A Variational Finite Element Method for Source Inversion for Convective-Diffusive Transport

We consider the inverse problem of determining an arbitrary source in a time-dependent convective-diffusive transport equation, given a velocity field and pointwise measurements of the concentration. Applications that give rise to such problems include determination of groundwater or airborne pollutant sources from measurements of concentrations, and identification of sources of chemical or biological attacks. To address ill-posedness of the problem, we employ Tikhonov and total variation regularization. We present a variational formulation of the first order optimality system, which includes the initial-boundary value state problem, the final-boundary value adjoint problem, and the space-time boundary value source problem. We discretize in the space-time volume using Galerkin finite elements. Several examples demonstrate the influence of the density of the sensor array, the effectiveness of total variation regularization for discontinuous sources, the invertibility of the source as the transport becomes increasingly convection-dominated, the ability of the space-time inversion formulation to track moving sources, and the optimal convergence rate of the finite element approximation

The potential of metering roundabouts: influence in transportation externalities

Roundabouts are increasingly being used on busy arterial streets for traffic calming purposes. However, if one roundabout leg is near a distribution hub, e.g. parking areas of shopping centers, the entry traffic volumes will be particularly high in peak hours. This paper investigated a partial-metering based strategy to reduce traffic-related costs in a corridor. Specifically, the resulting traffic performance, energy, environmental and exposure impacts associated with access roundabouts were studied in an urban commercial area, namely: a) to characterize corridor operations in terms of link-specific travel time, fuel consumption, carbon dioxide and nitrogen oxides emissions, and noise costs; b) to propose an optimization model to minimize above outputs; and c) to demonstrate the model applicability under different traffic demand and directional splits combinations. Traffic, noise and vehicle dynamics data were collected from a corridor with roundabouts and signalized intersections near a commercial area of Guimarães, Portugal. Microscopic traffic and emission modeling platforms were used to model traffic operations and estimate pollutant emissions, respectively. Traffic noise was estimated with a semi-dynamical model. Link-based cost functions were developed based on the integrated modeling structure. Lastly, a Sequential quadratic programming type approach was applied to find optimal timing settings. The benefit of the partial-metering system, in terms of costs, could be up to 13% with observed traffic volumes. The efficiency of the proposed system increased as entering traffic at the metered approaches increased (~7% less costs). The findings let one to quantify metering benefits near shopping areas

Average travel time estimations for urban routes that consider exit turning movements

This paper presents a methodology for real-time estimation of exit movement-specific average travel time on urban routes by integrating real-time cumulative plots, probe vehicles, and historic cumulative plots. Two approaches, component based and extreme based, are discussed for route travel time estimation. The methodology is tested with simulation and is validated with real data from Lucerne, Switzerland, that demonstrate its potential for accurate estimation. Both approaches provide similar results. The component-based approach is more reliable, with a greater chance of obtaining a probe vehicle in each interval, although additional data from each component is required. The extreme-based approach is simple and requires only data from upstream and downstream of the route, but the chances of obtaining a probe that traverses the entire route might be low. The performance of the methodology is also compared with a probe-only method. The proposed methodology requires only a few probes for accurate estimation; the probe-only method requires significantly more probes

Modelling signal platoon patterns by approach lane use and movement class

lane-based signal platoon progression model has been developed for estimating performance measures as a function of signal offsets, geometric design and flow conditions. This is part of a lane-based network model that involves the blockage of upstream intersection lanes by downstream queues (backward spread of congestion) and a capacity constraint applied to oversaturated upstream intersections. The model takes into account midblock lane changes that apply to signal platoon patterns. This is particularly important in evaluating closely-spaced intersections with high demand flows where vehicles have limited opportunities for lane changes between intersections. The modelling of signal platoon patterns is further enhanced by assigning two types of movements negotiating the network to special movement classes. These are the through movements at external approaches which become turning movements at downstream internal approaches, and the dogleg movements at staggered T intersections. These movements can be assigned to separate lanes and separate signal phases, and their second-by-second platoon patterns can be tracked through the network separately. This improves the quality of signal platoon modelling and is expected to produce better results in assessing signal coordination quality and optimising signal offsets. The use of special movement classes also helps to estimate unequal lane use cases at external approaches of a paired intersection system, a factor which also affects signal platoon patterns. A staggered T-intersection example is presented to demonstrate important aspects of modelling signal platoon patterns by approach lane use and movement class