Analysis of MMAP/PH(1), PH(2)/1 Preemptive Priority Queueing Model with Single Vacation, Repair and Impatient Customers

In this paper, we analyse a single server preemptive priority queue with phase-type vacation and repair, feedback, working breakdown, close-down and impatient customers. Customers arrive according to the Marked Markovian Arrival Process and their service time according to Phase-type distribution. If the High Priority customers need feedback, they lose their priority and join the Low Priority queue. At any instant, if the server is broken down, the server provide service with slow mode for that current customer and then the server will go into a repair process. When there are no customers present in both the queues, the server close-down the system and then goes on vacation. During the close-down and vacation period, high priority customers may balk. The Matrix Analytic Method is used to look into the number of consumers that are currently in the system. Analysis of the steady-state, the server active period, and the total cost are all discussed. Finally, some significant performance measures and numerical examples are given.