The variance of departure processes: puzzling behavior and open problems

The variance of departure processes: puzzling behavior and open problems

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Article ID: iaor20119081
Volume: 68
Issue: 3
Start Page Number: 385
End Page Number: 394
Publication Date: Aug 2011
Journal: Queueing Systems
Authors:
Keywords: GI/G/1 queues, M/M/1 queues
Abstract:

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.

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