ON THE M/G/1 FEEDBACK RETRIAL QUEUEING WITH ORBITAL SEARCH OF CUSTOMERS

Abstract

We consider a single server feedback retrial queueing system with orbital search. An arriving customer finding the server idle enters into service immediately; otherwise, the customer enters into an orbit. The service times are supposed to be arbitrarily distributed. An orbiting customer competes for service, the inter-retrial times are exponentially distributed. Upon completion of a service, the server stays idle for a while, waiting for either a new job or a job from the buffer. After the idle period, the server starts searching for blocked customers, according to the exponential distribution. During the searching time, the server cannot serve a customer. After the searching time the server gets a customer from the orbit if any, otherwise it stays idle again. After completing, the customer has an option to join the orbit as a feedback , customer or to leave the system forever. Various performance measures are derived, and numerical results are given.