Performance Analysis of Probabilistic Timed Automata Using Digital Clocks

Abstract

Probabilistic timed automata, a variant of timed automata extended with discrete probability distributions, is a modelling formalism suitable for describing formally both nondeterministic and probabilistic aspects of real-time systems, and is amenable to model checking against probabilistic timed temporal logic properties. However, the previously developed verification algorithms either suffer from high complexity, give only approximate results, or are restricted to a limited class of properties. In the case of classical (non-probabilistic) timed automata it has been shown that for a large class of real-time verification problems correctness can be established using an integral model of time (digital clocks) as opposed to a dense model of time. Based on these results we address the question of under what conditions digital clocks are sufficient for the performance analysis of probabilistic timed automata and show that this reduction is possible for an important class of systems and properties including probabilistic reachability and expected reachability. We demonstrate the utility of this approach by applying the method to the performance analysis of three probabilistic real-time protocols: the dynamic configuration protocol for IPv4 link-local addresses, the IEEE 802.11 wireless local area network protocol and the IEEE 1394 FireWire root contention protocol. concerns the ZeroConf dynamic configuration protocol for IPv4 link-local addresses [18] (preliminary results concerning this case study can be found in [37]). The second extends the results of [40], and investigates the performance of the contention resolution protocol of the IEEE 802.11 wireless local area network standard [33]. In the third case study we consider the root contention protocol of the IEEE 1394 FireWire standard [32], previously studied using probabilistic timed automata in [41,20]. In the latter two publications, the analysis was with respect to probabilistic reachability properties, whereas in this paper we study expected reachability properties.

Assume-Guarantee Verification for Probabilistic Systems

“…Using the digital clocks approach of [13], verifying real-time probabilistic systems can often be reduced to analysis of a PA with time steps encoded as a special action type. Such requirements are then naturally encoded as safety properties.…”

“…We use the PA model from [13] consisting of two components, one representing a new host joining the network (parameterised by K, the number of probes it sends before using an IP address), and the second representing the environment, i.e. the existing network.…”

Stochastic Games for Verification of Probabilistic Timed Automata

“…Full details of all these case studies, their parameters, and the properties checked are available. We present a comparison of our implementation with the two other existing techniques for reachability analysis of PTAs: backwards reachability [17] and digital clocks [15]. For the former, we use the implementation of [17] which uses PRISM as a back-end to analyse MDP.…”

“…There are three main existing algorithmic approaches to the verification of PTAs: (i) forwards reachability [16,5]; (ii) backwards reachability [17]; and (iii) digital clocks [15]. Forwards reachability is based on a symbolic forwards exploration, similar to the techniques implemented in state-of-the art tools for nonprobabilistic timed automata [6,18].…”

“…This computes exact values for both minimum and maximum reachability probabilities; however, the operations required to implement it are expensive, limiting its applicability. The digital clocks technique of [15] uses an efficient language-level translation to a probabilistic model with finite state semantics. This also gives precise values for minimum and maximum probabilities, but is only applicable to a restricted class of PTAs.…”