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A Note on Queueing Networks with Signals and Random Triggering Times

Published online by Cambridge University Press:  27 July 2009

Xiuli Chao
Xiuli Chao
Affiliation:
Division of Industrial and Management Engineering, Department of Mechanical and Industrial Engineering, New Jersey Institute of Technology, Newark, New Jersey 07102
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Abstract

There is a growing interest in networks of queues with customers and signals. The signals in these models carry commands to the service nodes and trigger customers to move instantaneously within the network. In this note we consider networks of queues with signals and random triggering times; that is, when a signal arrives at a node, it takes a random amount of time to trigger a customer to move with distribution depending on the source of the signal. By appropriately choosing the triggering times, we can obtain network models such that a signal changes a customer's service time distribution – for example, the signal increases or decreases the service time of a customer. We show that the stationary distribution of this model has a product form solution.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 8 , Issue 2 , April 1994 , pp. 213 - 219
Copyright
Copyright © Cambridge University Press 1994

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References

1.Chao, X. (1992). Networks of queues with customers, signals and arbitrary service time distributions. Operations Research (to appear).Google Scholar
2.Chao, X. & Pinedo, M. (1993). Generalized networks of queues with positive and negative arrivals. Probability in the Engineering and Informational Sciences 7: 301–334.Google Scholar
3.Gelenbe, E. (1991). Product form queueing networks with negative and positive customers. Journal of Applied Probability 28: 656–663.Google Scholar
4.Kelly, F. (1979). Reversibility and stochastic networks. New York: Wiley & Sons.Google Scholar
5.Miyazawa, M. (1993). Insensitivity and product form decomposability of reallocatable GSMP. Advances in Applied Probability 25: 415–437.Google Scholar
6.Ross, S.M. (1993). Introduction to probability models, 5th ed.San Diego, CA: Academic Press.Google Scholar
7.Walrand, J. (1983). A probabilistic look at networks of quasi-reversible queues. IEEE Transactions on Information Theory IT-29: 825–831.CrossRefGoogle Scholar