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 - Feb 2017

    Keywords

    • Asymptotics
    • Finite population
    • Processor sharing
    • asymptotics
    • finite population
    • processor sharing

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