Information cascades in a queueing system with parallel servers

When a customer makes an appointment at the doctor, call the plumber or reserve flight tickets, he joins a queue. By making the reservation, the customer can learn his position in the service provider's queue. If the customer is unsatisfied with his position, he might consider calling an alternative service provider, hoping to get a better position. In our model, the service is provided by $n$ parallel servers. Upon arrival to the system, each customer randomly chooses one server and inspects it. Then, he either joins it or inspects another queue. If he inspects another queue, he can join the shorter queue, or continue his search and inspect another queue. We assume that each inspection is associated with a fixed cost. The solution of this model is not straightforward even when $n=2$, and is characterized by cascades. In equilibrium, there exist isolated queue lengths (holes) at which customers inspect the other queue. In other queue lengths customers join the first queue. In some cases, there exist queue lengths at which customers adopt a mixed strategy.