Approximate network loading and dual-time-scale dynamic user equilibrium

In this paper we present a dual-time-scale formulation of dynamic user equilibrium (DUE) with demand evolution. Our formulation belongs to the problem class that Pang and Stewart (2008) refer to as differential variational inequalities. It combines the within-day time scale for which route and departure time choices fluctuate in continuous time with the day-to-day time scale for which demand evolves in discrete time steps. Our formulation is consistent with the often told story that drivers adjust their travel demands at the end of every day based on their congestion experience during one or more previous days. We show that analysis of the within-day assignment model is tremendously simplified by expressing dynamic user equilibrium as a differential variational inequality. We also show there is a class of day-to-day demand growth models that allow the dual-time-scale formulation to be decomposed by time-stepping to yield a sequence of continuous time, single-day, dynamic user equilibrium problems. To solve the single-day DUE problems arising during time-stepping, it is necessary to repeatedly solve a dynamic network loading problem. We observe that the network loading phase of DUE computation generally constitutes a differential algebraic equation (DAE) system, and we show that the DAE system for network loading based on the link delay model (LDM) of Friesz et al. (1993) may be approximated by a system of ordinary differential equations (ODEs). That system of ODEs, as we demonstrate, may be efficiently solved using traditional numerical methods for such problems. To compute an actual dynamic user equilibrium, we introduce a continuous time fixed-point algorithm and prove its convergence for effective path delay operators that allow a limited type of nonmonotone path delay. We show that our DUE algorithm is compatible with network loading based on the LDM and the cell transmission model (CTM) due to Daganzo (1995). We provide a numerical example based on the much studied Sioux Falls network.     

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.     

Modeling capacity flexibility of transportation networks

Flexibility of the transportation system is one of the important performance measures needed to deal with demand changes. In this paper, we provide a quantitative assessment of capacity flexibility for the passenger transportation network using bi-level network capacity models. Two approaches for assessing the value of capacity flexibility are proposed. One approach is based on the concept of reserve capacity, which reflects the flexibility with respect to changes in terms of demand volume only. The second approach allows for variations in the demand pattern in addition to changes in demand volume in order to more fully capture demand changes. Two models are developed in the second approach to consider two types of capacity flexibility. The total capacity flexibility allows all users to have both route choice and destination choice when estimating capacity flexibility. The limited capacity flexibility estimates how much more demand volume could be added to a fixed demand pattern by allowing the additional demand to deviate from the fixed demand pattern. Numerical examples are provided to demonstrate the different concepts of capacity flexibility for a passenger transportation system under demand changes.     

Modeling heterogeneous risk-taking behavior in route choice: A stochastic dominance approach

This paper proposes a unified approach to modeling heterogonous risk-taking behavior in route choice based on the theory of stochastic dominance (SD). Specifically, the first-, second-, and third-order stochastic dominance (FSD, SSD, TSD) are respectively linked to insatiability, risk-aversion and ruin-aversion within the framework of utility maximization. The paths that may be selected by travelers of different risk-taking preferences can be obtained from the corresponding SD-admissible paths, which can be generated using general dynamic programming. This paper also analyzes the relationship between the SD-based approach and other route choice models that consider risk-taking behavior. These route choice models employ a variety of reliability indexes, which often make the problem of finding optimal paths intractable. We show that the optimal paths with respect to these reliability indexes often belong to one of the three SD-admissible path sets. This finding offers not only an interpretation of risk-taking behavior consistent with the SD theory for these route choice models, but also a unified and computationally viable solution approach through SD-admissible path sets, which are usually small and can be generated without having to enumerate all paths. A generic label-correcting algorithm is proposed to generate FSD-, SSD-, and TSD-admissible paths, and numerical experiments are conducted to test the algorithm and to verify the analytical results.     

三维边坡稳定性分析的一种适用方法

基于空间曲面上一点的应力关系、曲面至边坡表面土柱上力的微分平衡方程、力矩平衡方程,只需要一个假定条件,得出了一种广泛适用的三维边坡稳定性分析法,并讨论了方法应用中的有关问题。算例表明,该方法计算结果是合理的,具有广泛的应用意义。     

边坡稳定分析中极限平衡法与强度折减法比较研究(Ⅱ)

分别用极限平衡法和有限元强度折减法对于高家坪高边坡开挖后防护前的边坡稳定性进行分析,综合两种方法的结果提出高边坡的防护方案;并且对防护后的高边坡,再次用两种方法进行整体稳定性分析。通过比较研究,强度折减法的可行性及优越性得到了充分论证。     

交通信息对驾驶员逐日路径选择行为影响研究

在无信息、发布历史信息和发布预测信息3种信息条件下,分别建立了驾驶员的路径理解行程时间期望值的更新模型.通过建立一个含有2条平行路径的简单路网,对3种交通信息条件下驾驶员逐日路径选择进行了仿真,结果表明:交通信息对驾驶员的作用与驾驶员路径选择的随机程度和对信息依赖程度有关;在3种交通信息条件下,路网均不能达到用户均衡平衡状态;交通信息的预测方法不同,预测信息对驾驶员路径选择的影响有差异.     

Optimal locations and travel time display for variable message signs

This paper first develops a network equilibrium model with the travel time information displayed via variable message signs (VMS). Specifically, the equilibrium considers the impact of the displayed travel time information on travelers’ route choices under the recurrent congestion, with the endogenous utilization rates of displayed information by travelers. The existence of the equilibrium is proved and an iterative solution procedure is provided. Then, we conduct the sensitivity analyses of the network equilibrium and further propose a paradox, i.e., providing travel time information via VMS to travelers may degrade the network performance under some poor designs. Therefore, we investigate the problem of designing the VMS locations and travel time display within a given budget, and formulate it as a mixed integer nonlinear program, solved by an active-set algorithm. Lastly, numerical examples are presented to offer insights on the equilibrium results and optimal designs of VMS.     

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.