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The Pointwise Stationary Approximation for Mt/Mt/s Queues Is Asymptotically Correct As the Rates Increase

Author

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  • Ward Whitt

    (AT&T Bell Laboratories, Murray Hill, New Jersey 07974-2070)

Abstract

Green, Kolesar and Svoronos (in press) and Green and Kolesar (in press) use numerical methods to investigate the behavior of multiserver Markov queues with a Poisson arrival process having a sinusoidal arrival rate. For this model they propose an approximation for long-run average performance measures called the pointwise stationary approximation (PSA), which consists of an appropriate weighted average of the performance measure that would result at each point in time if the system were stationary with the arrival rate that applies at that point in time. In this paper we verify their conjecture that PSA is asymptotically correct as the service and arrival rates increase with the instantaneous traffic intensity held fixed (corresponding to long arrival rate cycles). We actually establish both pointwise and average versions of this result for general time-dependent birth-and-death processes.

Suggested Citation

  • Ward Whitt, 1991. "The Pointwise Stationary Approximation for Mt/Mt/s Queues Is Asymptotically Correct As the Rates Increase," Management Science, INFORMS, vol. 37(3), pages 307-314, March.
    • Handle: RePEc:inm:ormnsc:v:37:y:1991:i:3:p:307-314
    DOI: 10.1287/mnsc.37.3.307
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