权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Stability and performance analysis of multi-dimensional sequences of random variables, with applications

多维随机变量序列的稳定性和性能分析及其应用

基本信息

批准号：
EP/L026767/1
负责人：
Vsevolod Shneer
金额：
$ 12.77万
依托单位：
Heriot-Watt University
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2014
资助国家：
英国
起止时间：
2014 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FL026767%2F1
关键词：
Stability performance analysis multi dimensional

项目摘要

In many applications the time-evolution of processes of interest may be represented as a random vector where the components are dependent but one of them has an easily predictable and understandable behaviour, while the other one is much more difficult to analyse. It is therefore of great importance to develop methods for the mathematical analysis of the behaviour of the entire sequence, using the knowledge on the behaviour of one of the components and on the dependence between the components.My main focus will be on stability, performance and optimality of such sequences of random variables, arising from various systems of applied interest. Stability may be loosely defined as the ability of a system to work in a well-controlled and well-predictable manner. Stability ensures a guaranteed quality of service to the customer and the use of resources below maximum capacity to the server. The question of stability is therefore a very important one and arguably the first question one needs to ask when studying a stochastic system. Once stability is established, one may ask various questions of performance and optimality and compare different governing algorithms (policies, strategies) with respect to different performance metrics.My research will lead to the creation of new advanced probability methods and hence will be a step forward in the area of stochastic modelling. It will also be beneficial in a number of application areas: wireless communication networks, economics, energy and potentially others. In wireless communication networks my results will shed light on the stability and throughputs achieved by some known transmission protocols and also on delays experienced by individual transmissions. I will also work on constructing new algorithms, achieving better performance (in terms of stability, throughput or delays) in specific networks of practical interest. I plan to construct decentralised (not requiring a presence of a central controlling entity) algorithms achieving the best possible stability characteristics. In economics, my results will be interesting from a theoretical point of view and will lead to a better understanding of the behaviour of numerous economic models. In energy I will investigate different storage strategies and find optimal ones with respect to a performance metric of interest (for example minimising the cost or minimising probability of a shortage).

在许多应用中，感兴趣的过程的时间演化可以表示为随机向量，其中分量是相关的，但是其中一个具有容易预测和理解的行为，而另一个则更难以分析。因此，这是非常重要的发展方法的数学分析的行为的整个序列，使用知识的行为之一的组件和组件之间的依赖关系。我的主要重点将是稳定性，性能和最优性等序列的随机变量，所产生的各种系统的应用兴趣。稳定性可以被松散地定义为系统以良好控制和良好可预测的方式工作的能力。稳定性确保了对客户的服务质量的保证，以及对服务器的资源使用低于最大容量。因此，稳定性问题是一个非常重要的问题，可以说是研究随机系统时需要问的第一个问题。一旦建立稳定性，人们可能会问各种问题的性能和最优性，并比较不同的治理算法（政策，战略）相对于不同的性能metrics.My研究将导致新的先进的概率方法的创建，因此将是一个进步的随机建模领域。它还将有益于许多应用领域：无线通信网络、经济、能源和潜在的其他领域。在无线通信网络中，我的研究结果将揭示一些已知的传输协议所实现的稳定性和吞吐量，以及个人传输所经历的延迟。我还将致力于构建新的算法，在实际感兴趣的特定网络中实现更好的性能（在稳定性，吞吐量或延迟方面）。我计划构建分散的（不需要存在一个中央控制实体）算法，实现最佳的稳定特性。在经济学中，我的研究结果从理论的角度来看将是有趣的，并将导致更好地理解许多经济模型的行为。在能源方面，我将研究不同的存储策略，并找到与感兴趣的性能指标相关的最佳策略（例如最小化成本或最小化短缺概率）。