Queueing Systems

, 68:385 | Cite as

The variance of departure processes: puzzling behavior and open problems



We consider the variability of queueing departure processes. Previous results have shown the so-called BRAVO effect occurring in M/M/1/K and GI/G/1 queues: Balancing Reduces Asymptotic Variance of Outputs. A factor of (1−2/π) appears in GI/G/1 and a factor of 1/3 appears in M/M/1/K, for large K. A missing piece in the puzzle is the GI/G/1/K queue: Is there a BRAVO effect? If so, what is the variability? Does 1/3 play a role?

This open problem paper addresses these questions by means of numeric and simulation results. We conjecture that at least for the case of light tailed distributions, the variability parameter is 1/3 multiplied by the sum of the squared coefficients of variations of the inter-arrival and service times.


Queueing theory Loss systems Asymptotic variance rate BRAVO 

Mathematics Subject Classification (2000)

60J27 60K25 


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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Mathematics, FEISSwinburne University of TechnologyHawthornAustralia

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