A Study on Random Evolution Associated with A M/M/1∞ Queueing System with Balking

Abstract

The arrival process in a queueing can be modified in several ways. One way is to allow arriving customers to leave the system without joining the queue. The act of a customer refusing to join the queue upon arrival is called balking. We consider an M/M/1/∞ queue with balking. The balking customers induce loss to the system and they alter the dynamics of the net profit. We associate various costs and analyze the Markov evolution of the net profit function. In this paper, we obtain the net profit function using the random evolution techniques.