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WAIT-AND-SEE STRATEGIES IN POLLING MODELS

Published online by Cambridge University Press:  25 November 2011

Frank Aurzada ,
Sergej Beck  and
Michael Scheutzow
Frank Aurzada
Affiliation:
Technische Universität Berlin, Institut für Mathematik, 10623 Berlin, Germany. E-mail: [email protected]; [email protected]; [email protected]
Sergej Beck
Affiliation:
Technische Universität Berlin, Institut für Mathematik, 10623 Berlin, Germany. E-mail: [email protected]; [email protected]; [email protected]
Michael Scheutzow
Affiliation:
Technische Universität Berlin, Institut für Mathematik, 10623 Berlin, Germany. E-mail: [email protected]; [email protected]; [email protected]
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Abstract

We consider a general polling model with N stations. The stations are served exhaustively and in cyclic order. Once a station queue falls empty, the server does not immediately switch to the next station. Rather, it waits at the station for the possible arrival of new work (“wait-and-see”) and, in the case of this happening, it restarts service in an exhaustive fashion. The total time the server waits idly is set to be a fixed, deterministic parameter for each station. Switchover times and service times are allowed to follow some general distribution, respectively. In some cases, which can be characterized, this strategy yields a strictly lower average queuing delay than for the exhaustive strategy, which corresponds to setting the “wait-and-see credit” equal to zero for all stations. This extends the results of Peköz [12] and of Boxma et al. [4]. Furthermore, we give a lower bound for the delay for all strategies that allow the server to wait at the stations even though no work is present.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 26 , Issue 1 , January 2012 , pp. 17 - 42
Copyright
Copyright © Cambridge University Press 2011

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