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), route length, and volume and service length of the customer at every stage of the route. For 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.