Stochastic Metrics for Debugging the Timing Behaviour of Real-Time Systems

Stochastic analysis techniques for real-time systems model the execution time of tasks as random variables. These techniques constitute a very powerful tool to study the behaviour of real-time systems. However, as they can not avoid all the timing bugs in the implementation, they must be combined with measurement techniques in order to gain more confidence in the implemented system. In this paper, a set of tools to measure, analyze and visualize traces of real-time systems is presented. These tools are driven by stochastic models. In order to find bugs in the timing behaviour of the system, two metrics, called "pessimism" and "optimism", are proposed. They are based on two random variables, the optimistic and the pessimistic execution time, which are also introduced in this paper. These metrics are used in the debugging tools to compare the model and the measured system in order to find errors. The metrics are examined in three case studies.