Marie Duflot

Probabilistic Model Checking of the CSMA/CD Protocol Using PRISM and APMC

Carrier Sense Multiple Access/Collision Detection (CSMA/CD) is the protocol for carrier transmission access in Ethernet networks (international standard IEEE 802.3). On Ethernet, any Network Interface Card (NIC) can try to send a packet in a channel at any time. If another NIC tries to send a packet at the same time, a collision is said to occur and the packets are discarded. The CSMA/CD protocol was designed to avoid this problem, more precisely to allow a NIC to send its packet without collision. This is done by way of a randomized exponential backoff process. In this paper, we analyse the correctness of the CSMA/CD protocol, using techniques from probabilistic model checking and approximate probabilistic model checking. The tools that we use are PRISM and APMC. Moreover, we provide a quantitative analysis of some CSMA/CD properties.

COSMOS: A Statistical Model Checker for the Hybrid Automata Stochastic Logic

This tool paper introduces \cosmos, a statistical model checker for the Hybrid Automata Stochastic Logic (HASL). HASL employs Linear Hybrid Automata (LHA), a generalization of Deterministic Timed Automata (DTA), to describe relevant execution paths of a Discrete Event Stochastic Process (DESP), a class of stochastic models which includes, but is not limited to, Markov chains. As a result HASL verification turns out to be a unifying framework where sophisticated temporal reasoning is naturally blended with elaborate reward-based analysis. COSMOS takes as input a DESP (described in terms of a Generalized Stochastic Petri Net), an LHA and an expression

Randomized dining philosophers without fairness assumption

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Petri nets compositional modeling and verification of Flexible Manufacturing Systems

representing the quantity to be estimated. It returns a confidence interval estimation of

Measuring Permissivity in Finite Games

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Computing Expected Absorption Times for Parametric Determinate Probabilistic Timed Automata

. COSMOS is written in C++ and is freely available to the research community.

A probabilistic property-specific approach to information flow

Abstract.We consider Lehmann-Rabin’s randomized solution to the well-known problem of the dining philosophers. Up to now, such an analysis has always required a “fairness” assumption on the scheduling mechanism: if a philosopher is continuously hungry then he must eventually be scheduled. In contrast, we modify here the algorithm in order to get rid of the fairness assumption, and we claim that the spirit of the original algorithm is preserved. We prove that, for any (possibly unfair) scheduling, the modified algorithm converges: every computation reaches with probability 1 a configuration where some philosopher eats. Furthermore, we are now able to evaluate the expected time of convergence in terms of the number of transitions. We show that, for some “malicious” scheduling, this expected time is at least exponential in the number N of philosophers.

Unavoidable Configurations of Parameterized Rings of Processes

Flexible Manufacturing Systems (FMS) are amongst the most studied types of systems, however due to their increasing complexity, there is still room for improvement in their modeling and analysis. In this paper we consider the design and the analysis of stochastic models of FMS in two complementary respects. First we describe a (stochastic) Petri Nets based compositional framework which enables to model an FMS by combination of an arbitrary number of basic components. Second we demonstrate how classical transient-analysis of manufacturing systems, including reliability and performability analysis, can be enriched by application of a novel, sophisticated stochastic logic, namely the Hybrid Automata Stochastic Logic (HASL). We demonstrate the proposed methodology on an FMS example.

Decidability of parameterized probabilistic information flow

In this paper, we extend the classical notion of strategies in turn-based finite games by allowing several moves to be selected. We define and study a quantitative measure for permissivity of such strategies by assigning penalties when blocking transitions. We prove that for reachability objectives, most permissive strategies exist, can be chosen memoryless, and can be computed in polynomial time, while it is in NP *** coNP for discounted and mean penalties.

HASL: an expressive language for statistical verification of stochastic models

We consider a variant of probabilistic timed automata called parametric determinate probabilistic timed automata}. Such automata are fully probabilistic: there is a single distribution of outgoing transitions from each of the automatons nodes, and it is possible to remain at a node only for a given amount of time. The residence time within a node may be given in terms of a parameter, and hence we do not assume that its concrete value is known. We claim that, often in practice, the maximal expected time to reach a given absorbing node of a probabilistic timed automaton can be captured using a parametric determinate probabilistic timed automaton. We give a method for computing the expected time for a parametric determinate probabilistic timed automaton to reach an absorbing node. The method consists in constructing a variant of a Markov chain with costs (where the costs correspond to durations), and is parametric in the sense that the expected absorption time is computed as a function of the models parameters. The complexity of the analysis is independent from the maximal constant bounding the values of the clocks, and is polynomial in the number of edges of the original parametric determinate probabilistic timed automaton.