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This paper studies an emerging business model of line-sitting in which customers seeking service can hire others (line-sitters) to wait in line on behalf of them. We develop a queueing-game-theoretic model that captures the interaction among customers, the line-sitting firm, and the service provider to examine the impact of line-sitting on the service provider’s revenue and customer welfare. We also contrast line-sitting with the well-known priority purchasing scheme, as both allow customers to pay extra to skip the wait. Our main results are as follows. First, we find that both accommodating line-sitting and selling priority can bring in extra revenue for the service provider, although by different means—selling priority increases revenue mainly by allowing the service provider to practice price discrimination that extracts more customer surplus, whereas line-sitting does so through demand expansion, attracting customers who would not otherwise join. Second, the priority purchasing scheme tends to make the customer population worse off, whereas line-sitting can be a win–win proposition for both the service provider and the customers. Nevertheless, having the additional option of hiring line-sitters does not always benefit customers as a whole because the demand expansion effect also induces negative congestion externalities. Finally, despite the fact that the service provider collects the priority payment as revenue but not the line-sitting payment, which accrues to the third-party line-sitting firm, we demonstrate that, somewhat surprisingly, accommodating line-sitting can raise more revenue for the service provider than directly selling priority. This paper was accepted by Charles Corbett, operations management.

How would the growing prevalence of real-time delay information affect a service system? We consider a single-server queueing system where customers arrive according to a Poisson process and the service time follows an exponential distribution. There are two streams of customers, one informed about real-time delay and the other uninformed. The customers’ uninformed behavior may be due to information ignorance or rational behavior in the presence of an information fee. We characterize the equilibrium behavior of customers with information heterogeneity and investigate how the presence of a larger fraction of informed customers affects the system performance measures, i.e., throughput and social welfare. We show that the effects of growing information prevalence on system performance measures are determined by the equilibrium joining behavior of uninformed customers. Perhaps surprisingly, we find that throughput and social welfare can be unimodal in the fraction of informed customers. In other words, some amount of information heterogeneity in the population can lead to more efficient outcomes, in terms of the system throughput or social welfare, than information homogeneity. For example, under a very mild condition, throughput in a system with an offered load of 1 will always suffer if there are more than 58% of informed customers in the population. Moreover, it is shown that for an overloaded system with offered load sufficiently higher than 1, social welfare always reaches its maximum when some fraction of customers is uninformed of the congestion level in real time. The online appendix is available at https://doi.org/10.1287/mnsc.2017.2747 . This paper was accepted by Gad Allon, operations management.

In many services, the quality or value provided by the service increases with the time the service provider spends with the customer. However, longer service times also result in longer waits for customers. We term such services, in which the interaction between quality and speed is critical, as customer-intensive services . In a queueing framework, we parameterize the degree of customer intensity of the service. The service speed chosen by the service provider affects the quality of the service through its customer intensity. Customers queue for the service based on service quality, delay costs, and price. We study how a service provider facing such customers makes the optimal \"quality-speed trade-off.\" Our results demonstrate that the customer intensity of the service is a critical driver of equilibrium price, service speed, demand, congestion in queues, and service provider revenues. Customer intensity leads to outcomes very different from those of traditional models of service rate competition. For instance, as the number of competing servers increases, the price increases, and the servers become slower. This paper was accepted by Sampath Rajagopalan, operations and supply chain management.

The ongoing shortage of organs for transplantation has generated an expanding literature on efficient and equitable allocation of the donated cadaveric organs. By contrast, organ donation has been little explored. In this paper, we develop a parsimonious model of organ donation to analyze the welfare consequences of introducing the donor-priority rule, which grants registered organ donors priority in receiving organs should they need transplants in the future. We model an individual’s decision to join the donor registry, which entails a trade-off between abundance of supply, exclusivity of priority, and cost of donating (e.g., psychological burden). Assuming heterogeneity in the cost of donating only, we find the introduction of the donor-priority rule leads to improved social welfare. By incorporating heterogeneity in the likelihood of requiring an organ transplant and in organ quality, we show that, in contrast to the literature, introducing the donor-priority rule can lower social welfare because of unbalanced incentives across different types of individuals. In view of the potentially undesirable social-welfare consequences, we consider a freeze-period remedy, under which an individual is not entitled to a higher queueing priority until after having been on the organ-donor registry for a specified period of time. We show this additional market friction helps rebalance the incentive structure, and in conjunction with the donor-priority rule, can guarantee an increase in social welfare by boosting organ supply without compromising organ quality or inducing excessively high costs of donating. This paper was accepted by Gad Allon, operations management.

We study a multiserver queueing model of a revenue-maximizing firm providing a service to a market of heterogeneous price- and delay-sensitive customers with private individual preferences. The firm may offer a selection of service classes that are differentiated in prices and delays. Using a deterministic relaxation, which simplifies the problem by preserving the economic aspects of price-and-delay differentiation while ignoring queueing delays, we construct a solution to the fully stochastic problem that is incentive compatible and near optimal in systems with large capacity and market potential. Our approach provides several new insights for large-scale systems: (i) the deterministic analysis captures all pricing, differentiation, and delay characteristics of the stochastic solution that are nonnegligible at large scale; (ii) service differentiation is optimal when the less delay-sensitive market segment is sufficiently elastic; (iii) the use of “strategic delay” depends on system capacity and market heterogeneity—and it contributes significant delay when the system capacity is underutilized or when the firm offers three or more service classes; and (iv) connecting economic optimization to queueing theory, the revenue-optimized system has the premium class operating in a “quality-driven” regime and the lower-tier service classes operating with noticeable delays that arise either endogenously (“efficiency-driven” regime) or with the addition of strategic delay by the service provider. This paper was accepted by Gérard Cachon, stochastic models and simulation.

Three fundamental questions when operating a service system are (1) how many employees to staff, and (2) how to route work to them, and (iii) how to pay them. These questions have often been studied separately; that is, the queueing and network-design literature that considers staffing and workload routing generally ignores payment, and the literature on employee payment generally ignores issues surrounding staffing and routing. In “Staffing, Routing, and Payment to Trade Off Speed and Quality in Large Service Systems,” D. Zhan and A.R. Ward study how the aforementioned three decisions jointly affect system throughput and the quality of the service delivered when the employers maximize their own payment. They find that the system manager should first solve a joint optimization problem to determine the staffing level, the routing policy, and the service speed, and second, design a payment contract under which the employees work at the desired service speed. Most common queueing models used for service-system design assume that the servers work at fixed (possibly heterogeneous) rates. However, real-life service systems are staffed by people, and people may change their service speed in response to incentives. The delicacy is that the resulting service speed is jointly affected by staffing, routing, and payment decisions. Our objective in this paper is to find a joint staffing, routing, and payment policy that induces optimal service-system performance. We do this under the assumption that there is a trade-off between service speed and quality and that employees are paid based on both. The employees selfishly choose their own service speed to maximize their own expected utility (which depends on the staffing through their busy time). The endogenous service-rate assumption leads to a centralized control problem in which the system manager jointly optimizes over the staffing, routing, and service rate. By solving the centralized control problem under fluid scaling, we find four different economically optimal operating regimes: critically loaded, efficiency driven, quality driven, and intentional idling (in which there is simultaneous customer abandonment and server idling). Then we show that a simple piece-rate payment scheme can be used to solve the associated decentralized control problem under fluid scaling.

Customers often wait in queues before being served. Because waiting is undesirable, customers may come back later (i.e., retry) when the queue is too long. However, retrial attempts can be costly as a result of transportation fees and service delays. This paper introduces a framework for rational retrial decisions in stationary queues. Our approach accommodates retrials in queues by replicating the Naor's model [ Naor P (1969) The regulation of queue size by levying tolls. Econometrica 37(1):15–24.] repeatedly over time periods. Within each period, we study an observable queue in which customers make rational state-dependent decisions to join, balk, or retry in a future period. We focus on a stationary environment where all arrivals, including new and retrying customers, will face the steady-state distribution of the system in equilibrium. Equilibrium analysis on customers’ decision making is necessary, as they choose optimal strategies corresponding to the stationary queueing dynamics that are in turn determined by their decisions. We characterize the equilibria in both stable and overloaded systems. We find the following: (1) Compared with a system without retrials, the additional option to retry can hurt consumer welfare. (2) Compared with the socially optimal decisions, surprisingly, self-interested customers retry insufficiently (they join overly long queues) when the retrial cost is low and retry too often when the retrial cost is high. (3) Self-interested (retrial) customers can generate positive externalities by smoothing workload over time.

In the Bitcoin system, large numbers of miners invest massive computing resources in the blockchain mining process in pursuit of Bitcoin rewards, which are comprised of a fixed amount of system-generated new block reward and a variable amount of user-submitted transaction fees. Here, transaction fees serve as the important tuner for the Bitcoin system to define the priorities in users’ transaction confirmation. In this paper, we aim to study the priority rule for queueing transactions based on their associated fees, and in turn users’ strategies in formulating their fees in the transaction confirmation game. We first establish a full-information game-theoretical model to study users’ equilibrium fee decisions; and then discuss three types of Nash equilibria, under which no, all and some users submit transaction fees. Moreover, we conduct empirical studies and design computational experiments to validate our theoretical analysis. The experimental results show that (1) users’ fee decisions will be significantly affected by their waiting time; (2) the reduced time costs, instead of transaction values, are the basis for users to evaluate their revenues; (3) longer waiting time and higher unit time cost drive users to submit transaction fees in pursuit of desired priorities; (4) with the required transaction fee increasing, the proportion of fee-submitting users decreases slowly at first followed by a sharp decline, and over-high required fees will make the transaction confirmation game end up with no users submitting fees.

Customers looking for service providers often face search frictions and have to trade off quality and availability. To understand customers’ search behavior when they are confronted with a large collection of vertically differentiated, congested service providers, we build a model in which arriving customers conduct a costly sequential search to resolve uncertainty about service providers’ quality and queue length and select one to join by optimal stopping rules. Customers search, in part, because of variations in waiting time across service providers, which, in turn, is determined by the search behavior of customers. Thus, an equilibrium emerges. We characterize customers’ equilibrium search/join behavior in a mean field model as the number of service providers grows large. We find that reducing either the search cost or customer arrival rate may increase the average waiting time in the system as customers substitute toward high-quality service providers. Moreover, with lower search costs, the improved quality obtained by customers may not make up for the prolonged wait, therefore degrading the average search reward and, more importantly, decreasing customer welfare; when customers search, their welfare can even be lower than if they are not allowed to search at all. This paper was accepted by Gad Allon, operations management.

In the operations research literature, the queue joining probability is monotonic decreasing in the queue length; the longer the queue, the fewer consumers join. Recent academic and empirical evidence indicates that queue-joining probabilities may not always be decreasing in the queue length. We provide a simple explanation for these nonmonotonic queue-joining strategies by relaxing the informational assumptions in Naor's model. Instead of imposing that the expected service time and service value are common knowledge, we assume that they are unknown to consumers, but positively correlated. Under such informational assumptions, the posterior expected waiting cost and service value increase in the observed queue length. As a consequence, we show that queue-joining equilibria may emerge for which the joining probability increases locally in the queue length. We refer to these as \"sputtering equilibria.\" We discuss when and why such sputtering equilibria exist for discrete as well as continuously distributed priors on the expected service time (with positively correlated service value).