Hybridization of a class of "second order" models of traffic flow

Despite the simultaneous progress of traffic modelling both on the macroscopic and microscopic front, recent works [E. Bourrel, J.B. Lessort, Mixing micro and macro representation of traffic flow: a hybrid model based on the LWR theory, Transport. Res. Rec. 1852 (2003) 193–200; D. Helbing, M. Treiber, Critical discussion of “synchronized flow”, Coop. Transport. Dyn. 1 (2002) 2.1–2.24; A. Hennecke, M. Treiber, D. Helbing, Macroscopic simulations of open systems and micro–macro link, in: D. Helbing, H.J. Herrmann, M. Schreckenberg, D.E. Wolf (Eds.), Traffic and Granular Flow ’99, Springer, Berlin, 2000, pp. 383–388] highlighted that one of the most promising way to simulate efficiently traffic flow on large road networks is a clever combination of both traffic representations: the hybrid modelling. Our focus in this paper is to propose two hybrid models for which the macroscopic (resp. mesoscopic) part is based on a class of second order model [A. Aw, M. Rascle, Resurection of second order models of traffic flow?, SIAM J. Appl. Math. 60 (2000) 916–938] whereas the microscopic part is a Follow-the Leader type model [D.C. Gazis, R. Herman, R.W. Rothery, Nonlinear follow-the-leader models of traffic flow, Oper. Res. 9 (1961) 545–567; R. Herman, I. Prigogine, Kinetic Theory of Vehicular Traffic, American Elsevier, New York, 1971]. For the first hybrid model, we define precisely the translation of boundary conditions at interfaces and for the second one we explain the synchronization processes. Furthermore, through some numerical simulations we show that the waves propagation is not disturbed and the mass is accurately conserved when passing from one traffic representation to another.

Modelling road traffic accidents using macroscopic second-order models of traffic flow

In this paper, we introduce a macroscopic model for road traffic accidents along highway sections. We discuss the motivation and the derivation of such a model, and we present its mathematical properties. The results are presented by means of examples where a section of a crowded one-way highway contains in the middle a cluster of drivers whose dynamics are prone to road traffic accidents. We discuss the coupling conditions and present some existence results of weak solutions to the associated Riemann Problems. Furthermore, we illustrate some features of the proposed model through some numerical simulations. © The authors 2012.

Road traffic congestion and public information - An experimental investigation

This paper reports laboratory experiments designed to study the impact of public information about past departure rates on congestion levels and travel costs. Our design is based on a discrete version of Arnott et al.'s (1990) bottleneck model. In all treatments, congestion occurs and the observed travel costs are quite similar to the predicted ones. Subjects' capacity to coordinate is not affected by the availability of public information on past departure rates, by the number of drivers or by the relative cost of delay. This seemingly absence of treatment effects is confirmed by our finding that a parameter-free reinforcement learning model best characterises individual behaviour.

Stated choices and benefit estimates in the context of traffic calming schemes:Utility maximization, regret minimization, or both?

This paper proposes a discrete mixture model which assigns individuals, up to a probability, to either a class of random utility (RU) maximizers or a class of random regret (RR) minimizers, on the basis of their sequence of observed choices. Our proposed model advances the state of the art of RU-RR mixture models by (i) adding and simultaneously estimating a membership model which predicts the probability of belonging to a RU or RR class; (ii) adding a layer of random taste heterogeneity within each behavioural class; and (iii) deriving a welfare measure associated with the RU-RR mixture model and consistent with referendum-voting, which is the adequate mechanism of provision for such local public goods. The context of our empirical application is a stated choice experiment concerning traffic calming schemes. We find that the random parameter RU-RR mixture model not only outperforms its fixed coefficient counterpart in terms of fit-as expected-but also in terms of plausibility of membership determinants of behavioural class. In line with psychological theories of regret, we find that, compared to respondents who are familiar with the choice context (i.e. the traffic calming scheme), unfamiliar respondents are more likely to be regret minimizers than utility maximizers. © 2014 Elsevier Ltd.