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

Abstract

We first consider a wide class of single-server queues with state dependent Markovian input including the finite capacity M/G/1 queue and the machine repair problem. We specify efficient and stable algorithms to compute the steady-state probabilities and the moments of the waiting time. Next we discuss the multi-server queue with Poisson input and general service times. We present for the steady-state probabilities good quality approximations to be computed from a stable recursive algorithm. As a by-product we obtain simple approximations for the delay probability and the moments of the waiting time. For the output process we derive tractable and good approximations for the moments of the interdeparture time. Also we discuss extensions to the finite capacity M/G/c queue and the machine repair problem with multiple repairmen having general repair times.