Analysis of an MX1, MX2/G1, G2/1 retrial queueing system with priority services, working breakdown, Bernoulli vacation, admission control and balking

A single server serves two classes of customers under non-preemptive priority service rule are studied. In addition to this working breakdown, admission control, balking and Bernoulli vacation are also investigated. Here, the customers arrive according to two independent compound Poisson processes and the service is in general distribution. Once the system gets a breakdown, the server proceeds the service at a slower speed for the current customer, after which, the repair will commence. Moreover, the server can not allow all the customers to enter into the system, there is an admission control policy to allow customers. Applying the supplementary variable technique, the Laplace transforms of time-dependent probabilities of system state are determined and further deduced the steady state results. Also, the average number of customers in the corresponding queues and the average waiting times are estimated. Finally, the numerical results are represented.