Approximate analysis on retrial queues with fixed number of retrials

Abstract

Retrial queueing system is a new class of queueing systems for analysis of the call retrial phenomenon which frequently occurs in communication systems. In the retrial queueing system, a customer arriving when all servers busy leaves the service facility temporarily and returns after random time to try again. Blocking probabilities are most important performance measures in this system. In this thesis, we consider M/M/1/1 and M/M/c/c retrial queueing systems where the maximum number of retrials is fixed to a predetermined number, K. This model introduces a new policy on the maximum number of customers and analytically intractable except K=1 case. We suggest a new method whic divide the retrial group into groups by numbers of retrials, and present approximate formulae for blocking probabilities of customers by the method. Retrial customer``s blocking probability varies with the number of retrials. These probabilities, especially that of a customer who leaves the system without being served, are important measures for cost analysis of communication systems. Traditional approaches in retrial queues, however, only considered new-arriving call``s blocking probability. In this study, all blocking probabilities that vary with the number of retrials were obtained by the new approximate method.