On the stationary distribution of queue lengths in a multi-class priority queueing system with customer transfers
The paper deals with a multi-class priority queueing system with customer transfers from lower priority queues to higher priority queues. Conditions for the queueing system to be stable/unstable are obtained. An auxiliary queueing system with an product-form solution for the stationary queue length distribution is considered. Sample path relationships between the queue lengths in the original queueing system and the auxiliary queueing system are obtained, which lead to bounds for the stationary distribution of the queue lengths in the original queueing system. Using matrix-analytic methods, it is shown that the tail asymptotics of the stationary distribution is exact geometric, if the queue with the highest priority is overloaded.
scientific article; zbMATH DE number 5636929
scientific article