Comparative Study on Continuous and Descrete Spatial Assignment Model for Metropolitan Area

现有的离散交通网络模型确定交通网络中每个环节的交通流量，由于计算量巨大，不适用于密集、大型的城市道路网络。在这项研究中，我们采用连续的方法来逼近一个高密度的网络，并考虑基于城市区域交通流连续分布假设的交通分配模型。首先，利用约束变分理论和有限元技术，建立了理论模型和有效的计算算法；与以往方法不同的是，该模型考虑了出行起点单一、出行目的地连续分布的用户均衡配流问题，并提出了一种计算城市区域广义交通流分布的连续介质近似模型。该模型对于大规模交通分配是有效的，并用假设数据进行了数值验证。计算结果与所提出模型的预期行为相吻合。

The current discrete transportation network models, which determine traffic flow on every link of a transportation network, are rather inapplicable to dense and large urban road network because of the huge amount of computational work involved. In this study we adopt a continuous approach to approximate a highly dense network and consider the traffic assignment model based on the assumption of continuous traffic flow distribution over the urban area. Two types of models are presented containing both theoretical and applied analysis of the continuous approach.First, a theoretical model, complete with an efficient computational algorithm, is constructed by using constrained variational theory and FEM technology. Distinguished from the previous approaches, this model deals with the user-equilibrium assignment with a single trip origin and continuously distributed trip destinations.With the intention of complementing the theoretical approach, a continuum approximation model is also proposed for computing the generalized traffic flow distribution over the urban area. This model is demonstrated to be efficient for the large-scale traffic assignment.The continuum models presented in this study are numerically tested with hypothetical data. The computational results coincide with the expected behavior of the proposed models.