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Continuous Polling on Graphs

Published online by Cambridge University Press:  27 July 2009

E. G. Coffman Jr  and
Aleksandr Stolyar
E. G. Coffman Jr
Affiliation:
AT & T Bell Laboratories, Murray Hill, New Jersey 07974
Aleksandr Stolyar
Affiliation:
Institute of Control Sciences, Profsoyuznaya ul. 65, GSP-312 Moscow, Russia
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Abstract

Past research on polling systems has been quite restricted in the form of the paths followed by the server. This paper formulates a general, continuous model of such paths that includes closed walks on graphs. Customers arrive by a Poisson process and have general service times. The distribution of arrivals over the path is governed by an absolutely continuous, but otherwise arbitrary, distribution. The main results include a characterization of the stationary state distribution and explicit formulas for expected waiting times. The formulas reveal an interesting decomposition of the system into two components: a fluid limit and an M/G/1 queue.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 7 , Issue 2 , April 1993 , pp. 209 - 226
Copyright
Copyright © Cambridge University Press 1993

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References

1.Coffman, E.G. Jr. & Gilbert, E.N. (1986). A continuous polling system with constant service times. IEEE Transactions on Information Theory IT-32: 584–591.CrossRefGoogle Scholar
2.Coffman, E.G. Jr. & Gilbert, E.N. (1987). Polling and greedy servers on the line. Queueing Systems 2: 115–145.CrossRefGoogle Scholar
3.Fuhrmann, S.W. & Cooper, R.B. (1985). Application of the decomposition principle in M/G/1 vacation models to two continuum cyclic queueing models—Especially token-ring LANs. AT&T Technology Journal 64: 1091–1098.Google Scholar
4.Fuhrmann, S.W. & Cooper, R.B. (1985). Stochastic decompositions in the M/G/1 queue with generalized vacations. Operations Research 33: 1117–1129.CrossRefGoogle Scholar
5.Konheim, A.C. & Levy, H. (1992). Descendant set: An efficient approach for the analysis of polling systems. Preprint. Department of Computer Science, Tel Aviv University, Israel.Google Scholar
6.Kroese, D.P. & Schmidt, V. (1992). A continuous polling system with general service times. Annals of Applied Probability 2: 906–927.CrossRefGoogle Scholar