The finite capacity multi-server queue with inhomogeneous arrival rate and discrete service time distribution — and its application to continuous service time problems

The finite capacity multi-server queueing model with inhomogeneous arrival rate and discrete service time distribution is developed. The system is formulated as an inhomogeneous Markov chain in discrete time. An algorithm is described to solve the model numerically. A method is then proposed for using this model to approximate the time dependent behaviour of multi-server queues with inhomogeneous arrival rate and continuous service time distribution. Empirical results are presented to show that this approximation will produce results that are accurate enough for most practical purposes.