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 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.
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Breuer, L. Continuity of the M/G/c queue. Queueing Syst 58, 321–331 (2008). https://doi.org/10.1007/s11134-008-9073-x
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DOI: https://doi.org/10.1007/s11134-008-9073-x