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Separability and Response Times in Stochastic Models (SPARTACOS)

随机模型中的可分离性和响应时间 (SPARTACOS)

基本信息

批准号：
EP/D047587/1
负责人：
Peter Harrison
金额：
$ 35.93万
依托单位：
Imperial College London
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2006
资助国家：
英国
起止时间：
2006 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FD047587%2F1
关键词：
Separability Response Times Stochastic Models

项目摘要

Quantitative methods are vital for the design of efficient systems: in ICT, communication networks and other logistical areas such as business processes and healthcare systems. However, the resulting models need to be both accessible to the designer, rather than only to the performance specialist, and efficient. A sufficiently expressive formalism is needed that can specify models at a high level of description and also facilitate separable -- and hence efficient -- mathematical solutions. Stochastic process algebra is a formalism that has the potential to meet these requirements and will be applied to system-state probabilities.To date, SPA has not addressed response times, a critical QoS metric, quantile targets of which are set in almost all transaction processing systems and others highly topical at the present time, e.g. the NHS. Separable solutions for (Laplace transforms of) response time density functions in networks will be sought in MPA using reversed processes, analogous to the method of RCAT. In addition, discrete state models are not always the most appropriate: it may be preferable to aggregate many objects of the same type into a single quantity, leading to a continuous state, or fluid model; cf. large numbers of gas molecules represented by a volume. Separable solutions will therefore be sought for both (Laplace transforms of) network response time density functions and for fluid SPA.Four main research areas are identified: theory and development of MPA, with respect to semantics, other formalisms like stochastic Petri-nets and efficient solution methods; algorithms for response time distributions and their moments in complex, single nodes; development of a theory and methodology to analyse response times in networks of interacting nodes; and a parallel theme on fluid process algebraic models.Regarding the first area, it is important to obtain a syntactic mapping from the most general form of MPA suitable for our separability analysis into established formalisms, both process algebraic and other. Application of our MPA formalism will be implemented as computer programs to find both product-forms as well as new, separable, non-product-forms.The study of response times will involve first analysis of single components and then interaction of components in an MPA framework. We will focus on direct methods to obtain the moments, from which often quantiles can also be estimated accurately.These results will be incorporated into networks: to give exact, separable results (analogous to conventional product-forms for state probabilities) in special cases, using reversed processes, and approximate results otherwise.Finally, a PhD student will explore the new area of fluid MPA where models have a continuous (real number) state and so are analysed through coupled differential equations. One objective is to find a separable solution as for state probabilities (above).The theoretical output offers the prospect of a revolutionary new approach to the quantitative design of systems of interacting processes: in ICT, commerce, the environment and perhaps biology through the fluid models. The practical impact will be to endow diverse system design tools with a powerful and efficient performance analysis capability. This will be overseen and disseminated through active collaboration with IBM and Metron Technology, culminating in a workshop to be hosted by IBM at Hursley Park in the final year of the project.

定量方法对于设计高效的系统至关重要：在ICT，通信网络和其他物流领域，如业务流程和医疗保健系统。然而，所产生的模型需要对设计师（而不仅仅是性能专家）和高效都是可访问的。一个充分表达的形式主义是必要的，可以指定模型在一个高层次的描述，也有利于可分离的-因此有效的-数学解决方案。随机进程代数是一种形式主义，有可能满足这些要求，并将被应用到系统状态probability.To日期，SPA还没有解决响应时间，一个关键的QoS度量，分位数的目标，其中设置在几乎所有的事务处理系统和其他高度热门的，在目前的时间，如NHS。网络中响应时间密度函数（的拉普拉斯变换）的可分离解将在MPA中使用类似于RCAT的方法的逆过程来寻求。此外，离散状态模型并不总是最合适的：最好是将许多相同类型的对象聚合成单个量，从而产生连续状态或流体模型;参见。用体积表示的大量气体分子。因此，将为这两个问题分别寻求解决办法（拉普拉斯变换）网络响应时间密度函数和流体SPA.四个主要的研究领域被确定：MPA的理论和发展，相对于语义，其他形式主义，如随机Petri网和有效的解决方法，算法的响应时间分布和他们的时刻在复杂的，单节点;发展一种理论和方法来分析相互作用节点网络中的响应时间;关于第一个领域，重要的是获得从适合于我们的可分性分析的MPA的最一般形式到已建立的形式主义的句法映射，都是代数的和其他的过程。我们的MPA形式主义的应用将被实现为计算机程序，以找到产品形式以及新的，可分离的，非产品的forms.The响应时间的研究将涉及到首先分析单个组件，然后在MPA框架中的组件的相互作用。我们将专注于获得矩的直接方法，通常分位数也可以准确估计。这些结果将被纳入网络：给出精确的、可分离的结果（类似于状态概率的常规乘积形式），在特殊情况下，使用反向过程，否则近似结果。最后，博士生将探索流体MPA的新领域，其中模型具有连续（真实的数）状态，因此通过耦合微分方程进行分析。一个目标是找到一个可分离的解决方案，为状态概率（上述）。理论输出提供了一个革命性的新方法的定量设计的相互作用的过程：在信息通信技术，商业，环境，也许生物通过流体模型的系统的前景。其实际影响将是赋予不同的系统设计工具强大而有效的性能分析能力。这将通过与IBM和Metron Technology的积极合作来监督和传播，最终将在项目的最后一年由IBM在赫斯利公园主办一个研讨会。