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On Queueing Networks with Signals and History-Dependent Routing

Published online by Cambridge University Press:  27 July 2009

Xiuli Chao  and
Michael Pinedo
Xiuli Chao
Affiliation:
Department of Industrial and Manufacturing Engineering, New Jersey Institute of Technology, Newark, New Jersey 07102
Michael Pinedo
Affiliation:
Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027
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Abstract

This paper extends product form results for queueing networks with signals to allow history-dependent routing. The signals in these models carry information to nodes and induce multiple customers to move simultaneously within the network. Two models are studied in this paper. In the first one we assume that routing probabilities of a departing customer from a given class of nodes depend on the amount of service just received by the customer and whether its departure is the result of an actual service completion or the result of an arriving signal. In the second model we assume that the routing probabilities of a customer depend on the number of times this customer's service has been interrupted by signals in the past as well as the cause of its departure. We show that both models possess simple product form solutions. These results provide a new dimension in modeling and analyzing practical systems.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 9 , Issue 3 , July 1995 , pp. 341 - 354
Copyright
Copyright © Cambridge University Press 1995

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