# Product form solution for g-networks with dependent service

Pavel Bocharov; Ciro D'Apice; Evgeny Gavrilov; Alexandre Pechinkin

RAIRO - Operations Research (2010)

- Volume: 38, Issue: 2, page 105-119
- ISSN: 0399-0559

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topBocharov, Pavel, et al. " Product form solution for g-networks with dependent service ." RAIRO - Operations Research 38.2 (2010): 105-119. <http://eudml.org/doc/105304>.

@article{Bocharov2010,

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.
},

author = {Bocharov, Pavel, D'Apice, Ciro, Gavrilov, Evgeny, Pechinkin, Alexandre},

journal = {RAIRO - Operations Research},

language = {eng},

month = {3},

number = {2},

pages = {105-119},

publisher = {EDP Sciences},

title = { Product form solution for g-networks with dependent service },

url = {http://eudml.org/doc/105304},

volume = {38},

year = {2010},

}

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

DA - 2010/3//

PB - EDP Sciences

VL - 38

IS - 2

SP - 105

EP - 119

AB -
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.

LA - eng

UR - http://eudml.org/doc/105304

ER -

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