Monotonicity results for MR/GI/1 queues

This paper considers queues with a Markov renewal arrival process and a particular transition matrix for the underlying Markov chain. We study the effect that the transition matrix has on the waiting time of the nth customer as well as on the stationary waiting time. The main theorem generalizes results of Szekli et al. and partly confirms their conjecture. In this context we show the importance of a new stochastic ordering concept.