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A Probabilistic Real-Time Calculus for Performance Evaluation

机译：绩效评估的概率实时微积分

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In this paper we develop a probabilistic real-time calculus for performance evaluation. The calculus applies a simple generative model of probabilities. Next to probabilistic action transitions, probabilistic time transitions are supported. An operational characterization is given in terms of a labelled transition system. the operational rules for the real-time part of the calculus are constructed in such a way, that the transition system can be interpreted as a discrete-time Markov chain. They further yield a constructive approach towards the efficient execution of processes and generation of transition graphs. On top of the operational rules, bisimulation equivalence is defined and proven to be a congruence for all operators. We define three different performance characteristics in terms of reward functions and prove that equivalent processes have an identical performance. Using an ergodic theorem of Markov chains, we further show how these performance figures can be computed in practice. We introduce an experimental software tool and we show how it can be applied to calculate the performance of a nontrivial real-time data communication protocol.
机译：在本文中，我们开发了概率的实时微积分进行绩效评估。微积分适用于简单的生成模型的概率。旁边的概率动作转换，支持概率的时间转换。根据标记的过渡系统给出了操作表征。用于实时部分的微积分的操作规则以这种方式构建，转换系统可以被解释为离散时间马尔可夫链。它们进一步产生了有效执行过程和转换图的产生的建设性方法。在操作规则之上，定义了双催化等价，并证明是所有运营商的一致性。我们在奖励函数方面定义了三种不同的性能特征，并证明了等效流程具有相同的性能。使用马尔可夫链的遍历定理，我们进一步展示了这些性能数字如何在实践中计算。我们介绍了一个实验软件工具，我们展示了如何应用于计算非竞争实时数据通信协议的性能。

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