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PRODUCT-FORM MARKOVIAN QUEUEING SYSTEMS WITH MULTIPLE RESOURCES

Published online by Cambridge University Press:  14 June 2019

Valeriy Naumov  and
Konstantin Samouylov
Valeriy Naumov
Affiliation:
Service Innovation Research Institute, Annankatu 8 A, 00120 Helsinki, Finland E-mail: valeriy.naumov@pfu.fi
Konstantin Samouylov
Affiliation:
Peoples' Friendship University of Russia (RUDN University), Miklukho-Maklaya St. 6, 117198 Moscow, Russian Federation E-mail: ksam@sci.pfu.edu.ru
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Abstract

In the paper, we study general Markovian models of loss systems with random resource requirements, in which customers at arrival occupy random quantities of various resources and release them at departure. Customers may request negative quantities of resources, but total amount of resources allocated to customers should be nonnegative and cannot exceed predefined maximum levels. Allocating a negative volume of a resource to a customer leads to a temporary increase in its volume in the system. We derive necessary and sufficient conditions for the product-form of the stationary probability distribution of the Markov jump process describing the system.

Keywords

loss systemMarkovian modelsmultiple resourcesrandom resource requirements
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 35 , Special Issue 1: Learning, Optimization, and Theory of G-Networks , January 2021 , pp. 180 - 188
Copyright
Copyright © Cambridge University Press 2019

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