Abstract
We study the flow of jobs on an infinite series of first-come-first-served queues. Jobs are placed in the buffer of the first queue and allowed to flow through the infinite tandem of queues. The service times of each job on consecutive queues form a stationary and ergodic sequence. We are interested in characterizing the flow of jobs asymptotically, after they have passed through a large number of queues. It is shown that the job flow reaches asymptotically a stationary state, which can be characterized in terms of the average service times of the jobs. They eventually form clusters, such that every two consecutive jobs belonging to the same cluster collide infinitely often, while jobs belonging to different clusters eventually cease to interact.
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