Token Based Parallel Processing Retrial Queueing System with a Probabilistic Joining Strategy for Priority Customers

We consider a single server retrial queueing system with parallel queues of ordinary and priority customers. Priority customers join the queues according to a probabilistic joining strategy until the ordinary queue is full. We also assume that there is a waiting room for the blocked ordinary customers and they make retrials from there, to enter into the ordinary queue. Priority customers on arrival, seeing both ordinary and priority queue as full loss the system forever. Customers receive service on the basis of a token system. Ordinary customers, upon arrival finding the ordinary queue as full, enter into the orbit. Ordinary customers make their retrials from the orbit in an exponential duration of time intervals to enter into the ordinary queue. Ordinary customer from the orbit make their retrials in an exponential duration of time intervals. Whenever the queue size of ordinary queue is less than N then the ordinary customer in the orbit successfully enter into the ordinary queue. Two types of customers arrive according to Marked Markovian Arrival Process (MMAP). Service times are assumed to follow phase type distributions. Steady-state analysis of the model is done. Some system characteristics are evaluated.