The combinatorics of birth–death processes and applications to queues

Authors:
W. Böhm;A. Krinik;S. G. Mohanty
Affiliations:
Department of Statistics, University of Economics, A-1090 Vienna, Austria;Department of Mathematics, California State Polytechnique University, Pomona, USA;Department of Statistics, McMaster University, Canada
Venue:
Queueing Systems: Theory and Applications
Year:
1997

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Abstract

In this paper we present a combinatorial technique which allows the derivation of the transition functions of general birth–death processes. This method provides a flexible tool for the transient analysis of Markovian queueing systems with state dependent transition rates, like M/M/c models or systems with balking and reneging.