A feed back retrial queueing system with two types of arrivals

A retrial queueing system with two types of customers and with feed back is considered. Type 1 customers arrive in batches of size k with probability ck and type 2 customers arrive singly according to two Poisson processes with rates [EQUATION] and λ2 respectively. Service time distri butions are different for both type of customers. If arriving customers are blocked due to server being busy, type 1 customers are queued in a priority queue of infinite capacity, while type 2 customers enter into a retrial group in order to seek service again after a random amount of time. For this system the joint distribution of the number of customers in the priority queue and in the retrial group is obtained in closed form. Some operating characteristics are derived and a numerical study is also carried out.