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Logarithmic asymptotics for a single-server processing distinguishable sources

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  • Ken Duffy
  • David Malone

Abstract

We consider a single-server first-in-first-out queue fed by a finite number of distinct sources of jobs. For a large class of short-range dependent and light-tailed distributed job processes, using functional large deviation techniques we prove a large deviation principle and logarithmic asymptotics for the joint waiting time and queue lengths distribution. We identify the paths that are most likely to lead to the rare events of large waiting times and long queue lengths. A number of examples are presented to illustrate salient features of the results. Copyright Springer-Verlag 2008

Suggested Citation

  • Ken Duffy & David Malone, 2008. "Logarithmic asymptotics for a single-server processing distinguishable sources," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(3), pages 509-537, December.
    • Handle: RePEc:spr:mathme:v:68:y:2008:i:3:p:509-537
    DOI: 10.1007/s00186-007-0189-2
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    References listed on IDEAS

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    1. Dembo, Amir & Zajic, Tim, 1995. "Large deviations: From empirical mean and measure to partial sums process," Stochastic Processes and their Applications, Elsevier, vol. 57(2), pages 191-224, June.
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