Computation of the state probabilities in M/G/1 queues with state dependent input and state dependent service

Abstract

For a single server queue with state dependent Markovian input and state dependent general service times we give a stable recursive algorithm to compute the steady-state probabilities. An integral representation of the coefficients in the recursive scheme is given. For service time distributions of phase type the computation of the coefficients simplifies considerably in that only matrix-vector operations are needed and no integrations.