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

Abstract

It is well known that strategic customers typically patronize service systems at a higher rate than the socially optimal one. Much literature has focused on inducing customers to patronize such systems at this latter rate. All of this literature considered non-idling policies that are the focus of queueing theory. We demonstrate that strategically imposing delays into such systems can improve the social welfare using the M/G/1 queue with orbit. This queue is a versatile model, that has been extensively studied in the literature 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 can decide whether to balk or join a virtual queue that is referred to as the 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 can be seen as extra delays that are imposed on customers that find a busy server. We further show that when customers are strategic there are certain ranges of the parameters where strategically 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, compare them and provide some insight on the optimal delay and level of information in such systems.