MaPhySto
Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

MPS-RR 2002-37
November 2002

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

by:

## 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 $n$.

Availability: [ gzipped ps-file ] [ pdf-file ]

This paper has now been published in Queueing Systems 46, 249-270 (2004)