The Duration Calculi are calculi for designing real-time software
embedded systems. The Calculi overviewed in the paper include the
Duration Calculus, the Extended Duration Calculus, the Mean Value
Calculus and the Probabilistic Duration Calculus. They are extensions
of an Interval Temporal Logic, and can accommodate some concepts of
mathematical analysis such as integrals, mean values, piecewise
continuity and differentiability of functions over continuous
time. The Calculi can be used to capture and refine real-time
requirements for hybrid systems, to define real-time
behaviour/semantics of computing systems, and to calculate system
dependability in terms of requirement satisfaction probability.