Auction-Based Queue Disciplines

Each one of several impatient agents has a job that needs to be processed by a server. The server can process the jobs sequentially, one at a time. Agents are privately informed about the realization of a random variable representing processing time. If the cost of delay is represented by a concave function of waiting time till job completion, the efficient shortest processing time first schedule arises in the equilibrium of a simple auction where agents bids for slots in the queue. If the cost function is convex, the equilibrium yields the anti-efficient longest processing time first schedule. In this case, the performance of the auction (both efficiency and revenue) can be improved by capping bids from above. Finally, we show that the ex-post incentive compatible mechanisms that minimize the expected total waiting cost cannot depend on the private information available to the agents.