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A practical technique for bounding the time between events in concurrent real-time systems

Showing that concurrent systems satisfy timing constraints on their behavior is difficult, but may be essential for critical applications. Most methods are based on some form of reachability analysis and require construction of a state space of size that is, in general, exponential in the number of components in the concurrent system. In an earlier paper with L. K. Dillon and J. E. Wileden, we described a technique for finding bounds on the time between events without enumerating the state space, but the technique applies chiefly to the case of logically concurrent systems executing on a uniprocessor, in which events do not overlap in time. In this paper, we extend that technique to obtain upper bounds on the time between events in maximally parallel concurrent systems. Our method does not require construction of the state space and the results of preliminary experiments show that, for at least some systems with large state spaces, it is quite tractable. We also briefly describe the application of our method to the case in which there are multiple processors, but several processes run on each processor.