Asymptotic Behavior of the Stationary Distributions in the GI/PH/c Queue with Heterogeneous Servers

摘要

This paper deals with the stable c-server queue with renewal input. The service time distributions may be different for the various servers. They are however all probability distributions of phase type. It is shown that the stationary distribution of the queue length at arrivals has an exact geometric tail of rate n, o < n < 1. It is further shown that the stationary waiting time distribution at arrivals has an exact exponential tail of decay parameter xi > 0. The quantities n and xi may be evaluated together by an elementary algorithm. For both distributions, the multiplicative constants which arise in the asymptotic forms may be fully characterized. These constants are however difficult to compute in general. (Author)