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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

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