Queues under stochastic priority switching

In this paper a generalised model of dynamic and stochastic changing priorities within an M/M/c queue is presented. Simulation and Markov chain models are given that describe the behaviour of such systems, and their stationarity is explored. Bounded approximations of the Markov models are given, and measures of their accuracy in approximating the infinite versions given. Finally the models are used to model a waiting list for surgical endoscopy with unknown service disciplines, fitting system parameters to reflect the queue behaviour. An exploration of behaviour under different class change parameters is given for a better understanding of the system.