Model checking for probabilistic timed automata

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 model-checking 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.