Optimal Customer Return Rate for an M/M/1 Queueing System with Retrials

Abstract

The zero capacity M/M/1 queue with returning customers is examined. Performance measures are calculated and an imposed optimal return rate is determined for customers who return until served. The optimal rate is then calculated for an arbitrary customer as a function of the return rate of the other customers, and limiting cases are analyzed. The other customers may then adjust their return rate each time the arbitrary customer adjusts his/hers until a fixed point solution is obtained. A comparison between systems is made.