Performance analysis of real-time rewriting models

Real-time systems usually involve a subtle interaction of a number of distributed components and have a high degree of parallelism, which makes their performance analysis quite complex. Thus, traditional techniques, such as simulation, fail to produce reasonable results. Formal methods pose an interesting solution but they usually lack the capabilities to reason about quantitative time and probabilistic properties, which play a vital role in performance analysis. This paper addresses this issue by presenting a formal approach for assessing the performance of a real-time system. To describe the evolution of the system, we use a real-time rewriting logic, in which we mechanize the extraction of quantitative information from a timed model. To evaluate the performance, we first consider the set of runs obtained from different initial input values that are not equivalent modulo the equational theory associated with the model. The overall performance of the system is then evaluated as the performance of each run weighted by its probability mass function. In order to illustrate the practical effectiveness of the proposed approach, we present the formal modeling and performance analysis of a simple search engine.