G-Networks with Multiple Classes of Negative and Positive Customers

Abstract In recent years a new class of queueing networks with “negative and positive” customers was introduced by one of the authors [5], and shown to have a nonstandard product form. This model has undergone several generalizations to include triggers or signals which are special forms of customers whose role is to move other customers from some queue to another queue [9, 10, 6, 7]. Positive customers are identical to the usual customers of a queueing network, while a negative customer which arrives to a queue simply destroys a positive customer. We call these generalized queueing networks G-networks. In this paper we extend the basic model of [5] to the case of multiple classes of positive customers, and multiple classes of negative customers. As in other multiple class queueing networks, a positive customer class is characterized by the routing probabilities and the service rate parameter at each service center while negative customers of different classes may have different “customer destruction” capabilities. In the present paper all service time distributions are exponential and the service centers can be of the following types: FIFO (first-in-first-out), LIFO/PR (last-in-first-out with preemption), PS (processor sharing), with class-dependent service rates.