Queues with slowly varying arrival and service processes

The authors examine a generalisation of the M/G/1 queue. The arrival and service processes are governed by a Markov chain which determines the rate of arrival and the service time distribution from a finite set. This Markov chain is assumed to vary ‘slowly’, so that analytical results may be derived for the stationary distribution of the queue length using an approach based on decomposability. The practical interest of this model stems from the numerous applications where the parameters of queueing systems are time varying, such as inventory models, telephone systems, time-sharing systems, computer networks with bursty traffic, etc. The authors also show how this approach can be extended to arbitrary network of queues and in particular to those with product form solution.