A Retrial Queuing System with Two Types of Batch Arrivals and with Feedback to Orbit

A retrial queuing system with two types of batch arrivals is considered. The arrivals are called type I and type II customers. The type I customers arrive in batches of size k with probability ck and type II customers arrive in batches of size k with probability dk (kgreater than0) according to two independent Poisson processes with rates ?_(1 ) c ?= ?_1 ?_(k=1)^???k c_k ? and ??_2?_ d ?= ?_2 ?_(k=1)^???k d_k ? respectively. Service time distributions are identical, independent and are different for both type of customers. If the arriving customers are blocked due to server being busy, type I customers are queued in a priority queue of infinite capacity where as type II customers enter into a retrial group of infinite capacity in order to seek service again after a random amount of time. All the customers in the retrial group behave independent of each other. The retrial time is exponentially distributed with rate ?. A type I or type II customer who has received service departs the system with probability (1-q) or returns to the retrial group with probability q. For this model the joint distribution of the number of customers in the priority queue and in the retrial group is obtained in closed form. Some particular models and operating characteristics are obtained. A real life example is given. Few numerical models are generated by assuming particular values to the parameters.