The variance of departure processes : puzzling behavior and open problems

Y. Nazarathy

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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/pi) 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 coeffcients of variations of the inter-arrival and service times.
Original languageEnglish
Place of PublicationEindhoven
PublisherEurandom
Number of pages9
Publication statusPublished - 2009

Publication series

NameReport Eurandom
Volume2009045
ISSN (Print)1389-2355

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