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Polling in a Closed Network

Published online by Cambridge University Press:  27 July 2009

Eltan Altman  and
Uri Yechiali
Eltan Altman
Affiliation:
INRIA, Centre Sophia Antipolis, 06565 Valbonne Cedex, France
Uri Yechiali
Affiliation:
Department of Statistics and Operations Research, Tel-Aviv University, Tel-Aviv 69978, Israel
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Abstract

We consider a closed queueing network with a fixed number of customers, where a single server moves cyclically between N stations, rending service in each station according to some given discipline (Gated, Exhaustive, or the Globally Gated regime). When service of a customer (message) ends in station j, it is routed to station k with probability Pjk. We derive explicit expressions for the probability generating function and the moments of the number of customers at the various queues at polling instants and calculate the mean cycle duration and throughput for each service discipline. We then obtain the first moments of the queues' length at an arbitrary point in time. A few examples are given to illustrate the analysis. Finally, we address the problem of optimal dynamic control of the order of stations to be served.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 8 , Issue 3 , July 1994 , pp. 327 - 343
Copyright
Copyright © Cambridge University Press 1994

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References

1.Altman, E., Konstantopoulos, P., & Liu, Z. (1992). Stability, monotonicity and invariant quantities in general polling systems. Queuing Systems 11: 35–57.CrossRefGoogle Scholar
2.Bertsekas, D. & Gallager, R. (1987). Data networks. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
3.Boxma, O.J., Levy, H., & Yechiali, U. (1992). Cyclic reservation schemes for efficient operation of multiple-queue single-server systems. Annals of Operations Research 35: 187–208.CrossRefGoogle Scholar
4.Eisenberg, M. (1972). Queues with periodic service and changeover time. Operations Research 20: 440–451.CrossRefGoogle Scholar
5.Resing, J. (1993). Private communication.Google Scholar
6.Sidi, M., Levy, H., & Fuhrmann, S.W. (1992). A queueing network with a single cyclically roving server. Queuing Systems 11: 121–144.CrossRefGoogle Scholar
7.Takagi, H. (1986). Analysis of polling systems. Cambridge, MA: MIT Press.Google Scholar
8.Takagi, H. (1990). Queueing analysis of polling models: An update. In Takagi, H. (ed.), Stochastic analysis of computer and communication systems. Amsterdam: North-Holland, pp. 267–318.Google Scholar
9.Yechiali, U. (1993). Analysis and control of polling systems. In Donantiello, L. & Nelson, R. (eds.), Performance evaluation of computer and communications systems. New York: Springer-Verlag, pp. 630–650.CrossRefGoogle Scholar