Improving the performance of polling models using forced idle times

TL;DR

This paper introduces four wait-and-see strategies for polling models where servers wait idly for new messages, improving average queueing delay performance under Poisson arrivals and general service times.

Contribution

It proposes novel wait-and-see strategies for polling models and derives formulas for mean delay, identifying when these strategies outperform traditional exhaustive approaches.

Findings

Wait-and-see strategies reduce mean delay in certain conditions.

Formulas for average queueing delay are derived.

Strategies outperform exhaustive approach under specific scenarios.

Abstract

We consider polling models in the sense of Takagi (MIT Press, 1986). In our case, the feature of the server is that it may be forced to wait idly for new messages at an empty queue instead of switching to the next station. We propose four different wait-and-see strategies that govern these waiting periods. We assume Poisson arrivals for new messages and allow general service and switchover time distributions. The results are formulas for the mean average queueing delay and characterisations of the cases where the wait-and-see strategies yield a lower delay compared to the exhaustive strategy.