Efficiently solving the user equilibrium traffic assignment problem with elastic demand (UE-TAPED) for transportation networks is a critical problem for transportation studies. Most existing UE-TAPED algorithms are designed using a sequential computing scheme, which cannot take advantage of advanced parallel computing power. Therefore, this study focuses on model decomposition and parallelization, proposing an origin-based formulation for UE-TAPED and proving an equivalent reformulation of the original problem. Furthermore, the alternative direction method of multipliers (ADMM) is employed to decompose the original problem into independent link-based subproblems, which can solve large-scale problems with small storage space. In addition, to enhance the efficiency of our algorithm, the parallel computing technology with optimal parallel computing schedule is implemented to solve the link-based subproblems. Numerical experiments are performed to validate the computation efficiency of the proposed parallel algorithm.

This paper addresses two shortcomings of the data-driven stochastic fundamental diagram for freeway traffic. The first shortcoming is related to the least-squares methods which have been widely used in establishing traffic flow fundamental diagrams. We argue that these methods are not suitable to generate the percentile-based stochastic fundamental diagrams, because the results generated by least-squares methods represent weighted sample mean, rather than percentile. The second shortcoming is widespread use of independent modeling methodology for a family of percentile-based fundamental diagrams. Existing methods are inadequate to coordinate the fundamental diagrams in the same family, and consequently, are not in alignment with the basic rules in probability theory and statistics. To address these issues, this paper proposes a holistic modeling framework based on the concept of mean absolute error minimization. The established model is convex, but non-differentiable. To efficiently implement the proposed methodology, we further reformulate this model as a linear programming problem which could be solved by the state-of-the-art solvers. Experimental results using real-world traffic flow data validate the proposed method.