Sensitivity to the Service-Time Distribution in the Nonstationary Erlang Loss Model

Jimmie L. Davis, William A. Massey and Ward Whitt
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Jimmie L. Davis: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332
William A. Massey: AT&T Bell Laboratories, Room 2C-120, Murray Hill, New Jersey 07974-0636
Ward Whitt: AT&T Bell Laboratories, Room 2C-178, Murray Hill, New Jersey 07974-0636

Management Science, 1995, vol. 41, issue 6, 1107-1116

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. We develop a simple, effective numerical algorithm for the M t /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-peakedness approximations, which exploit exact results for related infinite-server models.

Keywords: nonstationary queues; time-dependent arrival rates; nonhomogeneous Markov chains; transient behavior; Erlang loss model; blocking probability; insensitivity; infinite-server queues; modified-offered-load approximation (search for similar items in EconPapers)
Date: 1995
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Citations: View citations in EconPapers (15)

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