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.

^{}; D'Apice, Ciro

^{}; Gavrilov, Evgeny

^{}; Pechinkin, Alexandre

^{1}

@article{RO_2004__38_2_105_0, author = {Bocharov, Pavel and D'Apice, Ciro and Gavrilov, Evgeny and Pechinkin, Alexandre}, title = {Product form solution for g-networks with dependent service}, journal = {RAIRO - Operations Research - Recherche Op\'erationnelle}, pages = {105--119}, publisher = {EDP-Sciences}, volume = {38}, number = {2}, year = {2004}, doi = {10.1051/ro:2004015}, zbl = {1092.90010}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/ro:2004015/} }

TY - JOUR AU - Bocharov, Pavel AU - D'Apice, Ciro AU - Gavrilov, Evgeny AU - Pechinkin, Alexandre TI - Product form solution for g-networks with dependent service JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2004 SP - 105 EP - 119 VL - 38 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ro:2004015/ DO - 10.1051/ro:2004015 LA - en ID - RO_2004__38_2_105_0 ER -

%0 Journal Article %A Bocharov, Pavel %A D'Apice, Ciro %A Gavrilov, Evgeny %A Pechinkin, Alexandre %T Product form solution for g-networks with dependent service %J RAIRO - Operations Research - Recherche Opérationnelle %D 2004 %P 105-119 %V 38 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ro:2004015/ %R 10.1051/ro:2004015 %G en %F RO_2004__38_2_105_0

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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