Stochastic Control Problems in Wireless Communications

该提案涉及现代随机控制理论的解析和数值方法在无线通信问题中的应用。这里考虑了两大类问题。第一个问题涉及随机连接下的数据通信，其中移动源并不总是对收发器可用。人们对相关的轮询问题知之甚少。主要源不可用的时期会在备份工作负载中产生跳跃，这种跳跃取决于轮询策略。我们关注的是有效的扩散近似，它可以减少问题的维度，并允许使用最优控制方法，最终是有效的数值方法。任意成本函数，一般统计结构和有限或无限缓冲区，以及噪声信道，智能天线和同步自适应轮询的使用都是感兴趣的。主要的技术是大流量分析和扩散近似技术，它们允许用一个更简单的低维问题来近似控制问题，而数值方法是可用的或将被开发出来。第二类问题涉及由于切换时缺乏可用频率而导致的呼叫丢失。这被表述为控制问题，其中控制的是进入系统的新条目，有点类似于中继线访问/路由问题。由于调用的损失应该相对较少且代价高昂，因此大偏差理论是一个合适的工具。大偏差环境下的控制问题是非经典的。一种新的理论方法极大地促进了对诸如无线领域出现的问题的分析，也为数值方法提供了基础，而数值方法是任何“工程”理论的重要组成部分。关键词：无线通信，随机连接，大流量近似，轮询，大偏差，切换损失。

ECS-9979250KushnerThe proposal concerns the application of the analytical and numerical methods of modern stochastic control theory to problems in wireless communications. Two broad clases of problems are considered. The first concerns data communications under random connectivity, where the mobile sources are not always available to the transceiver. Little is known about the asociated polling problem. Periods of unavailability of major sources create jumps in the backed up workload, and this jump depends on the polling policy. We are concerned with efficient diffusion approximations that reduce the problem dimension and allow the use of optimal control methods, and ultimately efficient numerical methods. Arbitrary cost functions, general statistical structures and either finite or infinite buffers are of interest, as well as noisy channels, and the use of smart antennas and simultaneous adaptive polling. The main techniques are those of heavy traffic analysis and diffusion approximation, which should shed considerable insight by allowing an approximation of the control problem by a much simpler one of lower dimension for which numerical method are either available or will be developed.The second class of problems concerns the loss of calls due to lack of available frequencies on handover. This is formulated as a control problem, where what one controls are the new entries into the system, somwhat analogous to what is done in the trunk line access/routing problem. Since the loss of calls should be relatively rare and are costly, the theory of large deviations is an appropriate tool. The problems of control within a large deviations context are nonclassical. A new approach to the theory greatly facilitates such analysis to problems such as those arising in wirless, and also provides a basis for numerical methods, an essential component of any "engineering" theory.Key words:Wireless communications, random connectivity, heavy traffic approxima-tions, polling, large deviations, handover losses.