Modelling deadlock in open restricted queueing networks

Open restricted queueing networks give rise to the phenomenon of deadlock, whereby some customers may be unable to ever leave a server due to mutual blocking. This paper explores deadlock in queueing networks with limited queueing capacity, presents a method of detecting deadlock in discrete event simulations, and builds Markov chain models of these deadlocking networks. The three networks for which Markov models are given include single and multi-server networks for one and two node systems. The expected times to deadlock of these models are compared to results obtained using a simulation of the stochastic process, together with the developed deadlock detection method. This paper aims to be of value to simulation modellers of queues.