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This paper has investigated the growth pattern of traffic oscillations in the NGSIM vehicle trajectories data, via measuring the standard deviation of vehicle velocity involved in oscillations. We found that the standard deviation of the velocity increases in a concave way along vehicles in the oscillations. Moreover, all datasets collapse into a single concave curve, which indicates a universal evolution law of oscillations. A comparison with traffic experiment shows that the empirical and the experimental results are highly compatible and can be fitted by a single concave curve, which demonstrates that qualitatively the growth pattern of oscillations is not affected by type of bottleneck and lane changing behavior. We have shown theoretically that small disturbance with an angular frequency ω increases in a convex way in the initial stage in the traditional models presuming a unique relationship between speed and density, which obviously deviates from our findings. Simulations show that stochastic models in which the traffic state dynamically spans a 2D region in the speed-spacing plane can qualitatively or even quantitatively reproduce the concave growth pattern of traffic oscillations. [ABSTRACT FROM AUTHOR]

Abstract: Accurately estimating Origin–Destination (OD) trip tables based on traffic data has become crucial in many real-time traffic applications. The problem of OD estimation is traditionally modeled as a bilevel network design problem (NDP), which is challenging to solve in large-scale networks. In this paper, we propose a new one-level convex optimization formulation to reasonably approximate the bilevel structure, thus allowing the development of more efficient solution algorithms. This one-level approach is consistent with user equilibrium conditions, and improves previous one-level relaxed OD estimation formulations in the literature by ‘equilibrating’ path flows using external path cost parameters. Our new formulation can, in fact, be viewed as a special case of the user equilibrium assignment problem with elastic demand, and hence can be solved efficiently by standard path-based traffic assignment algorithms with an iterative parameter updating scheme. Numerical experiments indicate that this new one-level approach performs very well. Estimation results are robust to network topology, sensor coverage, and observation error, and can achieve further improvements when additional data sources are included. [Copyright &y& Elsevier]

Abstract: The method of successive averages is often used in iterative algorithms for solving various mathematical problems, and travel forecasting models in particular. In each iteration of these algorithms the current solution is averaged with an alternative solution generated by the algorithm. If the problem has an equivalent convex optimization formulation with a computable objective function, a line search can be used to determine the weight applied to the alternative solution, referred to as the step size. In the absence of a convex optimization formulation, the typical approach is to set the step size according to a predetermined sequence that is decreasing towards zero, such as 1/k where k is the iteration index. In this paper, we examine the use of a constant step size in the method of successive averages. A theoretical derivation shows that if the alternative solution generated by the algorithm is a linear function of the current solution, then using a constant step size is advantageous and substantially superior to using a sequence of decreasing step sizes. We conjecture that similar results may be expected in nonlinear differentiable problems as well. Numerical results are presented for a travel forecasting model that combines user-equilibrium route choice with an origin-destination-mode (ODM) choice model. The proposed algorithm is based on origin-based assignment, in conjunction with successive averaging of constant step sizes for the differentiable ODM model. The results show that a properly chosen constant step size leads to excellent convergence for both convex and non-convex models. A general strategy for choosing step sizes without a-priori knowledge is presented as well. [Copyright &y& Elsevier]