A heavy-traffic perspective on departure process variability

Peter W. Glynn and Rob J. Wang

Stochastic Processes and their Applications, 2023, vol. 166, issue C

Abstract: This paper studies the departure process from a single-server queue in heavy-traffic over time scales that are of diffusion time scale, and over time scales that are both shorter and longer than diffusion time scale. In addition, the paper shows how one can compute the variance of such Brownian departure processes using stochastic calculus methods. Furthermore, the paper studies the implications of these results for downstream queues that are fed by such departure processes, and shows that downstream equilibrium congestion depends on upstream departure variability over the downstream queue’s characteristic heavy traffic time scale. These results also shed further light on the discontinuity in departure process asymptotic variability that is known as the BRAVO effect.

Keywords: Asymptotic variability; Reflected Brownian motion; Departure processes; BRAVO effect; Heavy-traffic analysis; Tandem networks (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spa.2023.01.002

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