GOALI: Collaborative Education and Research on Stochastic Process Models in Telecommunication

这个项目发展了两种数学方法来分析通信中的问题。首先是入住率模型的大偏差分析。占用模型提供了一个简单、通用的概率结构，在许多领域都有应用。提出的大偏差方法不同于以前对这类模型的许多分析，并且是对它们的补充。受有线和无线通信问题的启发，该研究计划将开发可明确计算的大偏差渐近近似，并将开发诸如重要性抽样等方法，以便在非渐近状态下提供准确的结果。第二个主题是移动通信随机自适应算法的设计。该领域的应用范围较窄，是下一代高速无线接入系统的工程师特别感兴趣的领域。但是，在这个范围内，这些活动是一般的和基本的性质。本文的重点是发展无线调度算法的分析方法，以及新算法的发展。这个项目将为现代电信的两个重要领域发展数学方法，重点是对研究生进行广泛的大学/工业培训。该研究计划的一个关键组成部分是贝尔实验室和布朗大学对研究生的联合监督。对于参与的研究生，将有在朗讯科技的暑期实习机会，这将在许多方面补充更传统的培训。两个重点研究领域，即占用模型和无线调度，都是具有挑战性的智力问题，这些问题是由商业技术的发展所激发的。除了与特定的行业导师一起工作外，学生还有机会参加讲座和研讨会，并从接触各种各样的当前问题和正在发展的解决方法中获益。拟议的合作研究和相关的系列研讨会将有助于加强贝尔实验室和布朗大学之间的联系，活跃两所机构的学术氛围。这项研究的目标是在一个可能适用于未来问题的框架内，为解决当前感兴趣的问题提供坚实的、基本的数学基础。

This project develops two mathematical methods for the analysis of problems in communications. The first is the large deviations analysis of occupancy models. Occupancy models provide a simple, generic probabilistic construct that has found use in many fields. The proposed large deviations approach is different from and complementary to much of the previous analysis of such models. Motivated by problems from both wired and wireless communications, the research program will develop explicitly computable large deviation asymptotic approximations, and will also develop methods such as importance sampling to provide accurate results even in the non-asymptotic regime. The second topic is the design of stochastic adaptive algorithms for mobile communication. This area of application is narrower in scope, being of particular interest to engineers of next generation, high-rate wireless access systems. However, within that scope, the activities are general and fundamental in nature. The emphasis here is on the development of methods for the analysis of scheduling algorithms in wireless, and on the development of new algorithms. This project will develop mathematical methods for two important areas in modern telecommunication, with an emphasis on a broad university/industrial training of graduate students. A key component of the research program is the joint supervision of graduate students between Bell Labs and Brown University. For the graduate students that are involved, there will be summer internships at Lucent Technologies, which will supplement the more traditional training in a number of ways. Both research areas of focus, namely occupancy models and wireless scheduling, are challenging intellectual problems that are motivated by developing commercial technology. In addition to working with specific industrial mentors, the students also have the opportunity to attend talks, seminars and generally benefit from exposure to a wide variety of current problems and solution methods whose development is in progress. The proposed collaborative research and associated seminar series will help to strengthen the ties between Bell Labs and Brown University, invigorating the intellectual climate at both institutions. The goal of the proposed research is to provide solid, fundamental mathematical foundations for solving problems of current interest, in a framework that will likely be applicable to problems of the future.