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Some Effects of Nonstationarity on Multiserver Markovian Queueing Systems

Author

Listed:
  • Linda Green

    (Columbia University, New York, New York)

  • Peter Kolesar

    (Columbia University, New York, New York)

  • Anthony Svoronos

    (Columbia University, New York, New York)

Abstract

We examine the effects of nonstationarity on the performance of multiserver queueing systems with exponential service times and sinusoidal Poisson input streams. Our primary objective is to determine when and how a stationary model may be used as an approximation for a nonstationary system. We focus on a particular question: How nonstationary can an arrival process be before a simple stationary approximation fails? Our analysis reveals that stationary models can seriously underestimate delays when the actual system is only modestly nonstationary . Other findings include confirmation and elaboration of S. M. Ross's conjecture that expected delays increase with nonstationarity, and the identification of easily computed and tight lower and upper bounds for expected delay and the probability of delay. These empirical results are based on a series of computer experiments in which the differential equations governing system behavior are solved numerically.

Suggested Citation

  • Linda Green & Peter Kolesar & Anthony Svoronos, 1991. "Some Effects of Nonstationarity on Multiserver Markovian Queueing Systems," Operations Research, INFORMS, vol. 39(3), pages 502-511, June.
    • Handle: RePEc:inm:oropre:v:39:y:1991:i:3:p:502-511
    DOI: 10.1287/opre.39.3.502
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    Cited by:

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    4. Yang, Feng & Liu, Jingang, 2012. "Simulation-based transfer function modeling for transient analysis of general queueing systems," European Journal of Operational Research, Elsevier, vol. 223(1), pages 150-166.
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    13. Andrew M. Ross, 2010. "Computing Bounds on the Expected Maximum of Correlated Normal Variables," Methodology and Computing in Applied Probability, Springer, vol. 12(1), pages 111-138, March.
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