Development potential of the Northeast Passage based on a multinomial-logit-based stochastic user equilibrium model

We developed a multinomial-logit-based stochastic user equilibrium(MNL SUE)model incorporating time value of cargo to investigate future proportions of cargo flow through the Northeast Passage(NEP)and the Suez Canal Route between representative ports.We studied navigation during the ice-free and ice-covered seasons using sea ice projections for 2070 based on 1991–2021 NEP ice data.Sailing distance and time between selected ports are lower via the NEP than the Suez Canal Route.Under the scenario of year-round operation of the NEP,the proportion of cargo flow through the NEP is estimated to be 68.5%,which represents considerable commercial potential.Proportions are higher for the ice-free season and for ports at high latitudes.We also assessed flow under different scenarios.Under the scenario of fuel price increase,proportion of flow through the NEP in the ice-covered season is expected to increase.If time value is ignored,flow through the NEP is expected to increase all year round.If shippers become more cost-conscious,flow through the NEP is also expected to increase.

Sensitivity analysis for stochastic user equilibrium with elastic demand assignment model

This paper puts forward a rigorous approach for a sensitivity analysis of stochastic user equilibrium with the elastic demand （SUEED） model. First, proof is given for the existence of derivatives of output variables with respect to the perturbation parameters for the SUEED model. Then by taking advantage of the gradient-based method for sensitivity analysis of a general nonlinear program, detailed formulae are developed for calculating the derivatives of designed variables with respect to perturbation parameters at the equilibrium state of the SUEED model. This method is not only applicable for a sensitivity analysis of the logit-type SUEED problem, but also for the probit-type SUEED problem. The application of the proposed method in a numerical example shows that the proposed method can be used to approximate the equilibrium link flow solutions for both logit-type SUEED and probit-type SUEED problems when small perturbations are introduced in the input parameters.

A mixed stochastic user equilibrium model considering influence of advanced traveller information systems in degradable transport network

Advanced traveler information systems （ATIS） can not only improve drivers＇ accessibility to the more accurate route travel time information, but also can improve drivers＇ adaptability to the stochastic network capacity degradations. In this paper, a mixed stochastic user equilibrium model was proposed to describe the interactive route choice behaviors between ATIS equipped and unequipped drivers on a degradable transport network. In the proposed model the information accessibility of equipped drivers was reflected by lower degree of uncertainty in their stochastic equilibrium flow distributions, and their behavioral adaptability was captured by multiple equilibrium behaviors over the stochastic network state set. The mixed equilibrium model was formulated as a fixed point problem defined in the mixed route flows, and its solution was achieved by executing an iterative algorithm. Numerical experiments were provided to verify the properties of the mixed network equilibrium model and the efficiency of the iterative algorithm.

Cumulative prospect theory-based user equilibrium model with stochastic perception errors

The cumulative prospect theory(CPT) is applied to study travelers' route choice behavior in a degradable transport network. A cumulative prospect theory-based user equilibrium(CPT-UE) model considering stochastic perception error(SPE) within travelers' route choice decision process is developed. The SPE is conditionally dependent on the actual travel time distribution, which is different from the deterministic perception error used in the traditional logit-based stochastic user equilibrium. The CPT-UE model is formulated as a variational inequality problem and solved by a heuristic solution algorithm. Numerical examples are provided to illustrate the application of the proposed model and efficiency of the solution algorithm. The effects of SPE on the reference point determination, cumulative prospect value estimation, route choice decision and network performance evaluation are investigated.

A stochastic user equilibrium model solving overlapping path and perfectly rational issues

Traffic assignment has been recognized as one of the key technologies in supporting transportation planning and operations.To better address the perfectly rational issue of the expected utility theory(EUT)and the overlapping path issue of the multinomial logit(MNL)model that are involved in the traffic assignment process,this paper proposes a cumulative prospect value(CPV)-based generalized nested logit(GNL)stochastic user equilibrium(SUE)model.The proposed model uses CPV to replace the utility value as the path performance within the GNL model framework.An equivalent mathematical model is provided for the proposed CPV-based GNL SUE model,which is solved by the method of successive averages(MSA).The existence and equivalence of the solution are also proved for the equivalent model.To demonstrate the performance of the proposed CPV-based GNL SUE model,three road networks are selected in the empirical test.The results show that the proposed model can jointly deal with the perfectly rational issue and the overlapping path issue,and additionally,the proposed model is shown to be applicable for large road networks.

Modified stochastic user-equilibrium assignment algorithm for urban rail transit under network operation

Based on the framework of method of successive averages(MSA), a modified stochastic user-equilibrium assignment algorithm was proposed, which can be used to calculate the passenger flow distribution of urban rail transit(URT) under network operation. In order to describe the congestion's impact to passengers' route choices, a generalized cost function with in-vehicle congestion was set up. Building on the k-th shortest path algorithm, a method for generating choice set with time constraint was embedded, considering the characteristics of network operation. A simple but efficient route choice model, which was derived from travel surveys for URT passengers in China, was introduced to perform the stochastic network loading at each iteration in the algorithm. Initial tests on the URT network in Shanghai City show that the methodology, with rational calculation time, promises to compute more precisely the passenger flow distribution of URT under network operation, compared with those practical algorithms used in today's China.

Integrating Origin-Destination Survey and Stochastic User Equilibrium: A Case Study for Route Relocation

The paper analyses integrating origin-destination (O-D) survey results with stochastic user equilibrium (SUE) in traffic assignment. The two methods are widely used in transportation planning but their applications have not yet fully integrated. While O-D gives a generalized trip patterns, purpose and characteristics, SUE provides optimal trip distributions using the characteristics found in O-D survey. The paper utilized O-D and SUE in route relocation study for the town of Coamo in Puerto Rico. The O-D survey was used initially in studying possible trip distribution and assignment for the new route. Initial distribution and assignment of traffic to the existing roadway networks and the proposed route were allocated utilizing the O-D survey findings. The SUE was then used to optimize the assignments considering roadway characteristics such as number of lanes, capacity limits, free flow speed, signal spacing density, travel time and gasoline cost. The travel time was optimized through the Bureau of Public Roads (BPR) equation found in 2000 HCM. The optimal trips found from the SUE were then used to propose the final alignment of the new route. Traffic assignment from the SUE was slightly different from those initially assigned using O-D, indicating there was optimization. The assignment on new route was increased by 13.8% from the one assigned using O-D while assignment on the existing link was reduced by 22%.

Generalized nested logit-based stochasticuser equilibrium model with distance constraint of electric vehicles

Considering the range anxiety issue caused by the limited driving range and the scarcity of battery charging stations,the conventional multinomial logit(MNL)model with the overlapping path issue was used in route choice modeling to describe the route choice behavior of travelers effectively.Furthermore,the generalized nested logit-based stochastic user equilibrium(GNL-SUE)model with the constraints of multiple user classes and distance limits was proposed.A mathematical model was developed and solved by the method of successive averages.The mathematical model was proven to be analytically equivalent to the modified GNL-SUE model,and the uniqueness of the solution was also confirmed.The proposed mathematical model was tested and compared with the GNL-SUE model without a distance limit and the MNL-SUE model with a distance limit.Results show that the proposed mathematical model can effectively handle the range anxiety and overlapping path challenges.

A Discrete-Time Stochastic Traffic Assignment Model

A discrete time stochastic traffic assignment model is proposed. The model provides a discrete time description of the variations of flows on a road network during a day or a peak period. The congestion effect at links and link junctions are taken into account. The first in first out principle is enforced on all links at all periods of the day. A stochastic user equilibrium assignment is achieved when the tripmaker is unable to find better travel alternatives. A computational procedure is also presented.

Traffic assignment problem under tradable credit scheme in a bi-modal stochastic transportation network: A cumulative prospect theory approach

The traffic equilibrium assignment problem under tradable credit scheme(TCS) in a bi-modal stochastic transportation network is investigated in this paper. To describe traveler’s risk-taking behaviors under uncertainty, the cumulative prospect theory(CPT) is adopted. Travelers are assumed to choose the paths with the minimum perceived generalized path costs, consisting of time prospect value(PV) and monetary cost. At equilibrium with a given TCS, the endogenous reference points and credit price remain constant, and are consistent with the equilibrium flow pattern and the corresponding travel time distributions of road sub-network. To describe such an equilibrium state, the CPT-based stochastic user equilibrium(SUE) conditions can be formulated under TCS. An equivalent variational inequality(VI) model embedding a parameterized fixed point(FP) model is then established, with its properties analyzed theoretically. A heuristic solution algorithm is developed to solve the model, which contains two-layer iterations. The outer iteration is a bisection-based contraction method to find the equilibrium credit price, and the inner iteration is essentially the method of successive averages(MSA) to determine the corresponding CPT-based SUE network flow pattern. Numerical experiments are provided to validate the model and algorithm.

Reliability analysis of stochastic park-and-ride network

Park-and-ride （P＆R） facilities can alleviate the traffic burden in central urban areas by enabling car drivers to park at the perimeter of congested areas and continue their journeys with public transportation （e.g., metro and bus rapid transit）. Whether a P＆R scheme is successful depends on its attractiveness to car users. This paper presents anevaluation method for the reliability analysis of P＆R mode. Two indices, P＆R reliability and mode reliability, are in- troduced to represent the reliabilities of a transfer point and an entire trip, respectively. Then, a systematic reliability analysis is conducted for a stochastic P＆R network, where travelers can complete their journeys via two options： auto mode or P＆R mode. A variational inequality （VI） model is proposed and solved by a heuristic solution algorithm. Nu- merical results show that the P＆R facility reliability is significantly influenced by the capacity of parking facilities, the dispatching frequency of the connecting metro, and the metro fare. In addition, a higher level of total demand in the network has significant negative impacts on P＆R mode＇s attractiveness compared to auto mode.

ATIS与收费策略下多用户随机均衡的效率损失

考虑ATIS作用的交通网络,用户具有交通信息接受程度的异质性;进一步,考虑实施道路收费策略情形下,用户具有时间价值的异质性;基于这两类异质性,研究了ATIS下异质性交通网络的效率损失问题。用户对ATIS系统的响应程度,亦即ATIS信息遵从率,是影响ATIS系统运行效率的关键因素。因此,通过ATIS信息遵从率参数的引入,将用户分为不同类型。假设用户均按照随机方式进行择路,建立了基于时间准则与基于费用准则的多用户Logit-随机均衡变分不等式。当系统总出行成本包含收费时,建立了多用户双准则系统最优模型,界定了多用户Logit-随机均衡相对于多用户系统最优的效率损失,推导出效率损失上界;进一步分析了当路段阻抗函数为多项式情形时,引入了自由流出行时间参数,给出了双准则下效率损失上界的解析式,分析了效率损失上界与各参数之间的关系。研究结论表明,双准则下效率损失上界为ATIS信息遵从率的减函数;此外,效率损失上界与路段阻抗函数、用户时间价值及其对路网的熟悉程度、路网本身复杂程度等因素有关。最后,通过算例验证了结论的有效性。

考虑随机用户均衡的区县级电动汽车快充站规划

电动汽车渗透率的提高和城市化进程的发展使得区县级充电设施的建设具有重要意义。综合考虑用户充电需求时空分布和用户充电决策中的有限理性,提出一种面向区县的电动汽车快充站优化规划模型。首先,针对区县用户的出行特征,构建包含外部连接的交通网络拓扑扩展形式,采用出行链仿真捕捉用户快充需求;其次,结合影响用户充电选择的多种因素,建立用户充电决策模型并给出随机用户均衡条件;然后,建立以投资运行成本、用户绕行距离最小为目标的多场景快充站选址定容优化模型,通过多种线性化手段处理指数等式均衡约束,将优化问题转换为混合整数线性规划以高效求解;最后,以33节点交通系统为例对快充站规划结果进行分析,验证所提模型和线性近似方法的合理性。

随机用户均衡准动态交通分配模型

动态交通分配问题是交通科学研究的热点和难点,将动态交通分配方法应用于大规模网络往往产生过高的计算成本。通过研究准动态交通分配问题,降低动态交通分配中时间的连续性和动态交通分配模型的复杂性。采用路段行程时间计算公式定义一种新的剩余交通需求计算方法;然后考虑剩余交通需求在时段之间的传播过程和出行者对路网的熟悉程度差异,建立基于Logit的随机用户均衡准动态交通分配模型,基于逐次平均法设计模型的求解算法。最后通过Braess网络和九节点网络说明模型的应用情况,并分析模型参数的敏感度,验证模型的合理性与算法的有效性。本研究丰富了交通科学基础理论,为交通政策的制定提供参考依据。

Bounding the Inefficiency of the C-Logit Stochastic User Equilibrium Assignment

Compared with standard logit-based stochastic user equilibrium assignment model,the C-logit model describes route choice behavior in a more realistic way by considering the overlapping effect between routes.This paper investigates the inefficiency upper bounds of this model against the deterministic system optimum and the C-logit stochastic system optimum in terms of the total network travel time.It is found that the commonality factor of overlapping routes significantly affects the inefficiency bound,besides link congestion degree,total demand and the number of feasible routes.If the commonality factor is not considered,the efficiency loss resulting from selfishly stochastic travel behavior will be to large extent underestimated.

考虑列车随机延误的铁路网络客流均衡分配方法

铁路客流均衡分配是旅客出行选择的集中体现,对旅客列车开行方案和列车运行图等的评价和优化十分重要。实际运营中列车的随机延误会导致铁路旅客的出行时间发生变化,影响旅客的出行,尤其是换乘选择。考虑旅客在路径选择决策过程中的出行时间可靠性和不可靠性2个方面因素,提出一种考虑列车随机延误的铁路网络客流均衡分配方法。首先,构建旅客换乘网络,基于提出的期望−超额出行成本(METC)概念,考虑换乘过程中列车的延误概率,计算旅客的换乘成功概率和换乘周期选择;然后,进一步计算旅客出行路径的期望−超额成本,基于用户均衡条件,构建考虑列车随机延误的期望−超额客流均衡分配模型;最后,考虑到期望−超额出行成本的不可加性,结合相继平均法和k-最短路算法设计基于路径的客流分配算法,并对均衡模型进行求解。通过对一个简单算例和广珠铁路实例进行分析,结果表明:同时考虑出行时间的可靠性和不可靠性时,旅客的出行路径选择和换乘选择与仅考虑出行时间可靠性有较大差异,基于期望−超额的铁路网络客流分配模型可以更加准确地描述考虑列车随机延误的旅客的出行选择行为,证实了均衡分配方法的有效性。因此提出的客流分配方法可以为铁路网络旅客列车开行方案等的制定和优化提供理论依据。

通勤廊道停车共乘出行行为分析与停车收费优化

共乘出行可以提高车辆使用容量,减少交通出行量,从而有效缓解交通拥堵以及城市停车紧张。本文以单中心线性城市为研究背景,通过设置停车共乘会合点的方法,提出了一种基于停车共乘的交通管理方案。在停车共乘出行环境下,分析了自驾司机、共乘司机、共乘乘客的出行成本,构建了基于随机用户均衡的路径选择模型。以最小化系统总出行阻抗为目标,提出了一个双层规划模型来优化共乘停车收费。基于灵敏度分析的方法,分别应用了Frank-Wolfe和BFGS两种算法来求解提出的双层规划模型。最后,采用数值算例验证了提出的模型和算法的有效性。

Stochastic Route Choice Equilibrium Assignment for Travelers with Heterogeneous Regret Aversions

Most route choice models assume that people are completely rational.Recently,regret theory has attracted researchers'attentions because of its power to depict real travel behavior.This paper proposes a multiclass stochastic user equilibrium assignment model by using regret theory.All users are differentiated by their own regret aversion.The route travel disutility for users of each class is defined as a linear combination of the travel time and anticipated regret.The proposed model is formulated as a variational inequality problem and solved by using the self-regulated averaging method.The numerical results show that users'regret aversion indeed influences their route choice behavior and that users with high regret aversion are more inclined to change route choice when the traffic congestion degree varies.

基于累积前景理论的随机网络用户均衡模型

出行者行为假设对交通网络用户均衡建模具有重要影响,更符合人们的真实决策行为的累积前景理论,为随机交通网络中的路径选择行为研究提供了新的分析框架.基于累积前景理论,将出行者的路径选择决策与网络的随机性相结合,建立了随机网络用户均衡的等价变分不等式模型;提出了求解模型的算法,通过简单的算例对模型和算法的合理性进行验证.通过对参数进行灵敏度分析,发现模型可以较好的反映出行者的风险态度、出行者对网络服务水平的预期以及出行流量波动大小对网络均衡状态的影响.

基于累积前景理论的随机用户均衡交通分配模型

为了使交通分配更符合出行者的实际行为特征,基于累积前景理论,给出了交通流连续分布状态下路径前景的连续函数表达式,建立了随机用户均衡模型,并给出了等价的变分不等式.该模型同时考虑了交通系统的不确定性、出行者的感知误差以及建模者的观测误差.讨论了模型解的性质,设计了求解算法,并通过算例进行了验证.结果表明:在(0,1)区间内,当出行可靠性参数或风险态度参数值越大时,出行者对于风险的感知越敏感,越倾向于选择行程时间波动较小的路径;当感知误差较小或路网不确定性程度较大时,出行者的路径选择行为均逐渐趋于稳定.研究还表明,出行者的损失规避程度对网络均衡态的影响不明显.