Abstract: Customer strategic behavior regarding the join-or-balk dilemma in queueing systems with server vacations/failures has been studied intensively in the recent literature. The standard assumption in these studies is that joining customers are not allowed to renege later. In the present paper we relax this assumption and quantify the value of reneging for strategic customers who face a queueing system with server vacations/failures. To focus on the reneging feature, we study the customer strategic behavior in the simplest such system, that is in the M/M/1 queue with a server alternating between on and off periods. We show that the possibility of reneging has substantial effect on the equilibrium social welfare and throughput. In particular, as the reward from service varies in a given system, it becomes beneficial to activate or deactivate the option of reneging to ensure a higher welfare. Moreover, we show that the effect of the reneging option is particularly significant in the case where the original system with non-strategic customers is unstable.

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.

The performance analysis of the classical M / G / 1 queue, under a general mixed joining/balking strategy was carried out recently by Kerner (Stoch Mod 24:364–375, 2008), who used an analytic approach based on the supplementary variable method. The tractability of the corresponding queueing system with state-dependent arrival rates is particularly significant, as it has important applications in situations where the customers are strategic. In this paper, we present an alternative path for the analysis of the same system, using purely probabilistic arguments.