The intercept term of the asymptotic variance curve for some queueing output processes

Hautphenne, Sophie, Kerner, Yoav, Nazarathy, Yoni and Taylor, Peter (2015) The intercept term of the asymptotic variance curve for some queueing output processes. European Journal of Operational Research, 242 2: 455-464. doi:10.1016/j.ejor.2014.10.051


Author Hautphenne, Sophie
Kerner, Yoav
Nazarathy, Yoni
Taylor, Peter
Title The intercept term of the asymptotic variance curve for some queueing output processes
Journal name European Journal of Operational Research   Check publisher's open access policy
ISSN 0377-2217
1872-6860
Publication date 2015-04-16
Year available 2014
Sub-type Article (original research)
DOI 10.1016/j.ejor.2014.10.051
Open Access Status
Volume 242
Issue 2
Start page 455
End page 464
Total pages 10
Place of publication Amsterdam, Netherlands
Publisher Elsevier
Collection year 2015
Language eng
Formatted abstract
We consider the output processes of some elementary queueing models such as the M/M/1/K queue and the M/G/1 queue. An important performance measure for these counting processes is their variance curve v(t), which gives the variance of the number of customers in the time interval [0, t]. Recent work has revealed some non-trivial properties dealing with the asymptotic rate at which the variance curve grows. In this paper we add to these results by finding explicit expressions for the intercept term of the linear asymptote. For M/M/1/K queues our results are based on the deviation matrix of the generator. It turns out that by viewing output processes as Markovian Point Processes and considering the deviation matrix, one can obtain explicit expressions for the intercept term, together with some further insight regarding the BRAVO (Balancing Reduces Asymptotic Variance of Outputs) effect. For M/G/1 queues our results are based on a classic transform of D. J. Daley. In this case we represent the intercept term of the variance curve in terms of the first three moments of the service time distribution. In addition we shed light on a conjecture of Daley, dealing with characterization of stationary M/M/1 queues within the class of stationary M/G/1 queues, based on the variance curve.
Keyword Queueing
M/M/1/K queue
M/G/1 queue
Markovian point process
Output processes
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ
Additional Notes Published online ahead of print 3 Nov 2014

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2015 Collection
 
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