Sensitivity to the service-time distribution in the nonstationary Erlang loss model

Sensitivity to the service-time distribution in the nonstationary Erlang loss model

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Article ID: iaor1996642
Country: United States
Volume: 41
Issue: 6
Start Page Number: 1107
End Page Number: 1116
Publication Date: Jun 1995
Journal: Management Science
Authors: , ,
Keywords: service, markov processes
Abstract:

The stationary Erlang loss model is a classic example of an insensitive queueing system: the steady-state distribution of the number of busy servers depends on the service-time distribution only through its mean. However, when the arrival process is a nonstationary Poisson process, the insensitivity property is lost. The authors develop a simple, effective numerical algorithm for the Mt/PH/s/0 model with two service phases and a nonhomogeneous Poisson arrival process, and apply it to show that the time-dependent blocking probability with nonstationary input can be strongly influenced by the service-time distribution beyond the mean. With sinusoidal arrival rates, the peak blocking probability typically increases as the service-time distribution gets less variable. The influence of the service-time distribution, including this seemingly anomalous behavior, can be understood and predicted from the modified-offered-load and stationary-peakness approximations, which exploit exact results for related infinite-server models.

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