  We consider a queue with an unobservable backlog by the incoming users. There
is an information designer that observes the queue backlog and makes
recommendations to the users arriving at the queue whether to join or not to
join the queue. The arriving users have payoff relevant private types. The
users, upon arrival, send a message, that is supposed to be their type, to the
information designer if they are willing to hear a recommendation. The
information designer then creates a recommendation for that specific type of
user. The users have to pay a tax in exchange for the information they receive.
In this setting, the information designer has two types of commitments. The
first commitment is the recommendation policy and the second commitment is the
tax function. We combine mechanism design and information design to study a
queuing system with heterogeneous users. In this setting, the information
designer is a sender of the information in the information design aspect and a
receiver in the mechanism design aspect of the model. We formulate an
optimization problem that characterizes the solution of the joint design
problem. We characterize the tax functions and provide structural results for
the recommendation policy of the information designer.
