Wait-and-see strategies in polling models

  • Authors:

  • Frank Aurzada;Sergej Beck;Michael Scheutzow

  • Affiliations:

  • Technische universitä/t berlin, institut fü/r mathematik, 10623 berlin, germany. e-mail: aurzada@math.tu-berlin.de/ sergej.beck@hotmail.de/ ms@math.tu-berlin.de;Technische universitä/t berlin, institut fü/r mathematik, 10623 berlin, germany. e-mail: aurzada@math.tu-berlin.de/ sergej.beck@hotmail.de/ ms@math.tu-berlin.de;Technische universitä/t berlin, institut fü/r mathematik, 10623 berlin, germany. e-mail: aurzada@math.tu-berlin.de/ sergej.beck@hotmail.de/ ms@math.tu-berlin.de

  • Venue:
  • Probability in the Engineering and Informational Sciences
  • Year:
  • 2012

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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.