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For urban rail transit network, the space-time flow distribution can play an important role in evaluating and optimizing the space-time resource allocation. For obtaining the space-time flow distribution without the restriction of schedules, a dynamic assignment problem is proposed based on the concept of continuous transmission. To solve the dynamic assignment problem, the cell transmission model is built for urban rail transit networks. The priority principle, queuing process, capacity constraints and congestion effects are considered in the cell transmission mechanism. Then an efficient method is designed to solve the shortest path for an urban rail network, which decreases the computing cost for solving the cell transmission model. The instantaneous dynamic user optimal state can be reached with the method of successive average. Many evaluation indexes of passenger flow can be generated, to provide effective support for the optimization of train schedules and the capacity evaluation for urban rail transit network. Finally, the model and its potential application are demonstrated via two numerical experiments using a small-scale network and the Beijing Metro network.

The path choice behavior of battery electric vehicle (BEV) drivers is influenced by the lack of public charging stations, limited battery capacity, range anxiety and long battery charging time. This paper investigates the congestion/flow pattern captured by stochastic user equilibrium (SUE) traffic assignment problem in transportation networks with BEVs, where the BEV paths are restricted by their battery capacities. The BEV energy consumption is assumed to be a linear function of path length and path travel time, which addresses both path distance limit problem and road congestion effect. A mathematical programming model is proposed for the path-based SUE traffic assignment where the path cost is the sum of the corresponding link costs and a path specific out-of-energy penalty. We then apply the convergent Lagrangian dual method to transform the original problem into a concave maximization problem and develop a customized gradient projection algorithm to solve it. A column generation procedure is incorporated to generate the path set. Finally, two numerical examples are presented to demonstrate the applicability of the proposed model and the solution algorithm.