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Product form solution for g-networkswith dependentservice

Published online by Cambridge University Press:  15 April 2004

Pavel Bocharov ,
Ciro D'Apice ,
Evgeny Gavrilov  and
Alexandre Pechinkin
Pavel Bocharov
Affiliation:
Department of Probability Theory and Mathematical Statistics Peoples' Friendship University of Russia, Moscow, Russia; pbocharov@sci.pfu.edu.ru.; tropic_mos@rambler.ru.
Ciro D'Apice
Affiliation:
Department of Information Engineering and Applied Mathematics, University of Salerno, Italy; dapice@diima.unisa.it.
Evgeny Gavrilov
Affiliation:
Department of Probability Theory and Mathematical Statistics Peoples' Friendship University of Russia, Moscow, Russia; pbocharov@sci.pfu.edu.ru.; tropic_mos@rambler.ru.
Alexandre Pechinkin
Affiliation:
Institute of Informatics Problems Russian Academy of Sciences Moscow, Russia; APechinkin@ipiran.ru.
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Abstract

We consider a G-network with Poisson flow of positive customers.Each positive customer entering the network is characterized bya set of stochastic parameters: customer route, the length of customer route,customer volume and his service length at each route stage aswell. The following node types are considered:Negative customers arriving at each node also form a Poisson flow.A negative customer entering a node with k customers in service, withprobability 1/k chooses one of served positivecustomer as a “target”. Then, if the node is of a type 0the negative customer immediately “kills” (displaces from the network)the target customer, and if the node is of types 1–3the negative customer with given probability depending on parameters of thetarget customer route kills this customer and with complementary probability hequits the network with no service.A product form for the stationary probabilities of underlyingMarkov process is obtained.

Type
Research Article
Information
RAIRO - Operations Research , Volume 38 , Issue 2: Advances in modelling of complex systems , April 2004 , pp. 105 - 119
Copyright
© EDP Sciences, 2004

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