A Token Based Parallel Processing Queueing System with Priority

We consider a single server queueing model with two parallel queues in which one is finite buffer and the other is infinite. Customers arrive according to two independent Poisson processes and service time follows phase type distribution. Customers receive service on the basis of a token system. Customers in the infinite queue are ordinary customers and the customers in the finite queue are priority customers. Customer priority may be either by paying a cost or by any other means. Priority customers have the right to make the strategic decision regarding the queue to which he or she may join. Priority customers are provided service on the basis of token issued to such customers to access the service according to the rule: when \( N-1 \) customers of lower priority are consecutively served, the next to be served is from the priority line, if there is one waiting, thus ensuring there reduced waiting time. However they can join the lower priority queue in the case they find the waiting time less. This strategy will be discussed in the paper. We perform the steady state analysis and establish the stability condition of the queueing model. Some performance measures are also evaluated. Control problem has been discussed. Some numerical illustrations are provided.