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WAIT-AND-SEE STRATEGIES IN POLLING MODELS

Published online by Cambridge University Press:  25 November 2011

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]

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
Copyright
Copyright © Cambridge University Press 2011

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