Joining Longer Queues: Information Externalities in Queue Choice

A classic example that illustrates how observed customer behavior impacts other customers' decisions is the selection of a restaurant whose quality is uncertain. Customers often choose the busier restaurant, inferring that other customers in that restaurant know something that they do not. In an environment with random arrival and service times, customer behavior is reflected in the lengths of the queues that form at the individual servers. Therefore, queue lengths could signal two factors--potentially higher arrivals to the server or potentially slower service at the server. In this paper, we focus on both factors when customers' waiting costs are negligible. This allows us to understand how information externalities due to congestion impact customers' service choice behavior. In our model, based on private information about both the service-quality and queue-length information, customers decide which queue to join. When the service rates are the same and known, we confirm that it may be rational to ignore private information and purchase from the service provider with the longer queue when only one additional customer is present in the longer queue. We find that, due to the information externalities contained in queue lengths, there exist cycles during which one service firm is thriving whereas the other is not. Which service provider is thriving depends on luck; i.e., it is determined by the private signal of the customer arriving when both service providers are idle. These phenomena continue to hold when each service facility has multiple servers, or when a facility may go out of business when it cannot attract customers for a certain amount of time. Finally, we find that when the service rates are unknown but are negatively correlated with service values, our results are strengthened; long queues are now doubly informative. The market share of the high-quality firm is higher when there is service rate uncertainty, and it increases as the service rate decreases. When the service rates are positively correlated with unknown service values, long queues become less informative and customers might even join shorter queues.