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.     

Expirable parking reservations for managing morning commute with parking space constraints

When total parking supply in an urban downtown area is insufficient, morning commuters would choose their departure times not only to trade off bottleneck congestion and schedule delays, but also to secure a parking space. Recent studies found that an appropriate combination of reserved and unreserved parking spaces can spread the departures of those morning commuters and hence reduce their total travel cost. To further mitigate both traffic congestion and social cost from competition for parking, this study considers a parking reservation scheme with expiration times, where commuters with a parking reservation have to arrive at parking spaces for the reservation before a predetermined expiration time. We first show that if all parking reservations have the same expiration time, it is socially preferable to set the reservations to be non-expirable, i.e., without expiration time. However, if differentiated expiration times are properly designed, the total travel cost can be further reduced as compared with the reservation scheme without expiration time, since the peak will be further smoothed out. We explore socially desirable equilibrium flow patterns under the parking reservation scheme with differentiated expiration times. Finally, efficiencies of the reservation schemes are examined.     

Is equilibrium in transport pure Nash,mixed or Stochastic?

The classical theory of transport equilibrium is based on the Wardrop’s first principle that describes a Nash User Equilibrium (UE), where in no driver can unilaterally change routes to improve his/her travel times. A growing number of economic laboratory experiments aiming at testing Nash-Wardrop equilibrium have shown that the Pure Strategy Nash Equilibrium (PSNE) is not able to explain the observed strategic choices well. In addition even though Mixed Strategy Nash Equilibrium (MSNE) has been found to fit better the observed aggregate choices, it does not explain the variance in choices well. This study analyses choices made by users in three different experiments involving strategic interactions in endogenous congestion to evaluate equilibrium prediction. We compare the predictions of the PSNE, MSNE and Stochastic User Equilibrium (SUE). In SUE, the observed variations in choices are assumed to be due to perception errors. The study proposes a method to iteratively estimate SUE models on choice data with strategic interactions. Among the three sets of experimental data the SUE approach was found to accurately predict the average choices, as well as the variances in choices. The fact that the SUE model was found to accurately predict variances in choices, suggests its applicability for transport equilibrium models that attempt to evaluate reliability in transportation systems. This finding is fundamental in the effort to determining a behaviourally consistent paradigm to model equilibrium in transport networks. The study also finds that Fechner error which is the inverse of the scale parameter in the SUE model is affected by the group sizes and the complexity of the cost function. In fact, the larger group sizes and complexity of cost functions increased the variability in choices. Finally, from an experimental design standpoint we show that it is not possible to estimate a noise parameter associate to Fechner error in the case when the choices are equally probable.     

Network equilibrium models with battery electric vehicles

The limited driving ranges, the scarcity of recharging stations and potentially long battery recharging or swapping time inevitably affect route choices of drivers of battery electric vehicles (BEVs). When traveling between their origins and destinations, this paper assumes that BEV drivers select routes and decide battery recharging plans to minimize their trip times or costs while making sure to complete their trips without running out of charge. With different considerations of flow dependency of energy consumption of BEVs and recharging time, three mathematical models are formulated to describe the resulting network equilibrium flow distributions on regional or metropolitan road networks. Solution algorithms are proposed to solve these models efficiently. Numerical examples are presented to demonstrate the models and solution algorithms.     

非圆弧滑面滑坡中满足平衡条件的预应力锚索设计拉力的确定方法

在以往的设计计算中 ,对非圆弧滑坡预应力锚索的设计一般采用指定设计外力而根据整体平衡来确定锚索根数 ,并认为锚索作用力以集中荷载作用在滑面上 ,实际上由于作用在地面的荷载经滑体传递后发生了很大的扩散作用 ,且以往的计算方法是不能找到理论依据的 ,即不满足任何力及力矩的平衡条件 ,因而不尽合理 ,本文根据其受力特点从平衡条件出发 ,导出了确定锚索设计外力的迭代算法公式 ,对工程实际具有较大的理论意义。     

A capacity restraint transit assignment with elastic line frequency

This paper proposes a new formulation for the capacity restraint transit assignment problem with elastic line frequency, in which the line frequency is related to the passenger flows on transit lines. A stochastic user equilibrium transit assignment model with congestion and elastic line frequency is proposed and the equivalent mathematical programming problem is also formulated. Since the passenger waiting time and the line capacity are dependent on the line frequency, a fixed point problem with respect to the line frequency is devised accordingly. The existence of the fixed point problem has been proved. A solution algorithm for the proposed model is presented. Finally, a numerical example is used to illustrate the application of the proposed model and solution algorithm.     

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.     

密立根油滴实验中平衡电压和下落时间关系的研究

通过分析平衡电压和下落时间的隐函数关系表达式,推导出了两者之间的直接函数表达式和变化关系。同时用数值模拟和实验验证的方法,得到这样的结论：随着下落时间的逐渐增长,平衡电压是逐渐变小的,而且变化率是越来越小。实验过程中油滴质量的减小很好地解释了两者之间的变化关系。剔除掉由于电量减小造成的不合理数据可以提高实验的准确度。     

某软土地铁车站基坑纵向滑坡事故分析

狭长形地铁车站基坑在分层开挖过程中会形成临时纵向多级边坡。当挖方边坡位于软弱地层时,如果设计或施工不当将会面临基坑纵向失稳风险。针对某软土地铁深基坑纵向滑坡事故案例,在考虑参数变异性的基础上利用极限平衡法对坑内临时边坡展开调查分析,并从工程角度对土坡发生深层滑移破坏的原因进行探讨。调查结果表明： 第1级边坡的坡度是影响整体稳定性的关键因素,1∶1.75（V∶H）的施工坡度不能满足下卧软弱淤泥质土条件下该局部边坡的稳定性（失稳概率高达88.92%）,只有当坡度缓于1∶3时才能保证安全。为防止此类临时挖方边坡失稳,最后给出考虑土体强度参数变异性的最优边坡坡度。