Heavy traffic limits for queues with non-stationary path-dependent arrival processes

Kerry Fendick () and Ward Whitt ()
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Kerry Fendick: Johns Hopkins University Applied Physics Laboratory
Ward Whitt: Columbia University

Queueing Systems: Theory and Applications, 2022, vol. 101, issue 1, No 4, 113-135

Abstract: 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.

Keywords: Path-dependent stochastic processes; Generalized Polya process; Gaussian Markov process; Diffusion approximations; Queues; Heavy-traffic limit; Primary 60K25; Secondary 60F17; 90B22 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11134-021-09728-5

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