Macroscopic relations of urban traffic variables: Bifurcations, multivaluedness and instability

Recent experimental work has shown that the average flow and average density within certain urban networks are related by a unique, reproducible curve known as the Macroscopic Fundamental Diagram (MFD). For networks consisting of a single route this MFD can be predicted analytically; but when the networks consist of multiple overlapping routes experience shows that the flows observed in congestion for a given density are less than those one would predict if the routes were homogeneously congested and did not overlap. These types of networks also tend to jam at densities that are only a fraction of their routes’ average jam density.This paper provides an explanation for these phenomena. It shows that, even for perfectly homogeneous networks with spatially uniform travel patterns, symmetric equilibrium patterns with equal flows and densities across all links are unstable if the average network density is sufficiently high. Instead, the stable equilibrium patterns are asymmetric. For this reason the networks jam at lower densities and exhibit lower flows than one would predict if traffic was evenly distributed.Analysis of small idealized networks that can be treated as simple dynamical systems shows that these networks undergo a bifurcation at a network-specific critical density such that for lower densities the MFDs have predictably high flows and are univalued, and for higher densities the order breaks down. Microsimulations show that this bifurcation also manifests itself in large symmetric networks. In this case though, the bifurcation is more pernicious: once the network density exceeds the critical value, the stable state is one of complete gridlock with zero flow. It is therefore important to ensure in real-world applications that a network’s density never be allowed to approach this critical value.Fortunately, analysis shows that the bifurcation’s critical density increases considerably if some of the drivers choose their routes adaptively in response to traffic conditions. So far, for networks with adaptive drivers, bifurcations have only been observed in simulations, but not (yet) in real life. This could be because real drivers are more adaptive than simulated drivers and/or because the observed real networks were not sufficiently congested.     

Lane changing patterns of bane and benefit: Observations of an uphill expressway

A mechanism is unveiled by which congestion forms on a 3-lane, uphill expressway segment, and causes reductions in output flow. Vehicular lane-changing (LC) is key to the mechanism, particularly LC induced by speed disturbances (SDs) that periodically arise in the expressway’s median and center lanes. Early in the rush, when flow was relatively low in the shoulder lane, drivers readily migrated toward that lane to escape the oncoming SDs. The shoulder lane thus acted as a ‘release valve’ for the high vehicular accumulations created by the SDs, such that forced vehicular decelerations were short-lived. The release valve failed only later in the rush, when flow increased in the shoulder lane in response to rising demand. LC induced by the SDs thereafter became disruptive: the decelerations they imposed spread laterally, and a persistent queue formed in all lanes. Long-run output flow dropped each day by 4-11% once the queue engulfed the base of the incline, and impeded vehicle ascent.Subtle details of this mechanism became visible by examining thousands of vehicle trajectories that were extracted from a series of eleven roadside video cameras. Though these trajectories were collected from only a single day, we suspect that the findings can be generalized to other days at the present site, and to other sites. This is because: (i) conspicuous features of the mechanism were repeatedly observed in loop detector data that were measured over many days at the site; (ii) these macroscopic features are consistent with observations previously made at other sites; and (iii) the more subtle details unveiled by the trajectories are compatible with a general theory of multi-lane traffic.     

On the macroscopic stability of freeway traffic

A simple model of traffic flow is used to analyze the spatio-temporal distribution of flow and density on closed-loop homogeneous freeways with many ramps, which produce inflows and allow outflows. As we would expect, if the on-ramp demand is space-independent then this distribution tends toward uniformity in space if the freeway is either: (i) uncongested; or (ii) congested with queues on its on-ramps and enough inflow to cause the average freeway density to increase with time. In all other cases, however, including any recovery phase of a rush hour where the freeway’s average density declines, the distribution of flow and density quickly becomes uneven. This happens even under conditions of perfect symmetry, where the percentage of vehicles exiting at every off ramp is the same. The flow-density deviations from the average are shown to grow exponentially in time and propagate backwards in space with a fixed wave speed. A consequence of this type of instability is that, during recovery, gaps of uncongested traffic will quickly appear in the unevenly congested stream, reducing average flow. This extends the duration of recovery and invariably creates clockwise hysteresis loops on scatter-plots of average system flow vs. density during any rush hour that oversaturates the freeway. All these effects are quantified with formulas and verified with simulations. Some have been observed in real networks. In a more practical vein, it is also shown that the negative effects of instability diminish (i.e., freeway flows increase) if (a) some drivers choose to exit the freeway prematurely when it is too congested and/or (b) freeway access is regulated in a certain traffic-responsive way. These two findings could be used to improve the algorithms behind VMS displays for driver guidance (finding a), and on-ramp metering rates (finding b).     

Characterization of traffic oscillation propagation under nonlinear car-following laws

Unlike linear car-following models, nonlinear models generally can generate more realistic traffic oscillation phenomenon, but nonlinearity makes analytical quantification of oscillation characteristics (e.g, periodicity and amplitude) significantly more difficult. This paper proposes a novel mathematical framework that accurately quantifies oscillation characteristics for a general class of nonlinear car-following laws. This framework builds on the describing function technique from nonlinear control theory and is comprised of three modules: expression of car-following models in terms of oscillation components, analyses of local and asymptotic stabilities, and quantification of oscillation propagation characteristics. Numerical experiments with a range of well-known nonlinear car-following laws show that the proposed approach is capable of accurately predicting oscillation characteristics under realistic physical constraints and complex driving behaviors. This framework not only helps further understand the root causes of the traffic oscillation phenomenon but also paves a solid foundation for the design and calibration of realistic nonlinear car-following models that can reproduce empirical oscillation characteristics.     

Managing evacuation networks

This paper proposes a non-anticipative, adaptive, decentralized strategy for managing evacuation networks. The strategy is non-anticipative because it does not rely on demand forecasts, adaptive because it uses real-time traffic information, and decentralized because all the information is available locally. It can be used with a failed communication network.The strategy pertains to networks in which no links backtrack in the direction of increased risk. For these types of networks, no other strategy exists that can evacuate more people in any given time, or finish the evacuation in less time. The strategy is also shown to be socially fair, in the sense that the time needed to evacuate all the people exceeding any risk level is, both, the least possible, and the same as if less-at-risk individuals did not participate in the evacuation. The strategy can be proven optimal even when backflows happen due to driver gaming.     

高墩交通标志牌基础设计计算方法

高墩交通标志牌的基础既要承受墩柱自身的恒载,又要承受风荷载。文章阐述高墩交通标志牌及基础的设计参数,进行荷载和荷载效应的计算、墩柱截面验算,从结果对比分析中确定墩柱截面的合理尺寸及配筋,为类似的工程提供参考。     

An Adaptive Neuro-Fuzzy Inference System for estimating the number of vehicles for queue management at signalized intersections

Queue management is a valuable but underutilized technique which could be used to minimize the negative impacts of queues during oversaturated traffic conditions. One of the main obstacles of applying queue management techniques along signalized arterials is the unavailability of a robust and sufficiently accurate method for measuring the number of vehicles approaching a signalized intersection. The method based on counting vehicles as they enter and exit a specific detection zone with check-in and check-out detectors is unreliable because of the likely systematic under or over counting and the resulting cumulative errors. This paper describes the application of the Adaptive Neuro-Fuzzy Inference System (ANFIS) in the development of a new fuzzy logic-based approach for estimating the Number of Vehicles in a Detection Zone (NVDZ) by using detector time-occupancy data (instead of detector counts). Microscopic simulation results are used to evaluate the accuracy of the NVDZ estimates. Tests were carried out to determine the transferability of a tuned Fuzzy Inference System (FIS) and to check the sensitivity of the calibrated FIS to detection coverage, the location of the detection zone relative to the signalized (bottleneck) intersection, the length of the detection zone, and different signal timings at the bottleneck intersection. Results show that the NVDZ estimation based on fuzzy logic seems to be a feasible approach. Although the primary objective of developing the NVDZ estimation technique has been queue management, other applications such as ramp metering and incident detection could potentially use the same technique.     

北京市快速路速度—流量—密度关系研究

以北京市快速环路系统为研究对象,以大量的实测交通数据为基础,分析了流量-密度-速度三者之间的关系,据此来研究北京市快速环路交通流的运行特征;并利用不同的流密度模型进行相应的拟合,从而对各模型的适用范围和使用程度进行了对比分析,为进一步进行北京市快速路交通流特性的深入研究以及进行交通控制优化提供了基础。     

高速公路互通立交出口匝道安全评价

鉴于高速公路互通立交出口匝道交通事故频发的现状,分别采用基于公路安全评价指南和基于汽车行驶动力学的前、后两种方法对某高速公路出口匝道工程实例进行安全评价,然后对比前、后两种评价方法的异同,并分析基于交通心理学的速度感知误差对两种方法评价结果的影响。结果表明：相对于前者评价方法而言,后种评价方法的安全标准偏低;采用前者评价方法计算得到的互通立交出口匝道运行速度明显偏大,不满足行驶平衡的要求,即前者方法用于计算出口匝道的运行速度存在适应性问题;速度感知误差对后者评价方法判断结论的影响程度大于前者方法;出口匝道宜综合前、后两种方法进行安全评价。     

A new,non-canonical Poisson regression model for the prediction of crashes on low-volume rural roads

The purpose of the study was to compare the prediction power of a simplified non-canonical Poisson crash-prediction model to other model types. The model, fitted to serious and fatal crash data from 86 two-lane low-volume rural highway segments, showed a good fit, which was not significantly different from that of a negative binomial model. The application of the present model uses the linear form of the non-canonical Poisson model. Hence the simplification of the model versus other models results from the finding that the expected number of crashes per 1 km is directly proportional to the daily volume, unlike logarithmic functions in other models. In the non-canonical model, it is necessary to estimate only one parameter, whereas estimations of more parameters are needed in the negative binomial model.