A batch arrival priority queue with recurrent repeated demands, admission control and hybrid failure recovery discipline

We consider an unreliable single server retrial queue with batch arrivals, accepting two types of customers, say ordinary and transit. In addition, there is a fixed number of recurrent customers in a retrial box. Ordinary and transit customers arrive in batches according to a compound Poisson process while in addition, each individual customer is subject to control admission policy upon arrival. Admitted ordinary and transit customers who find upon arrival the server unavailable, join a queue and the retrial box respectively. Upon a service completion, recurrent customers always return in retrial box while ordinary and transit leave the system. The server is subject to a hybrid failure recovery discipline. This discipline combines both the preemptive repeat and the preemptive resume disciplines according to the type of the interrupted customer. For such a system we investigate the stability conditions and the joint queue length distribution in steady state, while operating characteristics and numerical results are also presented. Reliability analysis is investigated while a stochastic decomposition result is also proved.