The variance of departure processes: Puzzling behavior and open problems

Nazarathy, Yoni (2011) The variance of departure processes: Puzzling behavior and open problems. Queueing Systems, 68 3: 385-394. doi:10.1007/s11134-011-9249-7

Author Nazarathy, Yoni
Title The variance of departure processes: Puzzling behavior and open problems
Journal name Queueing Systems   Check publisher's open access policy
ISSN 0257-0130
Publication date 2011-08
Sub-type Article (original research)
DOI 10.1007/s11134-011-9249-7
Volume 68
Issue 3
Start page 385
End page 394
Total pages 10
Place of publication Secaucus, NJ, United States
Publisher Springer New York
Collection year 2012
Language eng
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.
Keyword Asymptotic variance rate
Loss systems
Queueing theory
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status Non-UQ
Additional Notes From the issue entitled "Special Issue on Open Problems" Published online: 17 August 2011.

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
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Citation counts: TR Web of Science Citation Count  Cited 2 times in Thomson Reuters Web of Science Article | Citations
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Created: Fri, 27 Apr 2012, 12:40:53 EST by Kay Mackie on behalf of School of Mathematics & Physics