DIFFUSION APPROXIMATIONS FOR CONTROLLED WEAKLY INTERACTING LARGE FINITE STATE SYSTEMS WITH SIMULTANEOUS JUMPS

• 成果类型: Article
• 署名作者: Budhiraja, Amarjit; Friedlander, Eric
• 署名单位: University of North Carolina; University of North Carolina Chapel Hill
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/17-AAP1303
• 发表日期: 2018
• 页码: 204-249
• 关键词: Asymptotic Optimality; stochastic networks; LIMIT-THEOREMS; CONVERGENCE; SEQUENCES

摘要

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 -> infinity. 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.