Application of Accelerated Equilibrium Traffic Assignments to Regional Planning Models
H Slavin, J Brandon, A Rabinowicz, S Sundaram, Caliper, US
Recently, there have been important advances in accelerating the computation of user equilibrium traffic assignments on large regional transportation networks. These advances not only both speed up planning model calculations but they also make impact analysis more precise and less prone to random error. In this paper, we describe these advances and present important information that has resulted from their application. We also provide recommendations on how to exploit these improvements in existing planning models.
One of these advances comes from multi-threading the algorithm used in most planning packages. Multi-threading is a form of parallel processing that is made possible by the availability of multi-core and multiple processor PCs. Although it requires a re-write of the software for the traffic assignment, the Frank-Wolfe (FW) method that underlies conventional user equilibrium traffic assignments is very well suited to multi-threading and we have achieved speedups that are proportional to the number of CPU cores available. With low cost computers offering 8 or more cores, the eightfold speedup reduces the burden of model calculations and also makes it possible to reach higher levels of convergence without an increase in computing time.
The other and more important advance comes from new UE algorithms that are origin or path-based that can reach much lower levels of convergence than the F-W method whose rate of convergence slows the longer it runs. For example, our origin user equilibrium (OUE) method based on Dial?s algorithm B converges more rapidly making it possible to compute solutions fairly quickly to previously unthinkable levels of convergence. By comparing solutions at different levels of convergence with highly converged solutions, we can quantify levels of convergence error in traffic assignments and assess their consequences.
From empirical testing of a variety of realistic assignment problems, we have concluded that much greater convergence than is typically used in regional models is needed for accurately forecasting the impacts associated with road and public transport projects. It also can be important for calculating the congested travel speeds that affect 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 tightly converged traffic assignment is not achieved. While some day equilibrium dynamic assignments will be used in planning models, static models are now the main source of congested skims. Unfortunately, due to long computational times and inefficient algorithms, many models are insufficiently calibrated and converged for forecasting purposes.
Lastly, we revisit and further investigate the value of tight convergence in traffic assignments. In our work we compared solutions from different levels of less converged solutions with highly converged solutions. We also investigate the point at which there are diminishing returns from increased convergence. While this will vary by region and local traffic conditions, our results show current levels of convergence are insufficient for normal traffic modeling and impact assessment and often lead to implausible results. However, when converged to gaps on the order of 10-5 or better, the traffic assignments are credible. Importantly, project impacts assessed in terms of travel time savings estimates are much more accurate and reliable.
Association for European Transport