Queueing Systems

, Volume 58, Issue 4, pp 321–331 | Cite as

Continuity of the M/G/c queue

Article

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 queue Continuity Piecewise deterministic Markov process Coupling Convergence speed 

Mathematics Subject Classification (2000)

60K25 60J05 60K15 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Institute of Mathematics and StatisticsUniversity of KentCanterburyUK

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