Separability and Response Times in Stochastic Models (SPARTACOS)

量化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。但是，生成的模型需要既可供设计人员访问，而不是仅供性能专家访问，而且还需要高效。需要一种具有足够表现力的形式主义，它可以在高级别的描述中指定模型，并促进可分离的--因此也是有效的--数学解决方案。随机进程代数是一种可能满足这些要求的形式化方法，并将应用于系统状态概率。到目前为止，SPA还没有解决响应时间，这是一个关键的Qos度量，几乎所有的事务处理系统和其他目前高度热门的系统，如NHS，都设定了响应时间的分位数目标。网络中响应时间密度函数(拉普拉斯变换)的可分离解将使用类似于RCAT方法的反向过程在MPA中进行求解。此外，离散状态模型并不总是最合适的：可能更可取的做法是将许多相同类型的对象聚合成单个数量，从而形成连续状态或流体模型；以体积表示的大量气体分子。因此，我们将为网络响应时间密度函数(拉普拉斯变换)和流体SPA寻找可分离的解。我们确定了四个主要研究领域：关于语义的MPA的理论和发展，其他形式如随机Petri网和有效求解方法；复杂单节点中响应时间分布及其矩的算法；分析相互作用节点的网络中的响应时间的理论和方法的发展；以及流体过程代数模型的平行主题。关于第一个领域，重要的是从最一般的适合于我们的可分离性分析的MP的形式到已建立的形式的语法映射，既包括过程代数，也包括其他形式。我们的MPA形式主义的应用将被实现为计算机程序，以寻找产品形式以及新的、可分离的、非产品形式。响应时间的研究将首先涉及单个组件的分析，然后是组件在MPA框架中的相互作用。我们将重点介绍直接获得矩的方法，从这些矩也可以准确地估计分位数。这些结果将被整合到网络中：在特殊情况下使用反向过程给出准确的、可分离的结果(类似于传统的状态概率乘积形式)，否则给出近似结果。最后，一名博士生将探索流体MPA的新领域，在该领域，模型具有连续(实数)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关于状态概率的可分离的解决方案。理论输出为相互作用过程系统的定量设计提供了一种革命性的新方法：通过流体模型，在ICT、商业、环境，也许还有生物学中。其实际影响将是赋予各种系统设计工具强大而高效的性能分析能力。这将通过与IBM和Metron Technology的积极合作来监督和传播，最终将在项目最后一年由IBM在赫斯利公园主办的研讨会上完成。

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.