Follow the crowd to avoid congestion with unknown service rate

This paper investigates the impact of unknown service rate on customers' joining behavior in service systems. In a single-server queue with known service rate, customers always prefer the shorter-queue strategy when multiple joining equilibria exist. When the service rate is unknown to customers, we identify the follow the crowd (FTC) behavior and show that there exist at least one joining equilibria and that all of them have a threshold structure; when multiple equilibria exist, customers prefer the longer-queue strategy when the realizations of service rate differ significantly. In a two-server two queue system with random assignment of one faster server and one slower server, we show that the shorter-queue strategy (with random tie breaking for identical queue lengths) is always an equilibrium; when the faster and slower servers differ significantly in speed, a pure strategy in which customers sometimes join the longer queue is an equilibrium and dominates the shorter-queue strategy in terms of expected customer utility.