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A heavy-traffic perspective on departure process variability

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  • Glynn, Peter W.
  • Wang, Rob J.

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.

Suggested Citation

  • Glynn, Peter W. & Wang, Rob J., 2023. "A heavy-traffic perspective on departure process variability," Stochastic Processes and their Applications, Elsevier, vol. 166(C).
    • Handle: RePEc:eee:spapps:v:166:y:2023:i:c:s0304414923000029
    DOI: 10.1016/j.spa.2023.01.002
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    References listed on IDEAS

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    1. Harrison, J. Michael & Shepp, L. A., 1984. "A tandem storage system and its diffusion limit," Stochastic Processes and their Applications, Elsevier, vol. 16(3), pages 257-274, March.
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    6. Peter W. Glynn & Rob J. Wang, 2018. "On the rate of convergence to equilibrium for reflected Brownian motion," Queueing Systems: Theory and Applications, Springer, vol. 89(1), pages 165-197, June.
    7. Ward Whitt & Wei You, 2020. "Heavy-traffic limits for stationary network flows," Queueing Systems: Theory and Applications, Springer, vol. 95(1), pages 53-68, June.
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