Product form solution for generalized-networks with dependent service

We consider a generalised-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 customers 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.