Product form solution for g-networks with dependent service
RAIRO - Operations Research - Recherche Opérationnelle, Volume 38 (2004) no. 2, pp. 105-119.

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: (0) an exponential node with c n servers, infinite buffer and FIFO discipline; (1) an infinite-server node; (2) a single-server node with infinite buffer and LIFO PR discipline; (3) a single-server node with infinite buffer and PS discipline. 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.

DOI: 10.1051/ro:2004015
Bocharov, Pavel ; D'Apice, Ciro ; Gavrilov, Evgeny ; Pechinkin, Alexandre 1

1 Institute of Informatics Problems Russian Academy of Sciences Moscow, Russia
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Bocharov, Pavel; D'Apice, Ciro; Gavrilov, Evgeny; Pechinkin, Alexandre. Product form solution for g-networks with dependent service. RAIRO - Operations Research - Recherche Opérationnelle, Volume 38 (2004) no. 2, pp. 105-119. doi : 10.1051/ro:2004015. http://archive.numdam.org/articles/10.1051/ro:2004015/

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