Abstract Probabilistic timed automata (PTAs) are a formalism for modelling systems whose behaviour incorporates both probabilistic and real-time characteristics. Applications include wireless communication protocols, automotive network protocols and randomised security protocols. This paper gives an introduction to PTAs and describes techniques for analysing a wide range of quantitative properties, such as "the maximum probability of the airbag failing to deploy within 0.02 seconds", "the maximum expected time for the protocol to terminate" or "the minimum expected energy consumption required to complete all tasks". We present a temporal logic for specifying such properties and then give a survey of available modelchecking techniques for formulae specified in this logic. We then describe two case studies in which PTAs are used for modelling and analysis: a probabilistic non-repudiation protocol and a task-graph scheduling problem.
Probabilistic Timed Automata REF (PTA) have been proposed to model both probabilistic and timed behaviors.
Model checking for probabilistic timed automata
Formal Methods in System Design
Computer Science