We define a discrete-time queueing network where there are restrictions on which queues can be served simultaneously. We give a policy for serving queues which is stable whenever it is possible to stabilize the queueing network.
Sequentially a player decides to play and his adversary decides . At time , a decision results in a vector payoff . Given is the average vector payoff at time , Blackwell’s Approachability Theorem is a necessary and sufficient condition so that, regardless of the adversary’s decisions, the player makes the sequence of vectors approach a convex set .
The Weighted Majority Algorithm is a randomized rule used to learn the best action amongst a fixed reference set.
We consider a model of a large number of single server queues. When a job arrives, we assume it chooses between queues. The job then chooses to join the shortest of these queues. We show that such choice can dramatically reduce queue sizes.
Here is the long run queue length; is the expected waiting time; is the arrival rate at the queue.
- The Hamilton-Jacobi-Bellman Equation.
- Heuristic derivation of the HJB equation.
- Continuous-time dynamic programs
- The HJB equation; a heuristic derivation; and proof of optimality.