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Approximating the Behavior of Nonstationary Single-Server Queues

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  • S. C. Moore

    (University of Missouri, Columbia, Missouri)

Abstract

This paper presents computationally efficient techniques for approximating several behavioral aspects of the M x ( t )/ E Y /1 queue. The nonstationary arrival stream allows demands for service to follow different distributions over different time intervals. Specific performance characteristics evaluated are the first two moments of queue length, virtual waiting time, and system utilization. These are based on approximating the distribution of Q ( t ) at the time points E [ T n ] by the distribution of Q n , where T n is the epoch of the n th departure and Q n = Q ( T n + 0). The results are in agreement with those obtained by simulation but require much less computing time. Sample results are presented for both stationary and nonstationary examples.

Suggested Citation

  • S. C. Moore, 1975. "Approximating the Behavior of Nonstationary Single-Server Queues," Operations Research, INFORMS, vol. 23(5), pages 1011-1032, October.
    • Handle: RePEc:inm:oropre:v:23:y:1975:i:5:p:1011-1032
    DOI: 10.1287/opre.23.5.1011
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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.
    2. Chaithanya Bandi & Nikolaos Trichakis & Phebe Vayanos, 2019. "Robust Multiclass Queuing Theory for Wait Time Estimation in Resource Allocation Systems," Management Science, INFORMS, vol. 65(1), pages 152-187, January.
    3. Chaithanya Bandi & Dimitris Bertsimas & Nataly Youssef, 2018. "Robust transient analysis of multi-server queueing systems and feed-forward networks," Queueing Systems: Theory and Applications, Springer, vol. 89(3), pages 351-413, August.

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