In the design of probabilistic timed systems, bounded requirements concerning behaviour that occurs within a given time, energy, or more generally cost budget are of central importance. Traditionally, such requirements have been model-checked via a reduction to the unbounded case by unfolding the model according to the cost bound. This exacerbates the state space explosion problem and significantly increases runtime. In this paper, we present three new algorithms to model-check time- and cost-bounded properties for Markov decision processes and probabilistic timed automata that avoid unfolding. They are based on a modified value iteration process, on an enumeration of schedulers, and on state elimination techniques. We can now obtain results for any cost bound on a single state space no larger than for the corresponding unbounded or expected-value property. In particular, we can naturally compute the cumulative distribution function at no overhead. We evaluate the applicability and compare the performance of our new algorithms and their implementation on a number of case studies from the literature.
Download