Retrial System with Three Retrial Policies Subject to Repairable Starting Failures

Abstract

Motivated by the computer and telecommunication networks, this study deals with a multi-server retrial system with customer geometric loss (balking is possible for each service request attempt) and feedback. Moreover, the server may fail when it begins preparing to serve the customers in the startup period. An arriving customer who finds all servers are busy or broken either joins the retrial orbit or balks. If the customer gets the service, then after the service, he may either leave the system or enter the orbit for another service. The system is investigated as a quasi- birth-and-death process and interesting system performance measures are calculated with the long-term distribution. The optimum parameter settings which would minimize the cost function are discussed numerically. Some numerical experiments are presented to compare three retrial policies in terms of the major performance measures. It is demonstrated that our study can be utilized for not only evaluating performance but also generating some counter-intuitive results about system behavior.