Sojourn time distributions and time scale separation results for multiclass state-dependent processor sharing systems with a finite service pool and exponential service requirements

Giannoulakis, I; Kontovasilis, K; Mitrou, N

dc.contributor.author	Giannoulakis, I	en
dc.contributor.author	Kontovasilis, K	en
dc.contributor.author	Mitrou, N	en
dc.date.accessioned	2014-03-01T01:37:06Z
dc.date.available	2014-03-01T01:37:06Z
dc.date.issued	2011	en
dc.identifier.issn	0166-5316	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/21445
dc.subject	Model reduction	en
dc.subject	Nearly complete decomposability	en
dc.subject	Sojourn time distribution	en
dc.subject	State-dependent processor sharing	en
dc.subject	Time scale separation	en
dc.subject.classification	Computer Science, Hardware & Architecture	en
dc.subject.classification	Computer Science, Theory & Methods	en
dc.subject.other	Decomposability	en
dc.subject.other	Model reduction	en
dc.subject.other	Sojourn time distributions	en
dc.subject.other	State-dependent	en
dc.subject.other	Time scale separation	en
dc.subject.other	Customer satisfaction	en
dc.subject.other	Lakes	en
dc.subject.other	Probability distributions	en
dc.subject.other	Sales	en
dc.subject.other	Time measurement	en
dc.subject.other	Time sharing systems	en
dc.title	Sojourn time distributions and time scale separation results for multiclass state-dependent processor sharing systems with a finite service pool and exponential service requirements	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.peva.2011.03.008	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.peva.2011.03.008	en
heal.language	English	en
heal.publicationDate	2011	en
heal.abstract	The paper addresses multiclass processor sharing systems with general state-dependent service rates, exponential service requirements and a finite service pool. By considering the amount of service received by a permanent customer and associating this service with the evolution of a Markov Reward process, the sojourn time distribution is formulated in terms of a matrix exponential expression. When the service rates are balanced, this expression can be diagonalized. Tail asymptotics are also discussed. The matrix exponential expression is subsequently exploited towards the study of time scale separation regimes. Unlike the standard practice of assuming a distinct time scale per class, the paper groups more realistically all customer classes in two time scales. Provably tight approximations, of a known, small degree of error, are developed for the sojourn time distribution of a given class (with either fast or slow dynamics), in terms of reduced models containing only the customer classes operating in the same time scale. The approximation for the fast classes gives rise to further characterization of the tail behavior. Additionally, the paper studies another, more specialized variant of the time scale separation regime, in which the service rates take a special form that leads to even simpler approximations. Finally, it is shown that the essence of the main results applies also to the more general setting of service requirement distributions with Markovian phase-type form. (C) 2011 Elsevier B.V. All rights reserved.	en
heal.publisher	ELSEVIER SCIENCE BV	en
heal.journalName	Performance Evaluation	en
dc.identifier.doi	10.1016/j.peva.2011.03.008	en
dc.identifier.isi	ISI:000292074000003	en
dc.identifier.volume	68	en
dc.identifier.issue	7	en
dc.identifier.spage	586	en
dc.identifier.epage	613	en