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Probabilistic behavior is omnipresent in computer controlled systems, inparticular, so-called safety-critical hybrid systems, because of variousreasons, like uncertain environments, or fundamental properties of nature. Inthis paper, we extend existing hybrid process algebra $ACP_{hs}^{srt}$ withprobability without replacing nondeterministic choice operator. In view of someshortcomings in existing approximate probabilistic bisimulation, we relax theconstrains and propose a novel approximate probabilistic bisimulation relation.After that, we present a performance evaluation language, CTRML, to reason overprobabilistic systems, which extend the results to real number. Along with thespecification language, we present a set of algorithms for the evaluation ofthe language. Additionally, we transfer the hybrid process algebra toprobabilistic transition system and show experimental results.

Formal modeling and performance evaluation for hybrid systems:a probabilistic hybrid process algebra-based approach