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The BRAVO Effect in Queues

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If you have a question about this talk, please contact Felix Fischer.

BRAVO stands for “Balancing Reduces Asymptotic Variance of Outputs”. Consider for example a stationary M/M/1/K queue and study the counting process of served customers. If the arrival rate is much lower than the service rate then the output process is “Poissonish”. For example the ratio of the variance of the number of outputs to the mean number of outputs is approximately unity. Similarly if the arrival rate is much higher than the service rate. But when the queue is balanced in the sense that the arrival rate is approximately equal to the service rate then this asymptotic variance ratio is approximately two thirds. This is BRAVO ! It turns out that this type of puzzling behavior occurs in a variety of queueing models.

In this talk we survey some results quantifying BRAVO as well as other aspects of queueing output processes.

This talk is part of the Optimization and Incentives Seminar series.

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