A two-queue Markovian polling system with two priority levels in the first queue

TL;DR

This paper analyzes a Markovian two-queue polling system with priority levels, deriving exact and asymptotic performance measures, including heavy-traffic and large switch-over time scenarios, supported by simulations.

Contribution

It introduces the first analysis of scaled delays with large switch-over times in Markovian polling systems, extending existing heavy-traffic results.

Findings

Derived exact joint queue length distributions.

Established asymptotic delay behavior in heavy traffic.

Analyzed effects of large switch-over times on delays.

Abstract

In this paper, we deal with a two-queue polling system attended by a single server. The server visits the queues according to a Markovian routing mechnism. There are two-class customers in the first queue. Customers of each queue are served in the exhaustive discipline. For this model, we study the joint number of customers, the cycle time and the waiting times. we are also devoted to deriving the exact asymptotics for the scaled delay in the heavy-traffic scenario. In addition, the scaled delays with large switch-over times are discussed for the first time in the Markovian polling systems. Finally, we provide some simulations to surpport the asymptotic results.