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On zero-avoiding transition probabilities of an r-node tandem queue: a combinatorial approach

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Walter Böhm ,
J. L. Jain  and
S. G. Mohanty
Walter Böhm*
Affiliation:
University of Economics, Vienna
J. L. Jain*
Affiliation:
University of Delhi
S. G. Mohanty*
Affiliation:
McMaster University, Hamilton
*
∗ Postal address: University of Economics, Institute of Statistics, Vienna, Austria.
∗∗ Postal address: Faculty of Mathematical Sciences, University of Delhi, Delhi 11007, India.
∗∗∗ Postal address: Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, Ont., Canada, L8S 4K1.
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Abstract

In this paper we present a simple combinatorial approach for the derivation of zero-avoiding transition probabilities in a Markovian r-node series Jackson network. The method we propose offers two advantages: first, it is conceptually simple because it is based on transition counts between the nodes and does not require a tensor representation of the network. Second, the method provides us with a very efficient technique for numerical computation of zero-avoiding transition probabilities.

Keywords

COMBINATORIAL METHODSLATTICE PATHS

MSC classification

Primary: 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.)
Secondary: 60K25: Queueing theory 90B15: Network models, stochastic
Type
Short Communications
Information
Journal of Applied Probability , Volume 30 , Issue 3 , September 1993 , pp. 737 - 741
Copyright
Copyright © Applied Probability Trust 1993 

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References

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