Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
The Complexity of Optimal Queuing Network Control
Mathematics of Operations Research
Markov Decision Processes: Discrete Stochastic Dynamic Programming
Markov Decision Processes: Discrete Stochastic Dynamic Programming
Optimal and heuristic policies for dynamic server allocation
Journal of Parallel and Distributed Computing - Special issue: Design and performance of networks for super-, cluster-, and grid-computing: Part I
A Generic Mean Field Convergence Result for Systems of Interacting Objects
QEST '07 Proceedings of the Fourth International Conference on Quantitative Evaluation of Systems
A class of mean field interaction models for computer and communication systems
Performance Evaluation
Grid brokering for batch allocation using indexes
NET-COOP'07 Proceedings of the 1st EuroFGI international conference on Network control and optimization
A mean field approach for optimization in discrete time
Discrete Event Dynamic Systems
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This paper investigates the limit behavior of Markov decision processes made of independent particles evolving in a common environment, when the number of particles goes to infinity. In the finite horizon case or with a discounted cost and an infinite horizon, we show that when the number of particles becomes large, the optimal cost of the system converges to the optimal cost of a deterministic system. Convergence also holds for optimal policies. We further provide insights on the speed of convergence by proving several central limits theorems for the cost and the state of the Markov decision process with explicit formulas for the limit. Then, our framework is applied to a brokering problem in grid computing. Several simulations with growing numbers of processors are reported. They compare the performance of the optimal policy of the limit system used in the finite case with classical policies by measuring its asymptotic gain.