Retrial queues with recurrent demand option

Abstract

The object of this paper is to analyze the model of a queueing system in which customers can call in only to request service: if the server is free, the customer enters service immediately. Otherwise, if the service system is occupied, the customer joins a source of unsatisfied customers called the orbit. On completion of each service the recipient of service has an option of leaving the system completely with probability 1−p or returning to the orbit with probability p. We consider two models characterized by the discipline governing the order of rerequests for service from the orbit. First, all the customers from the orbit apply at a fixed rate. Secondly, customers from the orbit are discouraged and reduce their rate of demand as more customers join the orbit. The arrival at and the demands from the orbit are both assumed to be according to the Poisson process. However, the service times for both primary customers and customers from the orbit are assumed to have a general distribution. We calculate several characteristic quantities of these queueing systems.