Sensitivity to the Service-Time Distribution in the Nonstationary Erlang Loss Model
Jimmie L. Davis, William A. Massey, Ward Whitt
Management Science · 1995 · Volume 41 · Issue 6
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
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