Batch sojourn time in polling systems on a circle

TL;DR

This paper analyzes the expected waiting times and batch sojourn times in a circular polling system with randomly arriving customer batches and uniform locations, using mean value analysis.

Contribution

It provides a novel closed-form expression for mean batch sojourn time in a circular polling system with random batch arrivals.

Findings

Derived the expected number of waiting customers within a distance of the server

Obtained a closed-form expression for mean batch sojourn time

Analyzed the impact of system parameters on waiting times

Abstract

In this paper, we analyze a polling system on a circle. Random batches of customers arrive at a circle, where each customer, independently, obtains a uniform location. A single server cyclically travels over the circle to serve all customers. Using mean value analysis, we derive the expected number of waiting customers within a given distance of the server and a closed form expression for the mean batch sojourn time.