Wait-and-see strategies in polling models

TL;DR

This paper analyzes a polling model with a wait-and-see strategy where the server waits at empty stations for a fixed time, showing it can reduce delays compared to traditional exhaustive service under certain conditions.

Contribution

It extends existing polling model results by characterizing when wait-and-see strategies outperform exhaustive service and provides a lower bound for delays with such strategies.

Findings

Wait-and-see can lower average queue delays under certain conditions.

The strategy's effectiveness depends on the fixed waiting times at stations.

A lower bound for delays in strategies allowing waiting at empty stations is established.

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 characterised, this strategy yields strictly lower average queueing delay than for the exhaustive strategy, which corresponds to setting the "wait-and-see credit" equal to zero for all stations. This extends results of Pek\"oz (Probability in the Engineering and Informational Sciences 13 (1999)) and of Boxma et al. (Annals of Operations Research 112 (2002)). Furthermore, we give a lower bound for the delay for {\it all} strategies that allow the server to wait at the stations even though no work is present.