Computational Methods for Single Server and Multi-Server Queues with Markovian Input and General Service Times

摘要

Efficient and stable algorithms to compute the steady state probabilities and the moments of the waiting time are specified. The multi-server queue with Poisson input and general service times is discussed. For the steady state probabilities, good quality approximations to be computed from a stable recursive algorithm are presented. As a by-product, simple approximations for the delay probability and the moments of the waiting time are obtained. For the output process, tractable and good approximations for the moments of the interdeparture time are derived. Extensions to the finite capacity M/G/c queue and the machine repair problem with multiple repairmen having general times were also examined.