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On finite capacity queues with time dependent arrival rates

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  • Tan, Xiaoqian
  • Knessl, Charles
  • Yang, Yongzhi (Peter)

Abstract

We consider the finite capacity M/M/1−K queue with a time dependent arrival rate λ(t). Assuming that the capacity K is large and that the arrival rate varies slowly with time (as t/K), we construct asymptotic approximations to the probability of finding n customers in the system at time t, as well as the mean number. We consider various time ranges, where the system is nearly empty, nearly full, or is filled to a fraction of its capacity. Extensive numerical studies are used to back up the asymptotic analysis.

Suggested Citation

  • Tan, Xiaoqian & Knessl, Charles & Yang, Yongzhi (Peter), 2013. "On finite capacity queues with time dependent arrival rates," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 2175-2227.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:6:p:2175-2227
    DOI: 10.1016/j.spa.2013.02.002
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    References listed on IDEAS

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    Cited by:

    1. Schwarz, Justus Arne & Selinka, Gregor & Stolletz, Raik, 2016. "Performance analysis of time-dependent queueing systems: Survey and classification," Omega, Elsevier, vol. 63(C), pages 170-189.

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