Equilibrium Balking Strategy in an Unobservable GI/M/c Queue with Customers’ Impatience

Abstract

We consider an equilibrium threshold balking strategy in an unobservable GI/M/c queue with customers' impatience. Upon arriving a customer decides whether to join or balk the queue based on random probability known as joining probability f. Once a customer decides to join the system it initiates an impatient timer with random duration T, such that, if customers' service is not completed before the timer expires, the customer abandons the system. The waiting time of a customer in system has been associated with a linear cost-reward structure for estimating the net benefit if a customer chooses to participate in the system. The study has been limited to unobservable queue where the information regarding system-length is unknown to the arriving customer. The proposed analysis is based on a root of the characteristic equation formed using the probability generating function of embedded pre-arrival epoch probabilities. Therefore, we obtain the stationary system-length distribution at pre-arrival and arbitrary epochs and thereby we obtain mean system sojourn time. Finally, we present numerical results in the form of graphs for observing net benefit against different model parameters. The proposed model has applications in the modeling of balking and impatient behavior of incoming calls in a call center, multi-core computing, multi-path routing in delay sensitive communications networks.