On Queues with Priority Determined by Feedback

Customers arrive to a two-priority queueing system according to a marked Poisson process. Both waiting rooms have infinite capacity. Customers are served one at a time according to FIFO discipline on priority basis: those in waiting line 1( P 1 ) are given priority over the ones in line 2( P 2 ). The service time is class-dependent phase type. After completion of service, high priority ( P 1 ) customers may feed back for service according to a Bernoulli process. Feed back customers are sent to the low priority ( P 2 ) queue. When at a service completion epoch of a P 1 customer, if there is none left behind in P 1 line, then the server goes to serve P 2 class. For the two-priority queueing system, we assume that P 2 customers are not allowed an additional feed back. Both preemptive and non-preemptive service disciplines are analysed. Waiting time distribution of both type of customers are derived. As a special case, the situation where there is no external entry to the P 2 line is discussed