Optimal Signaling Mechanisms in Unobservable Queues

We consider the problem of optimal information sharing in an unobservable single-server queue offering service at a fixed price to a Poisson arrival of delay-sensitive customers. The service provider observes the queue and may share state information with arriving customers. The customers, who are Bayesian and strategic, incorporate this information into their beliefs before deciding whether to join the queue. We pose the following question: Which signaling mechanism should the service provider adopt to maximize her expected revenue? We formulate this problem as an infinite linear program in the queue’s steady-state distribution and establish that, in general, the optimal signaling mechanism requires the service provider to strategically conceal information in order to incentivize customers to join. In particular, we show that a binary signaling mechanism with a threshold structure is optimal. Finally, we prove that coupled with an optimal fixed price, the optimal signaling mechanism generates the same expected revenue as the optimal state-dependent pricing mechanism. This suggests that in settings where state-dependent pricing is infeasible, signaling can be effective in achieving the optimal revenue. Our work contributes to the literature on dynamic Bayesian persuasion and provides many interesting directions for extensions.