Increasing social welfare with delays: Strategic customers in the M/G/1 orbit queue

Strategic customers typically patronize service systems at a higher rate than the socially optimal one. Much literature has focused on inducing customers to join such systems at this latter rate. This entire literature considers nonidling policies that are the focus of queueing theory. We demonstrate that strategically imposing delays into service systems can improve the social welfare using the M/G/1 queue with orbit. This versatile queueing model has been extensively studied from a performance evaluation perspective. In this system, customers who arrive and find the server idle begin immediately their service. However, strategic customers who find the server busy decide whether to balk or join a virtual queue, that is, an orbit. Then, each time the server finishes a service, he begins to retrieve a customer from the orbit and the corresponding retrieving time is not negligible. These retrieving times function as extra delays that are imposed on customers that find a busy server. We show that when customers are strategic, there are certain ranges of the parameters where delaying the orbit customers can increase the welfare of a system or even maximize it. To this end, we characterize and compute the equilibrium strategies for the customers' joining/balking dilemma. We consider both the unobservable and observable versions of the system, and provide some insight on the optimal delay and level of information in such systems. We further show that the welfare for this system is higher than the corresponding standard M/G/1 queue with the same delay.