Refined large deviations asymptotics for Markov-modulated infinite-server systems

Joke Blom, Koen De Turck and Michel Mandjes

European Journal of Operational Research, 2017, vol. 259, issue 3, 1036-1044

Abstract: Many networking-related settings can be modeled by Markov-modulated infinite-server systems. In such models, the customers’ arrival rates and service rates are modulated by a Markovian background process; additionally, there are infinitely many servers (and consequently the resulting model is often used as a proxy for the corresponding many-server model). The Markov-modulated infinite-server model hardly allows any explicit analysis, apart from results in terms of systems of (ordinary or partial) differential equations for the underlying probability generating functions, and recursions to obtain all moments. As a consequence, recent research efforts have pursued an asymptotic analysis in various limiting regimes, notably the central-limit regime (describing fluctuations around the average behavior) and the large-deviations regime (focusing on rare events). Many of these results use the property that the number of customers in the system obeys a Poisson distribution with a random parameter. The objective of this paper is to develop techniques to accurately approximate tail probabilities in the large-deviations regime. We consider the scaling in which the arrival rates are inflated by a factor N, and we are interested in the probability that the number of customers exceeds a given level Na. Where earlier contributions focused on so-called logarithmic asymptotics of this exceedance probability (which are inherently imprecise), the present paper improves upon those results in that exact asymptotics are established. These are found in two steps: first the distribution of the random parameter of the Poisson distribution is characterized, and then this knowledge is used to identify the exact asymptotics. The paper is concluded by a set of numerical experiments, in which the accuracy of the asymptotic results is assessed.

Keywords: Queueing; Communication networks; Markov-modulation; Rare events; Large deviations (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0377221716309006
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:259:y:2017:i:3:p:1036-1044

DOI: 10.1016/j.ejor.2016.10.050

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 ().