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On the stochastic domination for batch-arrival, batch-service and assemble-transfer queueing networks

Part of: Special processes Markov processes

Published online by Cambridge University Press:  14 July 2016

Antonis Economou
Antonis Economou*
Affiliation:
University of Athens
*
∗Postal address: Department of Mathematics, University of Athens, Panepistemiopolis, Athens 15784, Greece. Email address: [email protected]
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Abstract

Stochastic monotonicity properties for various classes of queueing networks have been established in the literature mainly with the use of coupling constructions. Miyazawa and Taylor (1997) introduced a class of batch-arrival, batch-service and assemble-transfer queueing networks which can be thought of as generalized Jackson networks with batch movements. We study conditions for stochastic domination within this class of networks. The proofs are based on a certain characterization of the stochastic order for continuous-time Markov chains, written in terms of their associated intensity matrices.

Keywords

Queueing networkstochastic orderbatch arrivalbatch serviceassemble transfer

MSC classification

Primary: 60K25: Queueing theory
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces 60J99: None of the above, but in this section
Type
Research Papers
Information
Journal of Applied Probability , Volume 40 , Issue 4 , September 2003 , pp. 1103 - 1120
Copyright
Copyright © Applied Probability Trust 2003 

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References

Chao, X. (1997). Partial balances in batch arrival batch service and assemble-transfer queueing networks. J. Appl. Prob. 34, 745–752.CrossRefGoogle Scholar
Chao, X., and Serfozo, R. (1998). Queueing networks with instantaneous sequential batch arrivals and sequential batch departures. Preprint.Google Scholar
Economou, A. (2000). A stochastic lower bound for assemble-transfer batch service queueing networks. J. Appl. Prob. 37, 881–889.Google Scholar
Economou, A. (2002). An alternative model for queueing systems with single arrivals, batch services and customer coalescence. Queueing Systems 40, 407–432.Google Scholar
Economou, A. (2003). Necessary and sufficient conditions for the stochastic comparison of Jackson networks. Prob. Eng. Inf. Sci. 17, 143–151.Google Scholar
Lindvall, T. (1992). Lectures on the Coupling Method. John Wiley, New York.Google Scholar
López, F. J., Martínez, S., and Sanz, G. (2000). Stochastic domination and Markovian couplings. Adv. Appl. Prob. 32, 1064–1076.Google Scholar
Massey, W. A. (1987). Stochastic orderings for Markov processes on partially ordered spaces. Math. Operat. Res. 12, 350–367.Google Scholar
Miyazawa, M., and Taylor, P. G. (1997) A geometric product-form distribution for a queueing network with non-standard batch arrivals and batch transfers. Adv. Appl. Prob. 29, 523–544.Google Scholar
Shaked, M., and Shanthikumar, J. G. (1994). Stochastic Orders and Their Applications. Academic Press, San Diego, CA.Google Scholar
Stoyan, D. (1983). Comparison Methods for Queues and Other Stochastic Models. John Wiley, Berlin.Google Scholar
Szekli, R. (1995). Stochastic Ordering and Dependence in Applied Probability (Lecture Notes Statist. 97). Springer, New York.Google Scholar
Yamashita, H., and Miyazawa, M. (1998). Geometric product form queueing networks with concurrent batch movements. Adv. Appl. Prob. 30, 1111–1129.CrossRefGoogle Scholar