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 sizes according to two different Poisson processes. Service time distributions are identical and independent and are different for both types of customers. If the arriving customers are blocked due to the server being busy, type I customers are queued in a priority queue of infinite capacity, whereas type II customers 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 probability or returns to the priority queue for reservice with the complement probability. A type II call who has received service leaves the system with a preassigned probability or rejoins the retrial group with complement probability. For this model, the joint distribution of the number of customers in the priority queue and in the retrial group is obtained in a closed form. Some particular models and operating characteristics are obtained. A numerical study is also carried out. 1. Introduction In the last three decades there has been significant contribution in the area of retrial queueing theory. For detailed survey one can see Yang and Templeton [1], Falin [2] and Choi and Chang [3]. Choi and Park [4] investigated an retrial queue with two type of customers in which the service time distribution for both types of customers are the same. Khalil et al. [5] investigated the above model at Markovian level in detail. Falin et al. [6] investigated a similar model, in which they assumed different service time distributions for both types of customers. In 1995, Choi et al. [7], studied an retrial queue with two types of customers and finite capacity. Atenica and Moreno [8] has analyzed a single server retrial queuing system with infinite buffer, Poisson arrivals, general distribution of service time, and linear retrial policy. If an arriving customer finds the server occupied, he joins a retrial group (called orbit) with probability and with complementary probability a priority queue in order to be served. After the customer is served completely, he will decide either to return to the priority queue for another service with probability or to leave the system forever with probability , where . They proved the ergodicity of the embedded Markov chain and obtained its stationary distribution function and the joint generating function of the number of customers in both groups in the steady-state