Queueing Network with Negative Customers and the Route Change

A queueing network with negative customers (G-network) is considered with the Poisson flow of positive customers, four types of nodes, and dependent service at different nodes. Every customer arriving at the network is determined by a set of random parameters: customer route, the length of customer route, customer size and its service time at each route stage as well. The arrival of a negative customer to a queuing system causes one of 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-network, the multidimensional stationary distribution of the network state probabilities is shown to be representable in the form of a product