Continuity of the M/G/c queue

摘要

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 F_n, leads to an approximation of the stationary distribution π of the original M/G/c queue by the stationary distributions π_n of the M/G/c queues with service time distributions F_n. 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.