Opaque queues : service systems with rationally inattentive customers

Classical models of service systems with rational and strategic customers assume queues to be either fully visible or invisible. In practice, however, most queues are only "partially visible" or "opaque", in the sense that customers are not able to discern precise queue length upon arrival. This is because assessing queue length and associated delays require time, attention, and cognitive capacity which are all limited. Service firms may influence this information acquisition process through their choices of physical infrastructure and technology. In this paper, we study rational queueing behavior when customers have limited time and attention. Following the theory of rational inattention, customers optimally select the type and amount of information to acquire and ignore any information that is not worth obtaining, trading off the benefits of information against its costs before deciding to join. We establish the existence and uniqueness of a customer equilibrium and delineate the impact of information costs. We show that although limited attention is advantageous for a firm in a congested system that customers value highly, it can be detrimental for less popular services that customers deem unrewarding. These insights remain valid when the firm optimally selects the price. We also discuss social welfare implications and provide prescriptive insights regarding information provision. Our framework naturally bridges visible and invisible queues, and can be extended to analyze richer customer behavior and complex queue structures, rendering it a valuable tool for service design.