Optimal control of a queue with high-low delay announcements: The significance of the queue

This article deals with strategic control of information in a single-server model. It considers an M/M/1 system with identical customers. There is a single cut-off number, and the level of congestion is said to be low (high) if the queue length is less than (at least) this value. The firm can dynamically change the admission fee according to the level of congestion. Arriving customers cannot observe the queue length, but they are informed about the current level of congestion and the admission fee. The article deals with finding the profit maximizing admission fee, using analytical and numerical methods. We observe that such a pricing regime can be used to increase the profit and the proportion of the increase relative to the single price unobservable queue is unbounded. We observe that the profit maximizing threshold is usually quite small and therefore raise a question whether there is a significant difference in profit when rather than being informed about the congestion level, customers only join the system when the server is idle. We also investigate this question considering the classical observable model.