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

Authors:
Tuan Phung-Duc;Hiroyuki Masuyama;Shoji Kasahara;Yutaka Takahashi
Affiliations:
Kyoto University, Sakyo-ku Kyoto, Japan;Kyoto University, Sakyo-ku Kyoto, Japan;Kyoto University, Sakyo-ku Kyoto, Japan;Kyoto University, Sakyo-ku Kyoto, Japan
Venue:
Proceedings of the 5th International Conference on Queueing Theory and Network Applications
Year:
2010

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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.