A monotonicity result for a single-server queue subject to a Markov-modulated Poisson process

Consider a single-server queue with zero buffer. The arrival process is a three-level Markov modulated Poisson process with an arbitrary transition matrix. The time the system remains at level i (i=1, 2, 3) is exponentially distributed with rate c alpha(i) The arrival rate at level i is lambda(i) and the service time is exponentially distributed with rate mu(i). In this paper we first derive an explicit formula for the loss probability and then prove that it is decreasing in the parameter c. This proves a conjecture of Ross and Rolski's for a single-server queue with zero buffer.