Urban form,commuting patterns and CO2 emissions: What differences between the municipality’s residents and its jobs?

This article investigates the links between urban form and commuting patterns, and the CO₂ emissions associated with them, in the municipalities that comprise the New Town of Marne-la-Vallée (NTMV) located in the Paris Region. The paper distinguishes between the commutes performed by residents and those generated by the jobs located in a municipality. The contribution of the paper is twofold. Firstly, it shows that the CO₂ emissions of commutes differ greatly depending on whether one considers residents or jobs: hence focusing on the travel behaviour of residents can lead to significant errors in the assessment of the CO₂ emissions generated by a municipality, and therefore its environmental sustainability. Secondly, the paper explores the relationship between commuting trips and several indicators of urban form: density, compactness, jobs-to-residents ratio, accessibility to public transport and distance from Paris. We highlight that high jobs-to-residents ratios tend to increase the proportion of jobs held by residents. Density and compactness are associated with more sustainable travel behaviour among residents, but not non-residents. Finally, the shape of the public transport system, which mainly connects the municipalities of the NTMV with Paris, tends to decrease the proportion of jobs held by residents, especially in the municipalities that are close to Paris, and does not allow non-residents, most of whom do not travel from Paris, to use public transport.     

A partial differential equation formulation of Vickrey’s bottleneck model,part I: Methodology and theoretical analysis

This paper is concerned with the continuous-time Vickrey model, which was first introduced in Vickrey (1969). This model can be described by an ordinary differential equation (ODE) with a right-hand side which is discontinuous in the unknown variable. Such a formulation induces difficulties with both theoretical analysis and numerical computation. Moreover it is widely suspected that an explicit solution to this ODE does not exist. In this paper, we advance the knowledge and understanding of the continuous-time Vickrey model by reformulating it as a partial differential equation (PDE) and by applying a variational method to obtain an explicit solution representation. Such an explicit solution is then shown to be the strong solution to the ODE in full mathematical rigor. Our methodology also leads to the notion of generalized Vickrey model (GVM), which allows the flow to be a distribution, instead of an integrable function. As explained by Han et al. (in press), this feature of traffic modeling is desirable in the context of analytical dynamic traffic assignment (DTA). The proposed PDE formulation provides new insights into the physics of The Vickrey model, which leads to a number of modeling extensions as well as connection with first-order traffic models such as the Lighthill–Whitham–Richards (LWR) model. The explicit solution representation also leads to a new computational method, which will be discussed in an accompanying paper, Han et al. (in press).