A Feedback Retrial Queueing System with Two Types of Batch Arrivals

A retrial queueing system with two types of batch arrivals, called type I and type II customers,is considered. Type I customers and type II customers arrive in batches of variable sizesaccording to two different Poisson processes. Service time distributions are identical and independentand are different for both types of customers. If the arriving customers are blocked due to the serverbeing busy, type I customers are queued in a priority queue of infinite capacity, whereas type IIcustomers enter into a retrial group in order to seek service again after a random amount of time. A type I customer who has received service departs the system with a preassigned probabilityor returns to the priority queue for reservice with the complement probability. A type II call whohas received service leaves the system with a preassigned probability or rejoins the retrial groupwith complement probability. For this model, the joint distribution of the number of customers inthe priority queue and in the retrial group is obtained in a closed form. Some particular models andoperating characteristics are obtained. A numerical study is also carried out