On the sojourn time distribution in a finite population Markovian processor sharing queue

Q. Zhen, J.S.H. van Leeuwaarden, C. Knessl

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

We consider a finite population processor sharing (PS) queue, with Markovian arrivals and an exponential server. Such a queue can model an interactive computer system consisting of a bank of terminals in series with a central processing unit. For systems with a large population N and a commensurately rapid service rate, or infrequent arrivals, we obtain various asymptotic results. We analyse the conditional sojourn time distribution of a tagged customer, conditioned on the number n of others in the system at the tagged customer's arrival instant, and also the unconditional distribution. The asymptotics are obtained by a combination of singular perturbation methods and spectral methods.We consider several space/time scales and parameter ranges, which lead to different asymptotic behaviours. We also identify precisely when the finite population model can be approximated by the standard infinite population M/M/1 - PS queue.

Original languageEnglish
Pages (from-to)33-59
Number of pages27
JournalIMA Journal of Applied Mathematics
Volume82
Issue number1
DOIs
Publication statusPublished - 2017

Fingerprint

Processor Sharing
Sojourn Time
Finite Population
Queue
Interactive computer systems
Computer terminals
Customers
Program processors
Singular Perturbation Method
Finite Models
Servers
Population Model
Spectral Methods
Instant
Time Scales
Server
Asymptotic Behavior
Unit
Series
Range of data

Keywords

  • Asymptotics
  • Finite population
  • Processor sharing

Cite this

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On the sojourn time distribution in a finite population Markovian processor sharing queue. / Zhen, Q.; van Leeuwaarden, J.S.H.; Knessl, C.

In: IMA Journal of Applied Mathematics, Vol. 82, No. 1, 2017, p. 33-59.

Research output: Contribution to journalArticleAcademicpeer-review

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AU - van Leeuwaarden, J.S.H.

AU - Knessl, C.

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