The pointwise stationary approximation for Mt/Mt/s queues is asymptotically correct as the rates increase

The pointwise stationary approximation for Mt/Mt/s queues is asymptotically correct as the rates increase

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Article ID: iaor19912146
Country: United States
Volume: 37
Issue: 3
Start Page Number: 307
End Page Number: 314
Publication Date: Mar 1991
Journal: Management Science
Authors:
Keywords: stochastic processes
Abstract:

Green, Kolesar and Svoronos and Green and Kolesar 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 weight 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. This paper verifies 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). It actually establishes both pointwise and average versions of this result for general time-dependent birth-and-death processes.

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