The BRAVO Effect in Queues
Yoni Nazarathy

BRAVO stands for "Balancing Asymptotic Variance Rate of Outputs". It is a ubiquitous phenomenon for many queueing systems. When a queueing system is operated at criticality such that the arrival rate is similar to the service rate, the long term variability of the number of outputs from the system exhibits a sharp drop in comparison to the operation of the system in a non-critical regime.

These are my publications related to BRAVO.

• On Busy Periods of the Critical GI/G/1 Queue and BRAVO, by Y. Nazarathy and Z. Palmowski. Appears in arXiv:2203.15456.
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• The variance of departure processes: puzzling behavior and open problems, by Yoni Nazarathy. Published in Queueing Systems.
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• The asymptotic variance of departures in critically loaded queues, by Ahmad Al Hanbali, Michel Mandjes, Yoni Nazarathy, Ward Whitt. Published in Advances in Applied Probability.
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• The asymptotic variance rate of the output process of finite capacity birth-death queues, by Yoni Nazarathy, Gideon Weiss. Published in Queueing Systems.
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• Diffusion Parameters of Flows in Stable Multi-class Queueing Networks, by Sarat Moka, Yoni Nazarathy, and Werner Scheinhardt. Appears in arXiv:1311.5610.
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• The intercept term of the asymptotic variance curve for some queueing output processes, by Sophie Hautphenne, Yoav Kerner, Yoni Nazarathy, and Peter Taylor. Appears in European Journal of Operational Research.
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• BRAVO for many-server QED systems with finite buffers, by Daryl J Daley, Johan SH Van Leeuwaarden, and Yoni Nazarathy. Appears in Advances in Applied Probability.
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There are still multiple open problems associated with the BRAVO effect.