Issue RAIRO Oper. Res. Volume 38, Number 2, April-June 2004 Advances in modelling of complex systems Page(s) 105 - 119 DOI 10.1051/ro:2004015

RAIRO Oper. Res. 38 (2004) 105-119
DOI: 10.1051/ro:2004015

Product form solution for g-networks with dependent service

Pavel Bocharov¹, Ciro D'Apice², Evgeny Gavrilov¹ and Alexandre Pechinkin<sup>3

1</sup>  Department of Probability Theory and Mathematical Statistics Peoples' Friendship University of Russia, Moscow, Russia; pbocharov@sci.pfu.edu.ru; tropic_mos@rambler.ru.
²  Department of Information Engineering and Applied Mathematics, University of Salerno, Italy; dapice@diima.unisa.it.
³  Institute of Informatics Problems Russian Academy of Sciences Moscow, Russia; APechinkin@ipiran.ru.

Abstract
We consider a G-network with Poisson flow of positive customers. Each positive customer entering the network is characterized by a set of stochastic parameters: customer route, the length of customer route, customer volume and his service length at each route stage as well. 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, with probability 1/k chooses one of served positive customer as a "target". Then, if the node is of a type 0 the negative customer immediately "kills" (displaces from the network) the target customer, and if the node is of types 1-3 the negative customer with given probability depending on parameters of the target customer route kills this customer and with complementary probability he quits the network with no service. A product form for the stationary probabilities of underlying Markov process is obtained.

© EDP Sciences 2004

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