An empirical comparison of alternative user equilibrium traffic assignment methods

Abstract

1. ABSTRACT This paper presents an empirical comparison of alternative methods for computing user equilibrium on large regional transportation networks. Specifically, it examines the solution characteristics, convergence behavior and associated computing times of link-based, origin-based, and path-based methods. The latter two methods use more memory and are computationally more demanding, but have been touted in the literature as converging more rapidly than the link-based Frank-Wolfe method or variants thereof, that are commonly employed in planning software. The principal motivation in searching for improved methods is achieving more rapid and/or tighter convergence in the computation of equilibrium. Greater convergence is needed for accurate forecasting the impacts associated with road and public transport projects and affects nearly all aspects and components of transportation models as well as being a major determinant of their internal consistency. Congested travel speeds are typically used to compute trip distribution and mode choice, and these speeds will be incorrect if a satisfactory traffic assignment is not achieved. Due to long computational times, many models are insufficiently calibrated and converged for forecasting purposes. This problem is partly the result of and is compounded by the slow convergence of the Frank-Wolfe algorithm. In order to perform this research, origin-based and path-based algorithms were coded following the existing literature and tested on networks on large networks of the type that are representative of regional travel demand forecasting efforts for major metropolitan regions. The algorithms coded were those described by Chen et al.(2002) and Dial (2006). An executable version of origin-based traffic assignment code written by one of its proponents (Bar-Gera, 2002) and made freely available for research was also tested. The new algorithms were compared with the current production version of the traffic assignment in TransCAD which is based upon the Frank-Wolfe algorithm and has been shown to be faster than other commercial implementations in the United States. Concurrent with this research, the F-W traffic assignment in TransCAD was multi-threaded leading to speedups in computation proportionate to the number of central processing units and/or CPU cores available. This raises the bar for new assignment algorithms, especially if they are less suitable than F-W for multi-threading.

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