Signaling service quality through queue disclosure

Abstract

Problem definition: We consider a single-server queueing system where service quality is either high or low. The server, who knows its exact quality level, can signal this quality information to customers by revealing or concealing its queue length. Based on this queue disclosure action and the observed queue length in the case of a revealed queue, customers decide whether to join the system. Academic/practical relevance: The queue disclosure action is regarded as a signal indicating the service quality. Methodology: We develop a signaling game and adopt the sequential equilibrium concept to solve it. We further apply the perfect sequential equilibrium as an equilibrium-refinement criterion. Results: In our baseline model, where all of the customers are uninformed of service quality, the pure-strategy perfect sequential equilibrium is always a pooling one, except at several discrete values of market size (measured by the potential arrival rate). When the market size is below a certain threshold, both high- and low-quality servers adopt queue concealment; otherwise, both types of servers adopt queue revelation. We also consider a general scenario in which the market is composed of both quality informed and uninformed customers. Under this setting, when the server conceals the queue, we can fully characterize customers’ equilibrium queueing strategies and the corresponding effective arrival rates. The unique sequential equilibrium outcome is still a pooling one when the market size is either below a lower threshold or above an upper threshold. A separating equilibrium can occur only when the market size falls between two thresholds; under that circumstance, the uninformed customers can infer the server’s quality from its queue disclosure behavior. Managerial implications: Under separating sequential equilibria, uninformed customers can fully infer the quality information and thus behave in an informed way. Unlike studies where queue disclosure is not regarded as a quality signal, our study reveals that the signaling effect of queue disclosure increases (decreases) the effective arrival rate of the high-quality (low-quality) server and also increases the customers’ total utility when the server is of low quality.