We consider a G-netwotk with Poisson flow of positive customers. Each positive customer entering the network is characterised 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 cn 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 °ow. 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
Product form solution for G-networks with dependent service
D'APICE, Ciro;
2003-01-01
Abstract
We consider a G-netwotk with Poisson flow of positive customers. Each positive customer entering the network is characterised 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 cn 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 °ow. 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 obtainedI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
