Follow the Crowd with Uncertain Service Capacity

Abstract

Problem definition: Customer joining behavior is of major concern for service systems where the service capacity is uncertain. Academic/practical relevance: It remains unclear whether customer inference of uncertain service capacity can lead to follow the crowd (FTC) behavior. Management can release capacity information, but how it affects system performance needs to be understood. Methodology: We use a single-server queue to analyze the joining behavior of customers who infer the actual service capacity based on the queue length upon arrival. We also characterize the impact of capacity information disclosure both analytically and numerically. Results: We find that when other customers’ tendency to join the service increases, a tagged customer can make more accurate inferences of service capacity based on queue length. This inference effect arises together with the congestion effect and can lead to FTC when it outweighs the latter. When multiple equilibria exist, we characterize the conditions under which the inference effect is significant at the aggregate customer level so that the joining equilibrium with a larger joining threshold is Pareto-optimal. Managerial implications: Management needs to be careful in setting the information disclosure policy, as the key problem parameters may affect its impact on system throughput and social welfare in opposite directions.