Heavy Traffic Limit for a Tandem Queue with Identical Service Times

TL;DR

This paper analyzes the behavior of a tandem queueing system with identical service times under heavy traffic conditions, deriving a limit process for the workload in the second queue when service times have infinite variance.

Contribution

It provides a novel heavy traffic limit theorem for a tandem queue with infinite-variance service times, focusing on embedded Markov chain analysis at specific arrival times.

Findings

Heavy traffic process limit established for the second queue

Results applicable to systems with infinite-variance service times

Insights into workload behavior at embedded time points

Abstract

We consider a two-node tandem queueing network in which the upstream queue is M/G/1 and each job reuses its upstream service requirement when moving to the downstream queue. Both servers employ the first-in-first-out policy. We investigate the amount of work in the second queue at certain embedded arrival time points, namely when the upstream queue has just emptied. We focus on the case of infinite-variance service times and obtain a heavy traffic process limit for the embedded Markov chain.