Interesting job talk by Shiliang Cui today. He walked through the logic of customers joining a queue. Customers get a reward once they receive service, but have a cost that is proportional to the time spent in queue. So rational customers can join the queue or balk at the length of the line and leave. Additionally, Shiliang added the concept of retrying, where the customer leaves now but comes back later to retry at the line. Customers pay a retrial cost for this inconvenience.
By comparing the benefit from receiving service to the queue and retrial costs, optimal policies for the behavior of the customer can be found. Typically, these policies have the form: join the queue and wait for service if there are N or less customers in queue and balk or retry otherwise (depending on retrial costs).
The interesting part are the Socially Optimal Policies. If all customers were to act in a way that maximizes the benefits to society as a whole, fewer people would wait in line and more people would balk or retry. This is because, as a utility maximizing individual, I do not consider the effect on others when I decide to wait in a queue. If I did, I would wait less often, because my waiting makes the queue longer for others, which increases their queueing costs. Though Shiliang didn’t make this comparison, I feel like this is an example of The Tragedy of the Commons. When everyone considers only their own interests, their actions have negative externalities on others. The more people that join the queue, the worse off everyone is.