Approximation Techniques for Timing Analysis of Complex Real-Time Embedded Systems

To date, many industrial embedded systems are very large, flexible, and highly configurable software systems, containing millions of lines of code and consisting of hundreds of tasks, many with real-time constraints, being triggered in complex, nested patterns. Furthermore, the temporal dependencies between tasks in such systems are difficult to determine analytically, and they vary the execution time and response time of tasks greatly. We refer to such systems as Complex Real-Time Embedded Systems (CRTES). To maintain, analyze and reuse such CRTES is very difficult and expensive, which, nevertheless, offers high business value in response to great concern in industry. Moreover, in such context, not only the functional behavior of systems has to be assured, but also non-functional properties such as the temporal behavior, i.e., the Worst-Case Response Time (WCRT) of the adhering tasks in systems has to be known. However, due to high complexity of such systems and the nature of the problem, the exact WCRT of tasks is impossible to find in practice, but may only be bounded. In addition, the existing relatively well developed theories for modeling and analysis of real-time systems are having problems, which limit their application in the context. In this thesis, we address this challenge, and present a framework for approximate timing analysis of CRTES that provides a tight interval of WCRT estimates of tasks by the usage of three novel contributions. The first contribution is a statistical approach to WCRT analysis of CRTES. The proposed algorithm combines Extreme Value Theory with other statistical methods in order to produce a probabilistic WCRT estimate, using response time data from either Monte Carlo simulations of a detailed model of the system, or time-stamped traces of the real system execution. The focus of the method is to give a WCRT prediction with a given probability of being exceeded, which potentially could be considered as an upper bound on the WCRT estimate, especially in the case where conventional timing analysis methods cannot be applied. The second contribution is a concrete process of formally obtaining the exact value of both Worst-Case Execution Time (WCET) and WCRT of tasks by using upper-part binary search algorithms together with a timed model checker, after a semantic-preserving model transformation. The underline premise is that the size and complexity of CRTES have to be reduced such that they can be manageable by the model checking tool. The third contribution is the application of an optimization algorithm, in this case a meta-heuristic search algorithm, on top of the traditional Monte Carlo simulation. Combining optimization and simulation has shown to yield substantially better results with respect to tight lower bounds on WCRT estimates of tasks in CRTES. In addition, a number of tools have been implemented and used for the evaluation of the research results. These evaluations, using four simulation models depicting two fictive but representative industrial control applications, give clear indication that the proposed methods have the potential to be both applicable and useful in practice.