Product Form Solution for a G-Network with Signals And Impatient Service

This paper presents some results on an exponential queuing network with signals and impatient service. Positive customers and signals arrive to each node according to a Poisson process. When the service is finished in a node, a positive customer moves to another node with fixed probabilities either as a positive customer or as a signal, or quits the network. Every signal is activated during a random exponentially distributed amount of time. Activated signals with fixed probabilities either move a customer from the node they arrive to another node or kill a positive a customer. Each customer can be served in a node at most a random time (“patient” time) distributed exponentially. When the patient service is finished, the customer with fixed probabilities state probabilities od such G-network in the case of positive customers processed by a single server in each node as well as in the case of an analogous symmetrical G-network in which service rate of a positive customer in a node depends on its state.