Abstract
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.
Highlights
The study and modelling of queueing networks with blocking is an important tool in many aspects of operational research, both analytically and through simulation
A deadlock detection method for the simulation model will be invaluable in modelling realistic deadlock resolution methods, ensuring correct models can be built of systems like this with circular blocking
In open restricted queueing networks the mutual exclusion condition is satisfied as customers cannot share servers; the wait for condition is satisfied due to the rules of Type I blocking; the no pre-emption condition is satisfied in networks that have no or non-pre-emptive priority; and the circular wait condition is satisfied if the queueing network contains a cycle where all nodes have limited queueing capacity
Summary
The study and modelling of queueing networks with blocking is an important tool in many aspects of operational research, both analytically and through simulation These models have applications in many varied settings such as healthcare, supply chains, manufacturing and communications systems. Queueing networks are described as open if customers can enter and leave the system from the exterior Restricted networks are those where at least one service centre has limited queueing space or capacity before it. That customer remains with its server until space becomes available at its destination During this time that server is unavailable to begin another customer’s service.
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