Response times in processor-shared queues with state-dependent arrival rates

C. Knessl; C. Tier; B. J. Matkowsky; Z. Schuss

doi:10.1080/15326348908807100

Response times in processor-shared queues with state-dependent arrival rates

C. Knessl, C. Tier, B. J. Matkowsky, Z. Schuss

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We consider M/M/1-PS queues where the arrival rate is a function of the instantaneous number of customers using the system. We obtain asymptotic approximations to the first two moments of the response time, conditioned on both the total service time and the number of customers in the system at time of arrival. In addition, we remove the conditioning on the number at time of arrival to obtain approximations to the response time conditioned on the service time only. Our approximations are valid for systems with small mean service requests and a rapid arrival rate that depends weakly on the number of customers present. Both open and closed systems are considered.

Original language	English
Pages (from-to)	83-113
Number of pages	31
Journal	Stochastic Models
Volume	5
Issue number	1
DOIs	https://doi.org/10.1080/15326348908807100
State	Published - 1989

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abstract = "We consider M/M/1-PS queues where the arrival rate is a function of the instantaneous number of customers using the system. We obtain asymptotic approximations to the first two moments of the response time, conditioned on both the total service time and the number of customers in the system at time of arrival. In addition, we remove the conditioning on the number at time of arrival to obtain approximations to the response time conditioned on the service time only. Our approximations are valid for systems with small mean service requests and a rapid arrival rate that depends weakly on the number of customers present. Both open and closed systems are considered.",

author = "C. Knessl and C. Tier and Matkowsky, {B. J.} and Z. Schuss",

note = "Funding Information: ACKNOWLEDGEMENTS This research was supported in part by NSF Grants DMS-84-06110 and DMS-86-20267 and grants from the U.S. Israel Binational Science Foundation and the Israel Academy of Sciences. C.K. was partially supported by an I.B.M. Graduate Fellowship and an NSF Postdoctoral Fellowship.",

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AU - Tier, C.

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Response times in processor-shared queues with state-dependent arrival rates

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