Geometric equilibrium distributions for queues with interactive batch departures

Abstract

Gelenbe et al. [1, 2] consider single server Jackson networks of queues which contain both positive and negative customers. A negative customer arriving to a nonempty queue causes the number of customers in that queue to decrease by one, and has no effect on an empty queue, whereas a positive customer arriving at a queue will always increase the queue length by one. Gelenbe et al. show that a geometric product form equilibrium distribution prevails for this network. Applications for these types of networks can be found in systems incorporating resource allocations and in the modelling of decision making algorithms, neural networks and communications protocols. In this paper we extend the res..