A generic class of first order node models for dynamic macroscopic simulation of traffic flows

Node models for macroscopic simulation have attracted relatively little attention in the literature. Nevertheless, in dynamic network loading (DNL) models for congested road networks, node models are as important as the extensively studied link models. This paper provides an overview of macroscopic node models found in the literature, explaining both their contributions and shortcomings. A formulation defining a generic class of first order macroscopic node models is presented, satisfying a list of requirements necessary to produce node models with realistic, consistent results. Defining a specific node model instance of this class requires the specification of a supply constraint interaction rule and (optionally) node supply constraints. Following this theoretical discussion, specific macroscopic node model instances for unsignalized and signalized intersections are proposed. These models apply an oriented capacity proportional distribution of the available supply over the incoming links of a node. A computationally efficient algorithm to solve the node models exactly is included.     

Schedule-based transit assignment model with vehicle capacity and seat availability

In this paper, we propose a new schedule-based equilibrium transit assignment model that differentiates the discomfort level experienced by sitting and standing passengers. The notion of seat allocation has not been considered explicitly and analytically in previous schedule-based frameworks. The model assumes that passengers use strategies when traveling from their origin to their destination. When loading a vehicle, standing on-board passengers continuing to the next station have priority to get available seats and waiting passengers are loaded on a First-Come-First-Serve (FCFS) principle. The stimulus of a standing passenger to sit increases with his/her remaining journey length and time already spent on-board. When a vehicle is full, passengers unable to board must wait for the next vehicle to arrive. The equilibrium conditions can be stated as a variational inequality involving a vector-valued function of expected strategy costs. To find a solution, we adopt the method of successive averages (MSA) that generates strategies during each iteration by solving a dynamic program. Numerical results are also reported to show the effects of our model on the travel strategies and departure time choices of passengers.     

Frequency-based transit assignment considering seat capacities

This paper proposes a frequency-based assignment model that considers travellers probability of finding a seat in their perception of route cost and hence also their route choice. The model introduces a “fail-to-sit” probability at boarding points with travel costs based on the likelihood of travelling seated or standing. Priority rules are considered; in particular it is assumed that standing on-board passengers will occupy any available seats of alighting passengers before newly boarding passengers can fill any remaining seats. At the boarding point passengers are assumed to mingle, meaning that FIFO is not observed, as is the case for many crowded bus and metro stops, particularly in European countries. The route choice considers the common lines problem and an user equilibrium solution is sought through a Markov type network loading process and the method of successive averages. The model is first illustrated with a small example network before being applied to the inner zone of London’s underground network. The effect of different values passengers might attach to finding a seat are illustrated. Applications of the model for transit planning as well as for information provision at the journey planner stage are discussed.     

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在城市轨道交通的线路网络形成、实行一票换乘并伴随投资主体多元化时,需要建立公平公正的票务清分机制,本文提出一个基于乘客旅行实际时间分布计算各路径上乘客比例的新方法.根据交通卡中的进出站的时间记录,计算出在一段时间内在一对出入站之间完成旅行的所有乘客的时间分布,以这个分布为依据计算在这段时间里各路径上的乘客比例.采用数值模拟的方法在一对有两条有效路径的出入站间产生乘客旅行时间的数据,然后根据这些数据进行客流比例计算.结果表明,即使两条路径的运营时间差异很小也能实现较准确的比例划分,这种动态计算客流分布的方法能更准确地反映实际客流分布.     

A path-based flow formulation for the traffic assignment problem

In order to improve cooperation between traffic management and travelers, traffic assignment is the key component to achieve the objectives of both traffic management and route choice decisions for travelers. Traffic assignment can be classified into two models based on the behavioral assumptions governing route choices: User Equilibrium (UE) and System Optimum (SO) traffic assignment. According to UE and SO traffic assignment, travelers usually compete to choose the least cost routes to minimize their own travel costs, while SO traffic assignment requires travelers to work cooperatively to minimize overall cost in the road network. Thus, the paradox of benefits between UE and SO indicates that both are not practical. Thus, a solution technique needs to be proposed to balance UE and SO models, which can compromise both sides and give more feasible traffic assignments. In this paper, Stackelberg game theory is introduced to the traffic assignment problem, which can achieve the trade-off process between traffic management and travelers. Since traditional traffic assignments have low convergence rates, the gradient projection algorithm is proposed to improve efficiency.     

Validation of a schedule‐based capacity restraint transit assignment model for a large‐scale network

This paper describes the application of a capacity restraint trip assignment algorithm to a real, large‐scale transit network and the validation of the results. Unlike the conventional frequency‐based approach, the network formulation of the proposed model is dynamic and schedule‐based. Transit vehicles are assumed to operate to a set of pre‐determined schedules. Passengers are assumed to select paths based on a generalized cost function including in‐vehicle and out‐of‐vehicle time and line change penalty. The time‐varying passenger demand is loaded onto the network by a time increment simulation method, which ensures that the capacity restraint of each vehicle during passenger boarding is strictly observed. The optimal‐path and path‐loading algorithms are applied iteratively by the method of successive averages until the network converges to the predictive dynamic user equilibrium. The Hong Kong Mass Transit Railway network is used to validate the model results. The potential applications of the model are also discussed.     

铁路枢纽折角车流数值变化的动态模拟

以解编车流作业规则和系统资源限制为约束,构造不同目标函数下铁路枢纽编组站作业分工数学模型,给出折角车流理论最大值和最小值及相应编组站作业分工方式及车流条件。基于折角车流变化的复杂性和多样性,将外部车流环境视为一个动态的随机输入,以特定铁路枢纽为背景用计算机模拟技术和遗传算法计算不同条件下折角车流数值解。通过对模拟数据趋势变化比较分析,提出铁路枢纽运输组织不应过分追求折角车流最小等结论。     

交通分配中的梯度投影算法及其改进模型

最近的研究表明基于路径的交通分配算法具有很强的生命力和广阔的应用前景。在这些算法中,梯度投影算法(GP)由于其极高的计算效率引起了研究者极大的兴趣。但是研究同样表明GP算法在求高精度分配解时遇到了收敛问题。文章首先介绍了GP算法的理论基础及算法步骤,然后分析了算法产生收敛问题的关键原因,针对其高精度解不能很好收敛的问题,采用二分法改进了其中关键的步长确定策略,提出了改进的GP算法(IGP,Improved GP),并通过计算实例比较了GP和IGP的表现,分析了IGP的优势。并用计算实例证明IGP在求解高精度分配解和整体收敛速度两方面都优于GP。     

A link-node complementarity model and solution algorithm for dynamic user equilibria with exact flow propagations

In this paper, we propose a link-node complementarity model for the basic deterministic dynamic user equilibrium (DUE) problem with single-user-class and fixed demands. The model complements link-path formulations that have been widely studied for dynamic user equilibria. Under various dynamic network constraints, especially the exact flow propagation constraints, we show that the continuous-time dynamic user equilibrium problem can be formulated as an infinite dimensional mixed complementarity model. The continuous-time model can be further discretized as a finite dimensional non-linear complementarity problem (NCP). The proposed discrete-time model captures the exact flow propagation constraints that were usually approximated in previous studies. By associating link inflow at the beginning of a time interval to travel times at the end of the interval, the resulting discrete-time model is predictive rather than reactive. The solution existence and compactness condition for the proposed model is established under mild assumptions. The model is solved by an iterative algorithm with a relaxed NCP solved at each iteration. Numerical examples are provided to illustrate the proposed model and solution approach. We particularly show why predictive DUE is preferable to reactive DUE from an algorithmic perspective.     

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Frank-Wolfe(FW)算法是一类广泛应用于求解交通分配问题的算法。它具有容易编程实现,所需内存少的特点。但是该算法收敛速度较慢,不能得到路径信息。为了提高算法的效率,本文研究三种流量更新策略(all-at-once, one-origin-at-a-time, one-OD-at-a-time)以及不同的步长搜索策略下的FW算法,其中步长搜索策略包括精确线性搜索方法(包括二分法、黄金分割法、成功失败法)和不精确的线性搜索方法(包括基于Wolfe-Powell收敛准则的搜索方法和Gao等提出的非单调线性搜索方法)。最后,本文将上述策略应用于四种不同规模的交通网络中,并给出较适合求解的组合。