Abstract

During the last years, many speed-up techniques for Dijkstra 's algorithm have been developed. As a result, computing a shortest path in a staticroad network is a matter of microseconds. However, only few of those techniques work in time-dependentnetworks. Unfortunately, such networks appear frequentely in reality: Roads are predictably congestured by traffic jams, and efficient timetable information systems rely on time-dependent networks. Hence, a fast technique for routing in such networks is needed. In this work, we present an exacttime-dependent speed-up technique based on our recent SHARC-algorithm. As a result, we are able to efficiently compute shortest paths in time-dependent continental-sized transportation networks, both of roads and of railways. Document type: Part of book or chapter of book

Abstract

International audience We introduce a continuous time stochastic broadcast calculus for mobile and wireless networks. The mobility between nodes in a network is modeled by a stochastic mobility function which allows to change part of a network topology depending on an exponentially distributed delay and a network topology constraint. We allow continuous time stochastic behavior of processes running at network nodes, e.g. in order to be able to model randomized protocols. The introduction of group broadcast and an operator to help avoid flooding allows us to define a novel notion of broadcast abstraction. Finally, we define a weak bisimulation congruence and apply our theory on a leader election protocol. Document type: Part of book or chapter of book

Abstract

Probabilistic model checking mainly concentrates on techniques for reasoning about the probabilities of certain path properties or expected values of certain random variables. For the quantitative system analysis, however, there is also another type of interesting performance measure, namely quantiles. A typical quantile query takes as input a lower probability bound p and a reachability property. The task is then to compute the minimal reward bound r such that with probability at least p the target set will be reached before the accumulated reward exceeds r. Quantiles are well-known from mathematical statistics, but to the best of our knowledge they have not been addressed by the model checking community so far. In this paper, we study the complexity of quantile queries for until properties in discrete-time finite-state Markov decision processes with non-negative rewards on states. We show that qualitative quantile queries can be evaluated in polynomial time and present an exponential algorithm for the evaluation of quantitative quantile queries. For the special case of Markov chains, we show that quantitative quantile queries can be evaluated in time polynomial in the size of the chain and the maximum reward. Document type: Part of book or chapter of book