A simple algorithm for the rate matrices of level-dependent QBD processes

Abstract

We develop a simple algorithm to compute the rate matrices of ergodic level-dependent quasi-birth-and-death processes, based on a matrix continued fraction representation and a probabilistic interpretation of those matrices. The algorithm is easier to implement and less memory-consuming than that developed by Bright and Taylor. We apply the algorithm to an infinite-server queueing system with a Markovian arrival process and exponentially distributed service times. We present some numerical results in order to demonstrate the efficiency of our algorithm.