Analysis of Priority Queueing System with Working Breakdown, Repair, Immediate Feedback and Bernoulli Vacation

We analyze an M^[X₁], M^[X₂]/G₁,G₂/1 queue with two classes of non-preemptive priority service based on working breakdown, repair, immediate feedback and Bernoulli vacation. The server may subject to random breakdown with parameter α, during high priority service (type I), then the server will complete the service for current customer at a slower service rate compared to the regular service rate. On the other hand, during low priority service (type II), it should go for repair immediately. After the completion of each high priority service, there are two choices. First, the server can go for vacation with probability θ, secondly, its serves the next customer which has the probability (1 – θ). In case of customer dissatisfaction after completion of high priority service, immediately they receive service again without joining queue with probability r, or else the customer gets an option to discard, which has a probability of (1 – r). We use the established norm, which is the corresponding steady state results for the time dependent probability generating functions. Along with that, the expected time of wait for the expected number of customers in the high and low priority queues are computed. Numerical results along with the graphical representations are shown elaborately.