MPS-RR 2002-37
November 2002

Transient properties of many-server queues and related QBD's

Søren Asmussen

Mats Pihlsgård

Abstract

The time $\tau(n)$ of first passage from queue length $x$ to queue length $n>x$ in an MAP/M/$c$ queue us considered. The mean and the Laplace transform is computed as solutions of systems of linear equations coming out by optional stopping of a martingale obtained as a stochastic integral of the exponential Wald martingale for Markov additive processes. Compared to existing techniques for QBD's, the approach has the advantage of being fa more efficient for large $n$.

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