Continuity of the M/G/c queue

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 of the original M/G/c queue by the stationary distributions n 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.

• Type: Journal
• Year: 2008
• Where: QUESTA
• Authors: Lothar Breuer
• Keywords: QUESTA 2008, Service Time, Service Time Distribution, Stationary Distributions