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.

Robust user equilibrium model based on cumulative prospect theory under distribution-free travel time

The assumption widely used in the user equilibrium model for stochastic network was that the probability distributions of the travel time were known explicitly by travelers. However, this distribution may be unavailable in reality. By relaxing the restrictive assumption, a robust user equilibrium model based on cumulative prospect theory under distribution-free travel time was presented. In the absence of the cumulative distribution function of the travel time, the exact cumulative prospect value(CPV) for each route cannot be obtained. However, the upper and lower bounds on the CPV can be calculated by probability inequalities.Travelers were assumed to choose the routes with the best worst-case CPVs. The proposed model was formulated as a variational inequality problem and solved via a heuristic solution algorithm. A numerical example was also provided to illustrate the application of the proposed model and the efficiency of the solution algorithm.

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.

A self-regulating pairwise swapping algorithm to search reliability-based user equilibrium

The violation of monotonicity on reliability measures(RMs)usually makes the mathematical programming algorithms less efficient in solving the reliability-based user equilibrium(RUE)problem.The swapping algorithms provide a simple and convenient alternative to search traffic equilibrium since they are derivative-free and require weaker monotonicity.However,the existing swapping algorithms are usually based on linear swapping processes which cannot naturally avoid overswapping,and the step-size parameter update methods do not take the swapping feature into account.In this paper,we suggest a self-regulating pairwise swapping algorithm(SRPSA)to search RUE.SRPSA comprises an RM-based pairwise swapping process(RMPSP),a parameter self-diminishing operator and a termination criterion.SRPSA does not need to check the feasibility of either solutions or step-size parameter.It is suggested from the numerical analyses that SRPSA is effective and can swap to the quasi-RUE very fast.Therefore,SRPSA offers a good approach to generate initial points for those superior local search algorithms.

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.

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.

Combinatorial Model Involving Mixed Deterministic Freight Volume Distribution and User's Equilibrium Assignment

Considering characteristics of Chinese urban mixed traffic,the author develops a combinatorial model involving the mixed deterministic traffic volume distribution and user's equilibrium (UE) assignment on the basis of symmetrical link travel time function (or deterrence).Its uniqueness and equivalance to the Wardropian principle of UE are also proved.Finally,we give the algorithm of model.

Alpha-reliable combined mean traffic equilibrium model with stochastic travel times

Based on the reliability budget and percentile travel time(PTT) concept, a new travel time index named combined mean travel time(CMTT) under stochastic traffic network was proposed. CMTT here was defined as the convex combination of the conditional expectations of PTT-below and PTT-excess travel times. The former was designed as a risk-optimistic travel time index, and the latter was a risk-pessimistic one. Hence, CMTT was able to describe various routing risk-attitudes. The central idea of CMTT was comprehensively illustrated and the difference among the existing travel time indices was analyzed. The Wardropian combined mean traffic equilibrium(CMTE) model was formulated as a variational inequality and solved via an alternating direction algorithm nesting extra-gradient projection process. Some mathematical properties of CMTT and CMTE model were rigorously proved. Finally, a numerical example was performed to characterize the CMTE network. It is founded that that risk-pessimism is of more benefit to a modest(or low) congestion and risk network, however, it changes to be risk-optimism for a high congestion and risk network.

Supply chain network equilibrium model with capacity constraints

The supply chain network with capacity constraints of manufacturers and retailers is considered.The linkage between supply chain network equilibrium and transportation network equilibrium is investigated.By analyzing the relationships among the manufacturers,retailers and consumers in the supply chain network and their own decisions concerning maximum profits,a combined variational inequality for the supply chain network equilibrium mode is proposed.Then an equivalent supernetwork of the supply chain network is constructed by adding additional links which denote the producing of manufactures and the handling of retailers.By the supernetwork,the supply chain network equilibrium model can be reformulated as a transportation network equilibrium model.Equivalent mathematical programming is,therefore,obtained based on the principle of a Wardrop user equilibrium.The corresponding Lagrange multiplier of the capacity constraints can be explained as the extra cost of marginal production when capacity is exceeded.A numerical example is given to illustrate the rationality of the model and the validity of the results.

An Engineering Application Tool for Visual Assessment of the Equilibrium Beach

An engineering application tool for prediction of the static equilibrium bay （ Beach Mod） is established to describe two bay shape formulas by use of the programming software ＂MATLAB＂ with a graphic user interface （ GUI）. The tool is user-friendly for engineering students for the design of beach shapes. This tool was tested through application on three types of beaches in Taiwan and Australia. By implementing the concept of Headland Control, the Beach Mod program allows users to draw a structure and create an ＇artificial headland. The results indicate that Beach Mod can efficiently forecast beach changes as well as MEPBAY, a competing software package, while boasting a better user interface.

Stochastic network equilibrium model with reliable travel time confidence level

In order to ensure on-time arrival when travelersmake their trips, the stochastic network assignment modelunder uncertainty of travel time is investigated. First, basedon travelers＇ route choice behavior, the reliable travel timeconfidence level （RTTCL）, which is the probability that a triparrives within the shortest average travel time plus theacceptable travel time difference, is defined. Then, areliability-based user equilibrium （RUE） model, whichhypothesizes that for each OD pair no traveler can improvehis/her RTTCL by unilaterally changing routes, is built.Since the traditional traffic assignment algorithms are notfeasible to solve the RUE model, a quasi method of successiveaverage （QMSA） is developed. Using Nguyen-Dupuis andSioux Falls networks, the model and the algorithm are tested.The results show that the QMSA algorithm can rapidlyconverge to a high accuracy for solving the proposed RUEmodel, and the RUE model can provide a good response totravelers＇ behavior in the stochastic network.

Modified origin-based algorithm for traffic equilibrium assignment problems

Key tactics of origin-based user equilibrium (OUE) algorithm was studied,which involved the algorithm procedure and several implementation issues.To speed up the convergence,update policies of flows,costs and bushes were proposed.The methods of step-size searching and bush construction are proved to be practical.The modified OUE algorithm procedure was also optimized to take the advantage of multi-thread process.Convergence performances were compared with those of other algorithms by different sizes of urban transportation networks.The result shows this modified OUE algorithm is more efficient and consumes less time to achieve the reasonable relative gap in practical applications.

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。

快慢车模式下早高峰时空乘车路径选择研究

研究早高峰通勤乘客的时空出行规律有助于更好地组织快慢车运营模式。本文从一种常见的快慢车运营模式出发,首先,根据乘客的起点车次和直达/换乘方案联合选择构建乘车路径;其次,以出行时间、早到/迟到延误和车内拥挤度作为早高峰通勤乘客出行选择的影响因素,对不同乘车路径下的出行成本进行构建;再次,以用户均衡理论建立乘车路径分配模型,并证明了该模型用户均衡路段解的存在性及唯一性;最后通过案例,对均衡模型进行验证。研究结果发现:短途乘客更愿意接受高拥挤但终点到达时刻接近工作开始时刻的车次,而长途乘客的车次选择分布较为均匀;除出行时间因素以外,延误惩罚和乘车拥挤同样影响早高峰通勤乘客的换乘行为,虽然换乘快车有可能降低出行时间,但高延误惩罚和拥挤成本会导致部分站点的乘客不选择换乘路径。

量化自我隐私顾虑的前因组态对隐私披露意愿的影响——权力-责任均衡视角

[研究目的]用户的隐私披露对以数据为驱动的量化自我企业而言十分重要,探究量化自我情境下隐私顾虑对隐私披露意愿的影响将为相关企业获取用户数据提供理论指导。[研究方法]基于权力与责任均衡理论,采用模糊集定性比较分析方法,以使用可穿戴设备的用户为研究对象,从量化自我主体视角分析导致隐私顾虑的前因组态,以及不同的隐私顾虑组态类型对隐私披露意愿的影响机制。[研究结论]研究发现:量化自我隐私顾虑的3种组态类型,分别是内生型隐私顾虑、外生型隐私顾虑和混合型隐私顾虑,且会对隐私披露意愿产生差异性影响。短期使用中产生的内生型隐私顾虑和长期使用中产生的混合型隐私顾虑会导致量化自我隐私披露意愿的降低;而在短期使用过程中产生的外生型隐私顾虑并不会降低隐私披露意愿,反而因为用户感知到政府的法律有效性,促进了在量化自我过程中的隐私披露。