# Heavy traffic limit for the workload plateau process in a tandem queue with identical service times

## TL;DR

This paper analyzes the heavy traffic limit behavior of the workload plateau process in a two-node tandem queue with identical service times, especially under infinite-variance conditions, revealing convergence to a Levy process-based limit.

## Contribution

It introduces the plateau process for workload analysis in tandem queues and establishes its convergence to a Levy process-based limit under heavy traffic with infinite-variance service times.

## Key findings

- Workload in the first queue converges under scaling.
- The plateau process converges to a Levy process-based limit.
- Comparison with previous limit processes using excursion theory.

## Abstract

We consider a two-node tandem queueing network in which the upstream queue is GI/GI/1 and each job reuses its upstream service requirement when moving to the downstream queue. Both servers employ the first-in-first-out policy. To investigate the evolution of workload in the second queue, we introduce and study a process M, called the plateau process, which encodes most of the information in the workload process. We focus on the case of infinite-variance service times and show that under appropriate scaling, workload in the first queue converges, and although the workload in the second queue does not converge, the plateau process does converges to a limit that is a certain function of two independent Levy processes. Using excursion theory, we compare a time changed version of the limit to a limit process derived in previous work.