Optimal flow control of an M/M/1 queue with a balanced budget

The following problem is considered. There are several users who send jobs to an M/M/1 queue and have privately observed information relating to their benefits from the rate of job submissions and their costs due to waiting in the queue. Each user's benefits and costs are unknown to the queue manager and to other users. The manager's objective is to achieve "optimal" flow control, where the optimality depends on arriving at an appropriate trade-off between delay and the job arrival rate assigned to each user: the allocations should be such that no user can be made better off by a reallocation without hurting at least one other user. Since the optimality calculation requires knowledge of the users' private information, we propose an algorithm that converges to the optimum, while inducing users to reveal information relating to their benefits and costs truthfully, and balances the manager's budget. Earlier work on this problem has produced a flow control algorithm that requires the queue manager to incur a potentially huge deficit; this leads to several theoretical and practical problems.<
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