G-networks with resets

Gelenbe Networks (G-networks) are a class of queuing models which include new types of customers called "signals," which are either "negative customers" and "triggers" [1, 2]. Queuing networks typically do not have provisions for some customers being used to eliminate other customers, or to redirect other customers among the queues. In other words, customers in traditional queuing netwroks cannot exert direct control on other customers. G-network models overcome some of these limitations and still preserve the computationally attractive "product form" property of certain Marovian queuing networks. In addition to ordinary customers, G-networks contain "negative customers" which eliminate normal customers, and "triggers" which move other customers from some queue to another [4, 5]. Multiple class versions of these models are discussed in [7, 8], and in [9] many additional results are provided. These queuing networks have generated much interest in the literature.