Queueing systems with rationally inattentive customers

Abstract

Problem definition: Classical models of queueing systems with rational and strategic customers assume queues to be either fully visible or invisible, while service parameters are known with certainty. In practice, however, people only have "partial information" on the service environment, in the sense that they are not able to fully discern prevalent uncertainties. This is because assessing possible delays and rewards is costly, as it requires time, attention, and cognitive capacity, which are all limited. On the other hand, people are also adaptive and endogenously respond to information frictions. Methodology: We develop an equilibrium model for a single-server queueing system with customers having limited attention. Following the theory of rational inattention, we assume that customers optimize their learning strategies by deciding the type and amount of information to acquire and act accordingly while internalizing the associated costs. Results: We establish the existence and uniqueness of a customer equilibrium when customers allocate their attention to learn uncertain queue lengths and delineate the impact of service characteristics. We provide a complete spectrum of the impact of information costs on throughput and show numerically that throughput might be nonmonotone. This is also reflected in social welfare if the firm's profit margin is high enough, although customer welfare always suffers from information costs. Managerial implications: We identify service settings where service firms and social planners should be most cautious for customers' limited attention and translate our results to advisable strategies for information provision and service design. For example, we recommend firms to avoid partial hindrance of queue-length information when a low-demand service is not highly valued by customers. For a popular service that customers value reasonably highly, however, partial hindrance of information is particularly advisable. Academiclpractical relevance: We propose a microfounded framework for strategic customer behavior in queues that links beliefs, rewards, and information costs. It offers a holistic perspective on the impact of information prevalence (and information frictions) on operational performance and can be extended to analyze richer customer behavior and complex queue structures, rendering it a valuable tool for service design.