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Asymptotic expansions for the sojourn time distribution in the M/G/1-PS queue

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  • Qiang Zhen
  • Charles Knessl

Abstract

We consider the M/G/1 queue with a processor sharing server. We study the conditional sojourn time distribution, conditioned on the customer’s service requirement, as well as the unconditional distribution, in various asymptotic limits. These include large time and/or large service request, and heavy traffic, where the arrival rate is only slightly less than the service rate. Our results demonstrate the possible tail behaviors of the unconditional distribution, which was previously known in the cases G = M and G = D (where it is purely exponential). We assume that the service density decays at least exponentially fast. We use various methods for the asymptotic expansion of integrals, such as the Laplace and saddle point methods. Copyright Springer-Verlag 2010

Suggested Citation

  • Qiang Zhen & Charles Knessl, 2010. "Asymptotic expansions for the sojourn time distribution in the M/G/1-PS queue," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(2), pages 201-244, April.
    • Handle: RePEc:spr:mathme:v:71:y:2010:i:2:p:201-244
    DOI: 10.1007/s00186-009-0290-9
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    Cited by:

    1. Jose Blanchet & Bert Zwart, 2010. "Asymptotic expansions of defective renewal equations with applications to perturbed risk models and processor sharing queues," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(2), pages 311-326, October.

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