A SINGLE SERVER RETRIAL QUEUEING SYSTEM WITH TWO TYPES OF BATCH ARRIVALS AND FINITE NUMBER OF RECURRENT REPEATED CUSTOMERS

Abstract

A single server retrial queueing system with two types (Type I and Type II) of batch arrivals andK recurrent calls is considered. The two batch arrivals follows compound Poisson processes with two different rates. The Type II customers enter into the orbit, if the server is busy. The retrial orbit consists of transit type II customers and a fixed numberK recurrent customers. The Type I customers are waiting in a queue before the server, if the service is not immediate. Service times distributions are identical independent distributions (transit and recurrent) and are different for type I customers, whereas the retrial time for both transit and recurrent customers are independently and exponentially distributed with different rates. For this model, the joint distribution of the number customers of type I, type II and recurrent in closed form has been obtained. Some particular models and operating characteristics are obtained. A numerical study is also carried out