Michel Roussignol

Bivariate Gamma wear processes for track geometry modelling, with application to intervention scheduling

This article discusses the intervention scheduling of a railway track, based on the observation of two dependent randomly increasing deterioration indicators. These two indicators are modelled through a bivariate Gamma process constructed by trivariate reduction. Empirical and maximum likelihood estimators are given for the process parameters and tested on simulated data. An expectation-maximisation (EM) algorithm is used to compute the maximum likelihood estimators. A bivariate Gamma process is then fitted to real data of railway track deterioration. Intervention scheduling is defined, ensuring that the railway track remains of good quality with a high probability. The results arecompared to those based on both indicators taken separately, and also on one single indicator. The policy based onthe joint information is proved to be safer than the other ones, which shows the potential of the bivariate model.

Characterization of the marginal distributions of Markov processes used in dynamic reliability

In dynamic reliability, the evolution of a system is described by a piecewise deterministic Markov process (It,Xt)t≥0 with state-space E×ℝd, where E is finite. The main result of the present paper is the characterization of the marginal distribution of the Markov process (It,Xt)t≥0 at time t, as the unique solution of a set of explicit integro-differential equations, which can be seen as a weak form of the Chapman-Kolmogorov equation. Uniqueness is the difficult part of the result.

A stochastic jump process applied to traffic flow modelling

The paper presents the main aspects of a stochastic conservative model of the evolution of the number of vehicles per road section. The model, defined in continuous time on a discrete space, follows a misanthrope Markovian process. It is a mesoscopic traffic model in the following sense: the vehicles are individually considered, but their dynamics are aggregated per section. The model parameters are supply and demand functions in equilibrium (i.e. a fundamental diagram). In order to model flows on a traffic network, different schemes of junction dynamics are proposed. The model properties in transient and stationary states are investigated analytically in simple cases and by simulation. The results show that the process presents classical properties of deterministic macroscopic model such as the propagation of shock or rarefaction wave for Riemann initial condition. On the other hand, one observes phenomena usually related to high order models, such as a wide scattering of the flow performances or the propagation (backward or forward according to the density level) of local perturbations, due to the stochasticity.

Piecewise deterministic Markov processes and maintenance modeling: application to maintenance of a train air-conditioning system

This paper deals with the preventive maintenance (PM) optimization of air-conditioning systems used aboard regional trains in France by the SNCF (French Railway Company). Two kinds of PM policies are envisioned: one with a single overhaul in the whole lifetime of the air-conditioning system, another with opportunistic replacements of components that are too old at each system failure. The air-conditioning system is formed of about 20 ageing and stochastically independent components. The envisioned PM policies make them functionally dependent, however. Both PM optimizations are performed with respect to the same cost function, involving the mean number of component replacements on some finite horizon. In view of its numerical assessment, a piecewise deterministic Markov processes (PDMP) model is used, both to model the maintained and the unmaintained system; a deterministic numerical scheme is next proposed, based on finite volume (FV) methods for PDMPs; owing to difficulties in its implementation, an approximation of this scheme is next used, which is much easier to implement than the initial FV scheme. As a result of using this method, it was finally possible to optimize both PM policies, which are both proved to lower the cost function of about 7 per cent.

A general framework for some asymptotic reliability formulas

The authors prove that certain reliability formulas which link asymptotic availability, mean normal operation time, mean time between failures, mean number of failures over a period of time and asymptotic Vesely rate, and which are well known in the case of modelling using a Markov jump process or an alternating renewal process, are also true in the context of more general modelling.

Modeling and quantification of aging systems for maintenance optimization

To conclude, this method quickly gives us reliability quantities that allow us to find an optimal maintenance. The methodology can be used for many systems. However the limitations are the number of aging components and the system complexity. Indeed, the computational time increases with those two parameters. In the future, we will try to apply this method with more complex systems and keep the computational time low. Focus will also be put on the determination of importance and sensibility indicators, in order to be able to identify the essential components of the systems, from the maintenance optimization point of view.

Generic First-Order Car-Following Models with Stop-and-Go Waves and Exclusion

A new Optimal Velocity (OV) car-following model is defined and explored. The model is solely based on an optimal speed function and a reaction time, and, oppositely to classical OV models, is intrinsically collision-free. If the model has uniform solutions, kink-antikink and soliton stop-and-go patterns can be described with a linear bounded optimal velocity function when the reaction time is high enough.

Stationary State Properties of a Microscopic Traffic Flow Model Mixing Stochastic Transport and Car-Following

We study the stationary properties of a microscopic traffic flow model related to a continuous time mass transport process. It is a stochastic collision-free mapping of a classical deterministic first order car-following model calibrated by the targeted speed function and the driver reaction time. The stationary states of the model are analytically treated for vanishing reaction time. Some approximations are calculated, assuming a product form of the invariant measure. When the reaction time is strictly positive, the process is studied by simulation. A relation between the parameters and the propagation of kinematic stop-and-go waves is identified as identical to the well-known stability condition of the car-following model. The results underline a negative impact of the driver reaction time parameter on the homogeneity of the flow in stationary state.