Conditional Waiting Time Analysis in Tandem Polling Queues

TL;DR

This paper develops a method to accurately analyze the mean conditional waiting time in a tandem polling queue network with Poisson arrivals and exponential service times, using a sample path approach.

Contribution

It introduces a novel sample path analysis technique to compute conditional waiting times in tandem polling queues, enhancing understanding of customer wait dynamics.

Findings

The method provides accurate conditional waiting time estimates.

Numerical studies demonstrate the approach's practical relevance.

The analysis reveals structural insights into queue dynamics.

Abstract

We analyze a tandem network of polling queues with two product types and two stations. We assume that external arrivals to the network follow a Poisson process, and service times at each station are exponentially distributed. For this system, we determine the mean conditional waiting time for an arriving customer using a sample path analysis approach. The approach classifies system state upon arrival into scenarios and exploits an inherent structure in the sequence of events that occur till the customer departs to obtain conditional waiting time estimates. We conduct numerical studies to show both the accuracy of our conditional waiting time estimates and their practical importance.