  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.
