论文标题
随机变量具有可测量性约束，并应用于机会性调度
Random Variables with Measurability Constraints with Application to Opportunistic Scheduling
论文作者
论文摘要
本文证明了关于随机元件的序列的表示，这些元素序列在Borel空间中采用值，并且相对于由Sigma代数的任意结合产生的Sigma代数可测量。这与Kallenberg的相关表示定理一起用于在离散的时间随机控制问题中与可测量性和因果关系约束，在离散的时间随机控制问题中表征多维决策向量，包括时间变化的通信网络的机会性调度问题。精炼了这些系统的网络容量定理，而无需通过引入两个可测量性假设并使用可构造集的理论来对状态空间进行隐式和任意复杂的扩展。提供了在描述性集合中使用众所周知的病理学的一个示例，以表明不可衡量的调度方案可以胜过所有可衡量的调度方案。
This paper proves a representation theorem regarding sequences of random elements that take values in a Borel space and are measurable with respect to the sigma algebra generated by an arbitrary union of sigma algebras. This, together with a related representation theorem of Kallenberg, is used to characterize the set of multidimensional decision vectors in a discrete time stochastic control problem with measurability and causality constraints, including opportunistic scheduling problems for time-varying communication networks. A network capacity theorem for these systems is refined, without requiring an implicit and arbitrarily complex extension of the state space, by introducing two measurability assumptions and using a theory of constructible sets. An example that makes use of well known pathologies in descriptive set theory is given to show a nonmeasurable scheduling scheme can outperform all measurable scheduling schemes.
