Mixed Gated/Exhaustive Service in a Polling Model with Priorities

TL;DR

This paper introduces a mixed gated/exhaustive service discipline for polling systems with priorities, improving high-priority customer wait times with minimal impact on low-priority customers, especially with larger switch-over times.

Contribution

It proposes a novel mixed service discipline for priority queues in polling systems and analyzes its impact on various performance metrics.

Findings

High priority customer waiting times decrease significantly.

Low priority customer waiting times are minimally affected or improved in some cases.

The discipline is especially beneficial in systems with larger switch-over times.

Abstract

In this paper we consider a single-server polling system with switch-over times. We introduce a new service discipline, mixed gated/exhaustive service, that can be used for queues with two types of customers: high and low priority customers. At the beginning of a visit of the server to such a queue, a gate is set behind all customers. High priority customers receive priority in the sense that they are always served before any low priority customers. But high priority customers have a second advantage over low priority customers. Low priority customers are served according to the gated service discipline, i.e. only customers standing in front of the gate are served during this visit. In contrast, high priority customers arriving during the visit period of the queue are allowed to pass the gate and all low priority customers before the gate. We study the cycle time distribution, the waiting time distributions for each customer type, the joint queue length distribution of all priority classes at all queues at polling epochs, and the steady-state marginal queue length distributions for each customer type. Through numerical examples we illustrate that the mixed gated/exhaustive service discipline can significantly decrease waiting times of high priority jobs. In many cases there is a minimal negative impact on the waiting times of low priority customers but, remarkably, it turns out that in polling systems with larger switch-over times there can be even a positive impact on the waiting times of low priority customers.