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We consider a two-node tandem queueing network in which the upstream queue isGI/GI/1 and each job reuses its upstream service requirement when moving to thedownstream queue. Both servers employ the first-in-first-out policy. Toinvestigate the evolution of workload in the second queue, we introduce andstudy a process M, called the plateau process, which encodes most of theinformation in the workload process. We focus on the case of infinite-varianceservice times and show that under appropriate scaling, workload in the firstqueue converges, and although the workload in the second queue does notconverge, the plateau process does converges to a limit that is a certainfunction of two independent Levy processes. Using excursion theory, we comparea time changed version of the limit to a limit process derived in previouswork.

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