949	222	5	,	,	PUNCT
cana-3949	222	6	c.m	c.m	PROPN
cana-3949	222	7	.	.	PROPN
cana-3949	222	8	and	and	CCONJ
cana-3949	222	9	lee	lee	PROPN
cana-3949	222	10	,	,	PUNCT
cana-3949	222	11	y.h	y.h	PROPN
cana-3949	222	12	.	.	PROPN
cana-3949	222	13	(	(	PUNCT
cana-3949	222	14	1990	1990	NUM
cana-3949	222	15	)	)	PUNCT
cana-3949	222	16	,	,	PUNCT
cana-3949	222	17	a	a	DET
cana-3949	222	18	study	study	NOUN
cana-3949	222	19	of	of	ADP
cana-3949	222	20	a	a	DET
cana-3949	222	21	two	two	NUM
cana-3949	222	22	phase	phase	NOUN
cana-3949	222	23	service	service	NOUN
cana-3949	222	24	,	,	PUNCT
cana-3949	222	25	operation	operation	NOUN
cana-3949	222	26	research	research	NOUN
cana-3949	222	27	letters	letter	NOUN
cana-3949	222	28	,	,	PUNCT
cana-3949	222	29	9	9	NUM
cana-3949	222	30	,	,	PUNCT
cana-3949	222	31	91–97	91–97	NUM
cana-3949	222	32	.	.	PUNCT
cana-3949	223	1	[	[	X
cana-3949	223	2	13	13	NUM
cana-3949	223	3	]	]	SYM
cana-3949	223	4	lavenberg	lavenberg	PROPN
cana-3949	223	5	,	,	PUNCT
cana-3949	223	6	g.	g.	PROPN
cana-3949	223	7	(	(	PUNCT
cana-3949	223	8	1988	1988	NUM
cana-3949	223	9	)	)	PUNCT
cana-3949	223	10	,	,	PUNCT
cana-3949	223	11	a	a	DET
cana-3949	223	12	perspective	perspective	NOUN
cana-3949	223	13	on	on	ADP
cana-3949	223	14	queueing	queue	VERB
cana-3949	223	15	models	model	NOUN
cana-3949	223	16	of	of	ADP
cana-3949	223	17	computer	computer	NOUN
cana-3949	223	18	performance	performance	NOUN
cana-3949	223	19	in	in	ADP
cana-3949	223	20	queueing	queue	VERB
cana-3949	223	21	theory	theory	NOUN
cana-3949	223	22	and	and	CCONJ
cana-3949	223	23	its	its	PRON
cana-3949	223	24	applications	application	NOUN
cana-3949	223	25	,	,	PUNCT
cana-3949	223	26	liber	liber	PROPN
cana-3949	223	27	amicorium	amicorium	NOUN
cana-3949	223	28	,	,	PUNCT
cana-3949	223	29	for	for	ADP
cana-3949	223	30	j.w	j.w	PROPN
cana-3949	223	31	.	.	PROPN
cana-3949	223	32	cohen	cohen	PROPN
cana-3949	223	33	;	;	PUNCT
cana-3949	223	34	cwi	cwi	PROPN
cana-3949	223	35	monograph	monograph	PROPN
cana-3949	223	36	7	7	NUM
cana-3949	223	37	.	.	PUNCT
cana-3949	224	1	[	[	X
cana-3949	224	2	14	14	NUM
cana-3949	224	3	]	]	PUNCT
cana-3949	224	4	pavai	pavai	NOUN
cana-3949	224	5	madheswari	madheswari	PROPN
cana-3949	224	6	,	,	PUNCT
cana-3949	224	7	s.	s.	PROPN
cana-3949	224	8	,	,	PUNCT
cana-3949	224	9	krishna	krishna	PROPN
cana-3949	224	10	kumar	kumar	PROPN
cana-3949	224	11	,	,	PUNCT
cana-3949	224	12	b.	b.	PROPN
cana-3949	224	13	,	,	PUNCT
cana-3949	224	14	poomalai	poomalai	PROPN
cana-3949	224	15	suganthi	suganthi	PROPN
cana-3949	224	16	,	,	PUNCT
cana-3949	224	17	(	(	PUNCT
cana-3949	224	18	2019	2019	NUM
cana-3949	224	19	)	)	PUNCT
cana-3949	224	20	,	,	PUNCT
cana-3949	224	21	analysis	analysis	NOUN
cana-3949	224	22	of	of	ADP
cana-3949	224	23	m	m	NOUN
cana-3949	224	24	/	/	SYM
cana-3949	224	25	g/1	g/1	NOUN
cana-3949	224	26	retrial	retrial	NOUN
cana-3949	224	27	queues	queue	NOUN
cana-3949	224	28	with	with	ADP
cana-3949	224	29	second	second	ADJ
cana-3949	224	30	optional	optional	ADJ
cana-3949	224	31	service	service	NOUN
cana-3949	224	32	and	and	CCONJ
cana-3949	224	33	customer	customer	NOUN
cana-3949	224	34	balking	balk	VERB
cana-3949	224	35	under	under	ADP
cana-3949	224	36	two	two	NUM
cana-3949	224	37	types	type	NOUN
cana-3949	224	38	of	of	ADP
cana-3949	224	39	bernoulli	bernoulli	PROPN
cana-3949	224	40	vacation	vacation	NOUN
cana-3949	224	41	schedule	schedule	NOUN
cana-3949	224	42	,	,	PUNCT
cana-3949	224	43	rairo	rairo	NOUN
cana-3949	224	44	-	-	PUNCT
cana-3949	224	45	operation	operation	NOUN
cana-3949	224	46	research	research	NOUN
cana-3949	224	47	,	,	PUNCT
cana-3949	224	48	53(2	53(2	NUM
cana-3949	224	49	)	)	PUNCT
cana-3949	224	50	,	,	PUNCT
cana-3949	224	51	415	415	NUM
cana-3949	224	52	–	–	PUNCT
cana-3949	224	53	443	443	NUM
cana-3949	224	54	.	.	PUNCT
cana-3949	225	1	[	[	X
cana-3949	225	2	15	15	NUM
cana-3949	225	3	]	]	X
cana-3949	225	4	shyamala	shyamala	PROPN
cana-3949	225	5	,	,	PUNCT
cana-3949	225	6	s.	s.	PROPN
cana-3949	225	7	and	and	CCONJ
cana-3949	225	8	vijayaraj	vijayaraj	VERB
cana-3949	225	9	,	,	PUNCT
cana-3949	225	10	r.	r.	PROPN
cana-3949	225	11	(	(	PUNCT
cana-3949	225	12	2020	2020	NUM
cana-3949	225	13	)	)	PUNCT
cana-3949	225	14	,	,	PUNCT
cana-3949	225	15	time	time	NOUN
cana-3949	225	16	dependent	dependent	ADJ
cana-3949	225	17	solution	solution	NOUN
cana-3949	225	18	of	of	ADP
cana-3949	225	19	two	two	NUM
cana-3949	225	20	stages	stage	NOUN
cana-3949	225	21	mx	mx	NOUN
cana-3949	225	22	/	/	SYM
cana-3949	225	23	g/1	g/1	NOUN
cana-3949	225	24	queue	queue	NOUN
cana-3949	225	25	model	model	NOUN
cana-3949	225	26	server	server	NOUN
cana-3949	225	27	vacation	vacation	NOUN
cana-3949	225	28	random	random	ADJ
cana-3949	225	29	setup	setup	NOUN
cana-3949	225	30	time	time	NOUN
cana-3949	225	31	and	and	CCONJ
cana-3949	225	32	balking	balk	VERB
cana-3949	225	33	with	with	ADP
cana-3949	225	34	bernoulli	bernoulli	NOUN
cana-3949	225	35	schedule	schedule	NOUN
cana-3949	225	36	.	.	PUNCT
cana-3949	226	1	aip	aip	PROPN
cana-3949	226	2	conference	conference	NOUN
cana-3949	226	3	proceedings	proceeding	NOUN
cana-3949	226	4	,	,	PUNCT
cana-3949	226	5	2261	2261	NUM
cana-3949	226	6	,	,	PUNCT
cana-3949	226	7	1	1	NUM
cana-3949	226	8	-	-	SYM
cana-3949	226	9	10	10	NUM
cana-3949	226	10	.	.	PUNCT
cana-3949	227	1	[	[	X
cana-3949	227	2	16	16	NUM
cana-3949	227	3	]	]	X
cana-3949	227	4	somasundaram	somasundaram	PROPN
cana-3949	227	5	,	,	PUNCT
cana-3949	227	6	b.	b.	PROPN
cana-3949	227	7	,	,	PUNCT
cana-3949	227	8	karpagam	karpagam	PROPN
cana-3949	227	9	,	,	PUNCT
cana-3949	227	10	s.	s.	PROPN
cana-3949	227	11	,	,	PUNCT
cana-3949	227	12	lokesh	lokesh	PROPN
cana-3949	227	13	,	,	PUNCT
cana-3949	227	14	r.	r.	PROPN
cana-3949	227	15	,	,	PUNCT
cana-3949	227	16	kavin	kavin	PROPN
cana-3949	227	17	sagana	sagana	PROPN
cana-3949	227	18	mary	mary	PROPN
cana-3949	227	19	,	,	PUNCT
cana-3949	227	20	a.	a.	NOUN
cana-3949	227	21	(	(	PUNCT
cana-3949	227	22	2023	2023	NUM
cana-3949	227	23	)	)	PUNCT
cana-3949	227	24	,	,	PUNCT
cana-3949	227	25	an	an	DET
cana-3949	227	26	m[x]/g/1	m[x]/g/1	ADJ
cana-3949	227	27	queue	queue	NOUN
cana-3949	227	28	with	with	ADP
cana-3949	227	29	optional	optional	ADJ
cana-3949	227	30	service	service	NOUN
cana-3949	227	31	and	and	CCONJ
cana-3949	227	32	working	working	NOUN
cana-3949	227	33	breakdown	breakdown	NOUN
cana-3949	227	34	,	,	PUNCT
cana-3949	227	35	ural	ural	ADJ
cana-3949	227	36	mathematical	mathematical	ADJ
cana-3949	227	37	journal,9,162	journal,9,162	PROPN
cana-3949	227	38	–	–	PUNCT
cana-3949	227	39	175	175	NUM
cana-3949	227	40	.	.	PUNCT
cana-3949	228	1	[	[	X
cana-3949	228	2	17	17	NUM
cana-3949	228	3	]	]	PUNCT
cana-3949	228	4	takagi	takagi	NOUN
cana-3949	228	5	.	.	PUNCT
cana-3949	228	6	,	,	PUNCT
cana-3949	228	7	h.	h.	PROPN
cana-3949	228	8	(	(	PUNCT
cana-3949	228	9	1991	1991	NUM
cana-3949	228	10	)	)	PUNCT
cana-3949	228	11	,	,	PUNCT
cana-3949	228	12	queueing	queue	VERB
cana-3949	228	13	analysis	analysis	NOUN
cana-3949	228	14	:	:	PUNCT
cana-3949	228	15	vacation	vacation	NOUN
cana-3949	228	16	and	and	CCONJ
cana-3949	228	17	priority	priority	NOUN
cana-3949	228	18	systems	system	NOUN
cana-3949	228	19	,	,	PUNCT
cana-3949	228	20	vol	vol	NOUN
cana-3949	228	21	.	.	PROPN
cana-3949	228	22	1	1	NUM
cana-3949	228	23	.	.	X
cana-3949	228	24	north	north	PROPN
cana-3949	228	25	holland	holland	PROPN
cana-3949	228	26	,	,	PUNCT
cana-3949	228	27	amsterdam	amsterdam	PROPN
cana-3949	228	28	.	.	PUNCT
cana-3949	229	1	https://www.rairo-ro.org/articles/ro/abs/2019/02/ro160250/ro160250.html	https://www.rairo-ro.org/articles/ro/abs/2019/02/ro160250/ro160250.html	PROPN
cana-3949	229	2	https://www.rairo-ro.org/articles/ro/abs/2019/02/ro160250/ro160250.html	https://www.rairo-ro.org/articles/ro/abs/2019/02/ro160250/ro160250.html	PROPN
cana-3949	229	3	https://www.researchgate.net/journal/ural-mathematical-journal-2414-3952?_tp=eyjjb250zxh0ijp7imzpcnn0ugfnzsi6inb1ymxpy2f0aw9uiiwicgfnzsi6inb1ymxpy2f0aw9uin19	https://www.researchgate.net/journal/ural-mathematical-journal-2414-3952?_tp=eyjjb250zxh0ijp7imzpcnn0ugfnzsi6inb1ymxpy2f0aw9uiiwicgfnzsi6inb1ymxpy2f0aw9uin19	NOUN