Computing Steady-State Probabilities of a Nonpreemptive Priority Multiserver Queue

Abstract

We consider a nonpreemptive priority exponential queue with multiple servers and two classes of customers—each with its own arrival and service rates. Our focus is on the computation of steady-state probabilities for problems in which the marginal distribution for the number of high priority customers in the system has a short tail. The model is formulated as a quasi-birth-and-death process and is solved by applying several variants of state reduction. The variants are designed to reduce the computation and storage requirements for handling problems of moderate size. A few numerical-examples are given at the end. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.