In this study, we analyze the reneging behavior of customers in a Markovian M/M/1 queue with an alternating service process, representing a normal operation mode and a working repair mode with reduced service speed. The customers are strategic and, as they continuously observe the system’s state, they decide whether to stay or to renege. For this model, we derive equilibrium customer reneging strategies and the corresponding performance measures of the system, considering both the baseline model with discrete units of customers and its fluid counterpart. To capture the effect of reneging, we compare their performance with similar systems, operating under a no-reneging policy. Both theoretical findings, as well as numerical experiments, reveal that allowing reneging significantly affects system performance. Finally, to assess the quality of the fluid approximation we conduct a numerical comparison between the fluid and the baseline version of the model.

Problem definition: We consider pricing of services with strategic customers who have heterogeneous delay costs motivated by transportation systems. Customers are strategic decision makers who weigh the reward from the transport service against the waiting cost for the vehicle at a transportation station. Customers arrive at the station according to a Poisson process, and the vehicle visits the station according to a renewal process. We analyze the optimal price and the equilibrium for different levels of information available to customers. Methodology/results: We represent the service system as a stochastic clearing process, heterogeneity in delay cost as a random variable, and heterogeneity in rewards as a positive affine transformation of delay cost. For each information level, we identify the equilibrium behavior of customers and solve the revenue-maximization problem based on this equilibrium. The equilibrium turns out to be unique in each case, and it is of a threshold form in the sense that for each value of the information, it is best to join either for all types of customers, only for those who are sufficiently price sensitive, only for those who are sufficiently delay sensitive, or for none. The optimal fee is also unique in nontrivial cases. This enables us to perform comparisons across different information structures. Managerial implications: The effect of heterogeneity depends highly on model parameters as well as the available information. For a fixed fee, an increase in heterogeneity has a positive overall impact on the customer population, whereas the effect on the revenue can be positive (slow service at a high fee) or negative (fast service at a low fee). Unlike with fixed fee, for the optimal fee, an increase in heterogeneity can have a negative overall effect on customers. Ignoring heterogeneity can lead to a substantial opportunity loss for the system.

In the recent strategic queueing literature, there is a large number of papers that study the join-or-balk dilemma in queueing systems with server’s on-off periods, modeling vacations and failures. These studies consider the customers as discrete units and adopt the assumption that reneging is not permitted. In the present paper, we depart from this framework and study the effect of the reneging option in such systems. We consider the fluid on-off model of the basic queue with vacations/failures and study reneging vs. no-reneging when customers are strategic. We derive the equilibrium customer strategies and the corresponding performance measures of the system, and we use them to study the equilibrium throughput and social welfare. The main finding is that the existence of the reneging option is very beneficial for overloaded systems, i.e., for such systems balking alone is not sufficient to achieve good outcomes. On the contrary, for underloaded systems the reneging option is not particularly valuable.

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.

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.

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.

We consider a state-dependent single-server queue with orbit. This is a versatile model for the study of service systems, where the server needs a non-negligible time to retrieve waiting customers every time he completes a service. This situation arises typically when the customers are not physically present at a system, but they have a remote access to it, as in a call center station, a communication node, etc. We introduce a probabilistic approach for the performance evaluation of this queueing system, that we refer to as the queueing and Markov chain decomposition approach. Moreover, we discuss the applicability of this approach for the performance evaluation of other non-Markovian service systems with state dependencies.

We consider a transportation station, where customers arrive according to a Poisson process, observe the delay information and the fee imposed by the administrator and decide whether to use the facility or not. A transportation facility visits the station according to a renewal process and serves all present customers at each visit. We assume that every customer maximizes her individual expected utility and the administrator is a profit maximizer. We model this situation as a two‐stage game among the customers and the administrator, where customer strategies depend on the level of delay information provided by the administrator. We consider three cases distinguished by the level of delay information: observable (the exact waiting time is announced), unobservable (no information is provided) and partially observable (the number of waiting customers is announced). In each case, we explore how the customer reward for service, the unit waiting cost, and the intervisit time distribution parameters affect the customer behavior and the fee imposed by the administrator. We then compare the three cases and show that the customers almost always prefer to know their exact waiting times whereas the administrator prefers to provide either no information or the exact waiting time depending on system parameters.

We consider a fluid queue with two modes of service, that represents a production facility, where the processing of the customers (units) is typically carried out at a much faster time-scale than the machine-related processes. We examine the strategic behavior of the customers, regarding the joining/balking dilemma, under two levels of information upon arrival. Specifically, just after arriving and before making the decision, a customer observes the level of the fluid, but may or may not get informed about the state of the server (fast/slow). Assuming that the customers evaluate their utilities based on a natural reward/cost structure, which incorporates their desire for processing and their unwillingness to wait, we derive symmetric equilibrium strategy profiles. Moreover, we illustrate various effects of the information level on the strategic behavior of the customers. The corresponding social optimization problem is also studied and the inefficiency of the equilibrium strategies is quantified via the Price of Anarchy (PoA) measure.

We consider a transportation station, where customers arrive according to a Poisson process. A transportation facility visits the station according to a renewal process and serves at each visit a random number of customers according to its capacity. We assume that the arriving customers decide whether to join the station or balk, based on a natural reward-cost structure. We study the strategic behavior of the customers and determine their symmetric Nash equilibrium strategies under two levels of information.

We consider a Markovian clearing queueing system, where the customers are accumulated according to a Poisson arrival process and the server removes all present customers at the completion epochs of exponential service cycles. This system may represent the visits of a transportation facility with unlimited capacity at a certain station. The system evolves in an alternating environment that influences the arrival and the service rates. We assume that the arriving customers decide whether to join the system or balk, based on a natural linear reward-cost structure. We study the balking behavior of the customers and derive the corresponding Nash equilibrium strategies under various levels of information.