G-networks with multiple classes of signals and positive customers

Abstract

G-networks are queueing models in which the types of customers one usually deals with in queues are enriched in several ways. In Gnetworks, positive customers are those that are ordinarily found in queueing systems; they queue up and wait for service, obtain service and then leave or go to some other queue. Negative customers have the specific function of destroying ordinary or positive customers. Finally triggers simply move an ordinary customer from one queue to the other. The term “signal” is used to cover negative customers and triggers. G-networks contain these three type of entities with certain restrictions; positive customers can move from one queue to another, and they can change into negative customers or into triggers when they leave a queue. On the other hand, signals (i.e. negative customers and triggers) do not queue up for service and simply disappear after having joined a queue and having destroyed or moved a negative customer. This paper considers this class of networks with multiple classes of positive customers and of signals. We show that with appropriate assumptions on service times, service disciplines, and triggering or destruction rules on the part of signals, these networks have a product form solution, extending earlier results.