Diffusion approximations for controlled stochastic networks: An asymptotic bound for the value function
Diffusion approximations for controlled stochastic networks: An asymptotic bound for the value function
复制标题
受控随机网络的扩散近似：值函数的渐近界
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
Arka P. Ghosh
中科院分区：
文献类型：
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作者：
A. Budhiraja;Arka P. Ghosh
研究一类大流量下具有一般到达时间和服务时间、概率路由和无限视界折现线性等待成本的统一网络的调度控制问题。引入了控制策略可容许性的自然非预期性条件。这个条件被认为适用于广泛的问题。利用这一可容许控制的公式和时间变换技术，我们建立了网络控制问题在所有可容许的排序控制策略上的代价的最小值是由一个相关的扩散控制问题（布朗控制问题）的值函数渐近有界的。这一结果为广泛网络的任何可接受控制策略的最佳可实现性能提供了一个有用的界限。
We consider the scheduling control problem for a family of unitary networks under heavy traffic, with general interarrival and service times, probabilistic routing and infinite horizon discounted linear holding cost. A natural nonanticipativity condition for admissibility of control policies is introduced. The condition is seen to hold for a broad class of problems. Using this formulation of admissible controls and a time-transformation technique, we establish that the infimum of the cost for the network control problem over all admissible sequencing control policies is asymptotically bounded below by the value function of an associated diffusion control problem (the Brownian control problem). This result provides a useful bound on the best achievable performance for any admissible control policy for a wide class of networks.