Queueing Systems

, Volume 58, Issue 4, pp 321–331

Continuity of the M/G/c queue

Article

DOI: 10.1007/s11134-008-9073-x

Cite this article as:
Breuer, L. Queueing Syst (2008) 58: 321. doi:10.1007/s11134-008-9073-x

Abstract

Consider an M/G/c queue with homogeneous servers and service time distribution F. It is shown that an approximation of the service time distribution F by stochastically smaller distributions, say Fn, leads to an approximation of the stationary distribution π of the original M/G/c queue by the stationary distributions πn of the M/G/c queues with service time distributions Fn. Here all approximations are in weak convergence. The argument is based on a representation of M/G/c queues in terms of piecewise deterministic Markov processes as well as some coupling methods.

Keywords

Multi-server queueContinuityPiecewise deterministic Markov processCouplingConvergence speed

Mathematics Subject Classification (2000)

60K2560J0560K15

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Institute of Mathematics and StatisticsUniversity of KentCanterburyUK