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Heavy traffic limits for queues with non-stationary path-dependent arrival processes
1Communications System Branch, Johns Hopkins University Applied Physics Laboratory, Laurel, MD 20723 USA.
Abstract:
In this paper, we develop a diffusion approximation for the transient distribution of the workload process in a standard single-server queue with a non-stationary Polya arrival process, which is a path-dependent Markov point process. The path-dependent arrival process model is useful because it has the arrival rate depending on the history of the arrival process, thus capturing a self-reinforcing property that one might expect in some applications. The workload approximation is based on heavy-traffic limits for (i) a sequence of Polya processes, in which the limit is a Gaussian-Markov process, and (ii) a sequence of P/GI/1 queues in which the arrival rate function approaches a constant service rate uniformly over compact intervals.
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