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

Part of: Operations research and management science Special processes

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

Information

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

Baccelli, F. and Massey, W. A. (1990) A transient analysis of the two-node series Jackson network. Technical Report, INRIA-Sophia, France.Google Scholar
Barton, D. E. and Mallows, C. L. (1965) Some aspects of a random sequence. Ann. Math. Statist. 36, 236–260.Google Scholar
Kreweras, G. (1965) Sur une classe de problèmes de dénombrement liés au treillis des partitions de entiers. Cahiers Bur. Univ. Rech. Opér. 6, 5–105.Google Scholar
Massey, W. A. (1984) An operator analytic approach to the Jackson network. J. Appl. Prob. 21, 379–393.Google Scholar
Massey, W. A. (1987) Calculating exit times for series Jackson networks. J. Appl. Prob. 27, 226–234.Google Scholar
McMahon, P. A. (1915) Combinatory Analysis, Vol. 1. Cambridge University Press.Google Scholar
Watanabe, T. and Mohanty, S. G. (1987) On an inclusion-exclusion formula based on the reflection principle. Discrete Math. 64, 281–288.Google Scholar
Zeilberger, D. (1983) Andre's reflection proof generalized to the many candidate ballot problem. Discrete Math. 44, 325–326.Google Scholar