Approximate product-forms and reversed processes for performance analysis (APROPOS)

在复杂的计算机和通信系统的定量设计中，对模型的需求是无可争议的，但它们的构建受到缺乏统一的方法论的阻碍，该方法论用于从较小的组件模型（反映系统本身的设计过程）构建大型模型。在过去的四十年里，各种特定的，通常是临时的，技术已经发展到当代的设计特征，从模拟多程序主机系统的网络到移动的网络的网络演算描述和电信系统和互联网的随机模型。不幸的是，这样的模型往往是指数（或更高）的增长，计算复杂性，一种现象，通常被称为状态空间explosion .The本建议的目的是提供技术和工具，用于获得有效的，主要是近似的，现代网络模型的解决方案。在几乎所有的复杂系统的分析中，目标是找到可分离的解决方案，允许子系统（组件）单独解决，然后以简单的方式将其解决方案组合起来。更具体地说，我们建议通过一个为期三年的项目，支持Marin作为RA，发展提案人和Andrea Marin博士最近取得的重要成果。上述结果导致了一些研究和辅导论文已被接受和/或在我们的研究领域的最高质量的国际场所提出。这是提议者的观点，研究是在一个膝盖在一个向上的曲线和机会，直接与一个冉冉升起的明星，如马林是一个不容错过的，如果在所有可能的;除了上述论文和教程，马林已赢得最佳论文奖在两个国际会议上，他在这方面的工作在过去的12个月。此外，在纽约举行的Sigmetrics 2010年会上所作的介绍受到了好评，并导致与国际领先研究人员进行了多次讨论，并制定了具体的合作计划-见支持案例。提出的理论研究将补充现有的分析技术，如嵌入式网络建模（QNM），这仍然是相关的，但缺乏表达能力的建模今天的系统。例如，随机Petri网（SPN）适合于描述虚拟资源系统，例如在云计算中使用的虚拟资源系统，这不是标准嵌入式网络的情况。类似地，具有批量移动的（非标准）网络在节能系统的模型中很重要（参见支持案例），但通常没有可分离的（或其他有效的）解决方案;与此相关的初步结果将在11月的Performance'10上作为海报展示。最后，优化是由我们独特的方法的能力，使用反向复合代理定理（RCAT），扰动规格，以创建可分离的解决方案，承认寻找最适合的产品形式的解决方案的可能性。基于这些理论和实践的发展，拟议项目的第一个目标是加强RCAT方法，以产品形式和半成品，适用于具有SPN规格的型号和具有批量移动的网络。也许更重要的是，任务在沿着路径传递时的响应时间的概率密度函数将在一类新的网络中进行研究;已经获得了初步结果，并将在上述海报中展示。这项工作是一个重大的进步，既定的方法，如Boxma和Daduna的，以及建议的PI以前。我们相信，在AESOP研究小组中，提案人和Marin之间三年不间断的合作将实现上述总结和目标下列出的目标。

The need for models in the quantitative design of complex computer and communicaton systems is indisputable but their construction is hampered by the lack of a uniform methodology for building large models from smaller component-models - mirroring the design process of the systems themselves. Various specific, often ad hoc, techniques have been developed over the last four decades in response to contemporary design features, beginning with queueing networks that modeled multiprogrammed mainframe systems through to network-calculus descriptions of mobile networks and stochastic models of telecommunication systems and the internet. Unfortunately, such models are prone to exponential (or higher) growth in computational complexity, a phenomenon often referred to as state-space explosion .The present proposal aims to provide techniques and tools for deriving efficient, mainly approximate, solutions to models of modern networks. As in almost all analyses of such complex systems, the aim is to find separable solutions, which allow subsystems (components) to be solved separately and their solutions to then be combined in a simple way. More specifically, we propose to develop the recent significant results obtained by the proposer and Dr Andrea Marin through a three-year project supporting Marin as the RA. The said results have led to a number of research and tutorial papers that have been accepted and/or presented at the highest quality international venues in our research area. It is the proposer's view that the research is at a knee in an upward curve and the opportunity to work directly with a rising-star such as Marin is one not to be missed if at all possible; in addition to the above papers and tutorials, Marin has won best paper awards at two international conferences for his work in this area in the last 12 months. Furthermore, the presentation at Sigmetrics 2010 in New York was well received and led to several discussions with leading international researchers and plans for specific collaboration - see the Case for Support. The theoretical research proposed will supplement existing analytical techniques, such as queueing network modeling (QNM), which are still relevant but are lacking in expressive power for modeling today's systems. For example, Stochastic Petri Nets (SPNs) are suitable for describing virtual resource systems, as used in cloud computing for example, which is not the case for standard queueing networks. Similarly, (non-standard) networks with batch movements are important in models of energy-efficient systems (see the Case for Support), but in general do not have separable (or other efficient) solutions; preliminary results relating to this will be presented as a poster at Performance'10 in November. Last, optimisation is facilitated by the ability of our unique approach, using the Reversed Compound Agent Theorem (RCAT), to perturb specifications so as to create separable solutions, admitting the possibility of searching for a best-fit product-form solution.Based on these theoretical and practical developments, the first objective of the proposed project is to enhance the RCAT-approach to product-forms and semi-product-forms for application in models with SPN specifications and in networks with batch-movements. Perhaps even more importantly, the probability density function of the response time of tasks in passing along a path will be investigated in a new class of networks; preliminary results have already been obtained and will also be presented in the aforementioned poster. This work is a substantial advance on established approaches, such as Boxma and Daduna's as well as that of the proposed PI previously. We believe that three years of uninterrupted collaboration between the proposer and Marin in the AESOP research group will attain the goals summarised above and listed under Objectives .