Analysis of <i>MMAP</i>/<i>PH</i><SUP align="right">(1)</SUP>, <i>PH</i><SUP align="right">(2)</SUP>/1 non-preemptive priority queueing model with phase-type vacation and repair, feedback, b

We consider a single server non-preemptive priority queue with phase-type vacation and repair, feedback, breakdown, close-down, and reneging. 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, it will immediately 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 renege. 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.