Distribution of Processor-Sharing Customers for a Large Closed System with Multiple Classes

A closed processor-sharing (PS) system with multiple customer classes is considered. The system consists of one infinite server (IS) station and one PS station. For a system with a large number of customers, a saturated PS station, and an arbitrary number of customer classes, asymptotic approximatio...

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Bibliographische Detailangaben
Veröffentlicht in:	SIAM Journal on Applied Mathematics. - Society for Industrial and Applied Mathematics, 1966. - 60(2000), 4, Seite 1330-1339
1. Verfasser:	Berger, Arthur (VerfasserIn)
Weitere Verfasser:	Kogan, Yaakov
Format:	Online-Aufsatz
Sprache:	English
Veröffentlicht:	2000
Zugriff auf das übergeordnete Werk:	SIAM Journal on Applied Mathematics
Schlagworte:	Heavy traffic approximation Queueing theory S0036139998346063 Mathematics Applied sciences Behavioral sciences


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245	1	0	\|a Distribution of Processor-Sharing Customers for a Large Closed System with Multiple Classes
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520			\|a A closed processor-sharing (PS) system with multiple customer classes is considered. The system consists of one infinite server (IS) station and one PS station. For a system with a large number of customers, a saturated PS station, and an arbitrary number of customer classes, asymptotic approximations to the stationary distribution of the total number of customers at the PS station are derived. The asymptotics for the probability mass function is described by a quasipotential function, which defines the exponential decay for the distribution, and a state-dependent preexponential factor. Both functions have an explicit expression in terms of the solution at each point x of a polynomial equation whose order equals the number of classes and whose coefficients are explicit functions of x. The quasi-potential function at its minimum point provides the logarithmic asymptotics for the normalization constant, and the asymptotic approximation for the variance is inversely proportional to the second derivative of the quasi-potential function at its minimum point. The complementary probability distribution is computed using the normal approximation and its refinements, which do not require repeated solution of polynomial equations. Numerical results demonstrate the range of applicability of the approximations. The results can be applied to the problem of dimensioning bandwidth and of admission control for different data sources in packet-switched communication networks.
540			\|a Copyright 2000 Society for Industrial and Applied Mathematics
650		4	\|a Heavy traffic approximation
650		4	\|a Queueing theory
650		4	\|a S0036139998346063
650		4	\|a Mathematics \|x Mathematical procedures \|x Approximation
650		4	\|a Applied sciences \|x Systems science \|x Closed systems
650		4	\|a Mathematics \|x Applied mathematics \|x Statistics \|x Applied statistics \|x Descriptive statistics \|x Statistical distributions \|x Distribution functions \|x Probability distributions
650		4	\|a Mathematics \|x Applied mathematics \|x Statistics \|x Applied statistics \|x Descriptive statistics \|x Statistical distributions \|x Distribution functions \|x Probability distributions \|x Discrete probability distributions \|x Probability mass distributions
650		4	\|a Mathematics \|x Mathematical expressions
650		4	\|a Mathematics \|x Pure mathematics \|x Algebra \|x Polynomials
650		4	\|a Behavioral sciences \|x Psychology \|x Cognitive psychology \|x Decision theory \|x Operations research \|x Queuing theory \|x Queueing networks
650		4	\|a Mathematics \|x Mathematical expressions \|x Mathematical functions \|x Hypergeometric functions \|x Generating function
650		4	\|a Mathematics
650		4	\|a Applied sciences \|x Computer science \|x Computer engineering \|x Computer networking \|x Network servers
655		4	\|a research-article
700	1		\|a Kogan, Yaakov \|e verfasserin \|4 aut
773	0	8	\|i Enthalten in \|t SIAM Journal on Applied Mathematics \|d Society for Industrial and Applied Mathematics, 1966 \|g 60(2000), 4, Seite 1330-1339 \|w (DE-627)266884121 \|w (DE-600)1468266-7 \|x 00361399 \|7 nnns
773	1	8	\|g volume:60 \|g year:2000 \|g number:4 \|g pages:1330-1339
856	4	0	\|u https://www.jstor.org/stable/118553 \|3 Volltext
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952			\|d 60 \|j 2000 \|e 4 \|h 1330-1339