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

点击翻译按钮获取中文摘要

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).