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首页> 外文期刊>IEEE Transactions on Information Theory >On the Queue-Overflow Probability of Wireless Systems: A New Approach Combining Large Deviations With Lyapunov Functions
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On the Queue-Overflow Probability of Wireless Systems: A New Approach Combining Large Deviations With Lyapunov Functions

机译：无线系统的队列溢出概率：一种将大偏差与Lyapunov函数相结合的新方法

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摘要

In this paper, we study the queue-overflow probability of wireless scheduling algorithms. In wireless networks operated under queue-length-based scheduling algorithms, there often exists a tight coupling between the service-rate process, the system backlog process, the arrival process, and the stochastic process governing channel variations. Although one can use sample-path large-deviation techniques to form an estimate of the queue-overflow probability, the formulation leads to a difficult multidimensional calculus-of-variations problem. In this paper, we present a new technique to address this complexity issue. Using ideas from the Lyapunov function approach in control theory, this technique maps the complex multidimensional calculus-of-variations problem to a 1-D calculus-of-variations problem, and the latter is often much easier to solve. Further, under appropriate conditions, we show that when a scheduling algorithm minimizes the drift of a Lyapunov function at each point of every fluid sample path, the algorithm will be optimal in the sense that it maximizes the asymptotic decay rate of the probability that the Lyapunov function value exceeds a given threshold. We believe that these results can potentially be used to study the queue-overflow probability of a large class of wireless scheduling algorithms and to design new scheduling algorithms with optimal overflow probabilities.
机译：在本文中，我们研究了无线调度算法的队列溢出概率。在基于队列长度的调度算法下运行的无线网络中，服务速率过程，系统积压过程，到达过程以及控制信道变化的随机过程之间通常存在紧密的联系。尽管可以使用样本路径大偏差技术来估计队列溢出概率，但是这种表达方式导致了一个困难的多维变异数问题。在本文中，我们提出了一种解决此复杂性问题的新技术。运用控制理论中Lyapunov函数方法的思想，该技术将复杂的多维变量计算问题映射到一维变量计算问题，后者通常更容易解决。此外，在适当的条件下，我们表明，当调度算法使每个流体样本路径的每个点处的Lyapunov函数的漂移最小时，该算法将在最大化Lyapunov概率的渐近衰减率的意义上是最优的函数值超过给定阈值。我们相信这些结果可以潜在地用于研究一大类无线调度算法的队列溢出概率，并设计具有最佳溢出概率的新调度算法。

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