CONTROLLED STOCHASTIC NETWORKS IN HEAVY TRAFFIC: CONVERGENCE OF VALUE FUNCTIONS

• 成果类型: Article
• 署名作者: Budhiraja, Amarjit; Ghosh, Arka P.
• 署名单位: University of North Carolina; University of North Carolina Chapel Hill; Iowa State University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/11-AAP784
• 发表日期: 2012
• 页码: 734-791
• 关键词: open processing networks; Asymptotic Optimality; skorokhod problem; Singular control; convex duality; SYSTEM

摘要

Scheduling control problems for a family of unitary networks under heavy traffic with general interarrival and service times, probabilistic routing and an infinite horizon discounted linear holding cost are studied. Diffusion control problems, that have been proposed as approximate models for the study of these critically loaded controlled stochastic networks, can be regarded as formal scaling limits of such stochastic systems. However, to date, a rigorous limit theory that justifies the use of such approximations for a general family of controlled networks has been lacking. It is shown that, under broad conditions, the value function of the suitably scaled network control problem converges to that of the associated diffusion control problem. This scaling limit result, in addition to giving a precise mathematical basis for the above approximation approach, suggests a general strategy for constructing near optimal controls for the physical stochastic networks by solving the associated diffusion control problem.