G-networks: A versatile approach for work removal in queueing networks

Abstract

G-networks (or queueingnetworks with negative customers, signals, triggers, etc.) are characterized by the following feature: in contrast with the normal positive customers, negative customers arriving to a non-empty queue remove an amount of work from the queue. In its simplest version, a negative customer deletes an ordinary positive customer according to some strategy. Extensions of the model result when a negative customer removes a random batch of customers, all the work from the queue or indeed a random amount of work that does not necessarily correspond to an integer number of positive customers. Since Gelenbe (E. Gelenbe, Neural Computation 1 (1989) 502–510; E. Gelenbe, Journal of Applied Probability 28 (1991) 656–663) introduced the notion of negative customers, there has been an increasing interest not only in queueingnetworks but also in the single server node case. Significant progress in the analysis of this versatile class of networks has enriched queueing theory as well as contributed to the development of real applications in fields such as computers, communications and manufacturing. This paper presents a survey of the main results and methods of the theory of G-networks.