G-network with the route change

Queueing networks with negative customers (G-networks), Poisson flow of positive customers, non-exponential nodes, and dependent service at the different nodes are under consideration. Every customer arriving at the network is defined by a set of random parameters: customer route, the length of customer route, customer volume and its service time at each route stage as well. The arrival of a negative customer to a queuing system causes one of the ordinary (or “positive”) customers to be removed (or “killed”) if any is present. The “killed” customer continues its way along the new random route. For such G-networks, the multidimensional stationary distribution of the network state probabilities is shown to be representable in product form.