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February 2018 Diffusion approximations for controlled weakly interacting large finite state systems with simultaneous jumps
Amarjit Budhiraja, Eric Friedlander
Ann. Appl. Probab. 28(1): 204-249 (February 2018). DOI: 10.1214/17-AAP1303

Abstract

We consider a rate control problem for an $N$-particle weakly interacting finite state Markov process. The process models the state evolution of a large collection of particles and allows for multiple particles to change state simultaneously. Such models have been proposed for large communication systems (e.g., ad hoc wireless networks) but are also suitable for other settings such as chemical-reaction networks. An associated diffusion control problem is presented and we show that the value function of the $N$-particle controlled system converges to the value function of the limit diffusion control problem as $N\to\infty$. The diffusion coefficient in the limit model is typically degenerate; however, under suitable conditions there is an equivalent formulation in terms of a controlled diffusion with a uniformly nondegenerate diffusion coefficient. Using this equivalence, we show that near optimal continuous feedback controls exist for the diffusion control problem. We then construct near asymptotically optimal control policies for the $N$-particle system based on such continuous feedback controls. Results from some numerical experiments are presented.

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Amarjit Budhiraja. Eric Friedlander. "Diffusion approximations for controlled weakly interacting large finite state systems with simultaneous jumps." Ann. Appl. Probab. 28 (1) 204 - 249, February 2018. https://doi.org/10.1214/17-AAP1303

Information

Received: 1 March 2016; Published: February 2018
First available in Project Euclid: 3 March 2018

zbMATH: 06873683
MathSciNet: MR3770876
Digital Object Identifier: 10.1214/17-AAP1303

Subjects:
Primary: 60H30 , 60K35 , 93E20
Secondary: 60J28 , 60J70 , 60K25 , 91B70

Keywords: ad hoc wireless networks , asymptotic optimality , diffusion approximations , Mean field approximations , propagation of chaos , rate control , Stochastic control , Stochastic networks

Rights: Copyright © 2018 Institute of Mathematical Statistics

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Vol.28 • No. 1 • February 2018
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