Stationary analysis of a single server retrial queue with priority and vacation
Summary: We study a single server retrial queue with Bernoulli vacations and a priority queue. A customer who finds the server busy upon arrival either joins the priority queue with probability \(\alpha\) or leaves the service area and enters a retrial group (orbit) with probability \(\bar{\alpha}\) (\(= 1 - \alpha\)). Using the supplementary variable technique, we find the joint probability generating function of the number of customers in the priority queue and of the number of customers in the retrial group in a closed form. Also, we find explicit expressions for the mean queue length and the mean waiting time for both queues, and we derive steady-state performance measures for the system. We show that the general stochastic decomposition law for \(M\)/\(G\)/\(1\) vacation models holds for our system too. Some special cases and numerical results are also discussed.
scientific article; zbMATH DE number 5603386