Markov processes on a semi-infinite strip and the geometric tail algorithm

Many queuing processes have a semi-infinite strip in the two-dimensional plane as state space. As an alternative to well-established algorithms for the computation of steady-state probabilities, such as the matrix-geometric method and the spectral method, this article discusses a simple and easy-to-implement algorithm which is based on the geometric tail behavior of the steady-state probabilities. Some numerical comparisons between this algorithm and the spectral method are presented.