The variance of departure processes: puzzling behavior and open problems

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Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.3/202142

Title: The variance of departure processes: puzzling behavior and open problems
Author(s): Nazarathy, Yoni
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.
Publication type: Journal article
Source: Queueing Systems, Vol. 68, no. 3 (Aug 2011), pp. 385-394
Publication year: 2011
FOR Code(s): 0102 Applied Mathematics; 0103 Numerical and Computational Mathematics; 0104 Statistics
Keyword(s): Asymptotic variance rate; BRAVO; Loss systems; Queueing theory
Publisher: Springer
ISSN: 0257-0130
Publisher URL: http://dx.doi.org/10.1007/s11134-011-9249-7
Peer reviewed