Decomposition of Queueing Networks with Dependent Service and Negative Customers

Queueing networks with negative customers (G-networks) and dependent service at different nodes are studied. Every customer arriving, at the network is defined by a set of random parameters: his route over the network (a sequence of nodes visited by the customers), of the route. For route length, and volume and service length of the customer at every stage of the route. For example, G-networks, which are the analogs of BCMP-networks, the multidimensional stationary distribution of the network state probabilities is shown to be representable in product form.