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

Sophie Hautphenne, Yoav Kerner, Yoni Nazarathy and Peter Taylor

European Journal of Operational Research, 2015, vol. 242, issue 2, 455-464

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.

Keywords: Queueing; M/M/1/K queue; M/G/1 queue; Markovian Point Process; Output processes (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S037722171400873X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:242:y:2015:i:2:p:455-464

DOI: 10.1016/j.ejor.2014.10.051

Access Statistics for this article

European Journal of Operational Research is currently edited by Roman Slowinski, Jesus Artalejo, Jean-Charles. Billaut, Robert Dyson and Lorenzo Peccati

More articles in European Journal of Operational Research from Elsevier
Bibliographic data for series maintained by Catherine Liu ().