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.     

An alternative model in traffic flow equations

The kinetic theory for traffic flow equations can be approached using the Grad’s method. This method, which is derived from the kinetic gas theory, was developed for the Paveri-Fontana equation when a special desired velocity model is assumed. A closure relation for the set of macroscopic equations is found when the density, the average velocity and the velocity variance are the relevant variables chosen to describe the system. Simulation results are also shown and a qualitative comparison with other models in the literature is presented.     

The evolution of urban traffic control: changing policy and technology

Abstract

The history of urban traffic control (UTC) throughout the past century has been a continued race to keep pace with ever more complex policy objectives and consistently increasing vehicle demand. Many benefits can be observed from an efficient UTC system, such as reduced congestion, increased economic efficiency and improved road safety and air quality.

There have been significant advances in vehicle detection and communication technologies which have enabled a series of step changes in the capabilities of UTC systems, from early (fixed time) signal plans to modern integrated systems. A variety of UTC systems have been implemented throughout the world, each with individual strengths and weaknesses; this paper seeks to compare the leading commercial systems (and some less well known systems) to highlight the key characteristics and differences before assessing whether the current UTC systems are capable of meeting modern transport policy obligations and desires.

This paper then moves on to consider current and future transport policy and the technological landscape in which UTC will need to operate over the coming decades, where technological advancements are expected to move UTC from an era of limited data availability to an era of data abundance.     

An analytical approximation for the macroscopic fundamental diagram of urban traffic

This paper shows that a macroscopic fundamental diagram (MFD) relating average flow and average density must exist on any street with blocks of diverse widths and lengths, but no turns, even if all or some of the intersections are controlled by arbitrarily timed traffic signals. The timing patterns are assumed to be fixed in time. Exact analytical expressions in terms of a shortest path recipe are given, both, for the street’s capacity and its MFD. Approximate formulas that require little data are also given.For networks, the paper derives an upper bound for average flow conditional on average density, and then suggests conditions under which the bound should be tight; i.e., under which the bound is an approximate MFD. The MFD’s produced with this method for the central business districts of San Francisco (California) and Yokohama (Japan) are compared with those obtained experimentally in earlier publications.     

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).     

Empirical assessment of urban traffic congestion

This paper presents an empirical assessment of urban traffic congestion in Central London, UK. Compared with freeways or motorways, urban networks are relatively less studied because of its complexity and availability of required traffic data. This paper introduces the use of automatic number plate recognition technology to analyze the characteristic of urban traffic congestion in Central London. We also present the use of linear regression to diagnose the observed congestion and attribute them to different causes. In particular, we distinguish the observed congestion into two main components: one due to recurrent factors and the other due to nonrecurrent factors. The methodologies are illustrated through a case study of Central London Area. It is found that about 15% of the observed congestion in the region is due to nonrecurrent factors such as accidents, roadwork, special events, and strikes. Given the significance of London, the study will be valuable for transport policy evaluation and appraisal in other global cities. Copyright © 2013 John Wiley & Sons, Ltd.     

Comparing traffic state estimators for mixed human and automated traffic flows

This article addresses the problem of modeling and estimating traffic streams with mixed human operated and automated vehicles. A connection between the generalized Aw Rascle Zhang model and two class traffic flow motivates the choice to model mixed traffic streams with a second order traffic flow model. The traffic state is estimated via a fully nonlinear particle filtering approach, and results are compared to estimates obtained from a particle filter applied to a scalar conservation law. Numerical studies are conducted using the Aimsun micro simulation software to generate the true state to be estimated. The experiments indicate that when the penetration rate of automated vehicles in the traffic stream is variable, the second order model based estimator offers improved accuracy compared to a scalar modeling abstraction. When the variability of the penetration rate decreases, the first order model based filters offer similar performance.     

Understanding the structure of hyper-congested traffic from empirical and experimental evidences

We study in this paper the structure of traffic under hypercongestion, which is a controversial issue between traditional two-phase traffic theory and Kerner’s three-phase theory. By analyzing video traffic data from a section of the Nanjing Airport Highway, it is found that traffic states inside hypercongestion are not homogeneous, which contradicts the existence of a “Homogeneous Congested Traffic” state claimed in two-phase traffic theory. Analysis of vehicle trajectories and velocities obtained from an experimental car-following study with a platoon of 25 vehicles also confirms the above findings. Furthermore, it is also found from the video traffic data that the structure of hypercongested traffic varies only slightly with location, which might be due to small jams inside hypercongested traffic merging into larger ones slowly and/or larger jams sometimes breaking into small ones. Finally, the implications of our observations on traffic modeling have been discussed.     

Modelling and simulation of transportation system effectiveness to reduce traffic congestion: a system dynamics framework

ABSTRACT

This paper is designed to evaluate and improve the effectiveness of transportation systems and reduce traffic congestion through the use of simulation models and scenario development. A system dynamics framework is used to test and evaluate the alternatives of future strategies for the city of Surabaya, Indonesia. Some factors affecting the effectiveness of transport systems include operational effectiveness and service effectiveness, as well as uncertainty. To improve the effectiveness of transportation systems, several strategies can be implemented, such as subsidizing public transportation, increasing the cost of private vehicle parking fees, raising taxes on private vehicles, and reducing delays in public transportation through scenario development. Scenario results show that, by pursuing these strategies, effectiveness could be improved by 80% as the impact of the increase in operational and service effectiveness, helping to mitigate traffic congestion. Congestion could be reduced to 70% (on average) due to the decrease in daily traffic.     

Properties of a well-defined macroscopic fundamental diagram for urban traffic

A field experiment in Yokohama (Japan) revealed that a macroscopic fundamental diagram (MFD) linking space-mean flow, density and speed exists on a large urban area. It was observed that when the highly scattered plots of flow vs. density from individual fixed detectors were aggregated the scatter nearly disappeared and points grouped along a well defined curve. Despite these and other recent findings for the existence of well-defined MFDs for urban areas, these MFDs should not be universally expected. In this paper we investigate what are the properties that a network should satisfy, so that an MFD with low scatter exists. We show that the spatial distribution of vehicle density in the network is one of the key components that affect the scatter of an MFD and its shape. We also propose an analytical derivation of the spatial distribution of congestion that considers correlation between adjacent links. We investigate the scatter of an MFD in terms of errors in the probability density function of spatial link occupancy and errors of individual links’ fundamental diagram (FD). Later, using real data from detectors for an urban arterial and a freeway network we validate the proposed derivations and we show that an MFD is not well defined in freeway networks as hysteresis effects are present. The datasets in this paper consist of flow and occupancy measures from 500 fixed sensors in the Yokohama downtown area in Japan and 600 loop detectors in the Twin Cities Metropolitan Area Freeway network in Minnesota, USA.     

Stochastic cell transmission model (SCTM): A stochastic dynamic traffic model for traffic state surveillance and assignment

The paper proposes a first-order macroscopic stochastic dynamic traffic model, namely the stochastic cell transmission model (SCTM), to model traffic flow density on freeway segments with stochastic demand and supply. The SCTM consists of five operational modes corresponding to different congestion levels of the freeway segment. Each mode is formulated as a discrete time bilinear stochastic system. A set of probabilistic conditions is proposed to characterize the probability of occurrence of each mode. The overall effect of the five modes is estimated by the joint traffic density which is derived from the theory of finite mixture distribution. The SCTM captures not only the mean and standard deviation (SD) of density of the traffic flow, but also the propagation of SD over time and space. The SCTM is tested with a hypothetical freeway corridor simulation and an empirical study. The simulation results are compared against the means and SDs of traffic densities obtained from the Monte Carlo Simulation (MCS) of the modified cell transmission model (MCTM). An approximately two-miles freeway segment of Interstate 210 West (I-210W) in Los Ageles, Southern California, is chosen for the empirical study. Traffic data is obtained from the Performance Measurement System (PeMS). The stochastic parameters of the SCTM are calibrated against the flow-density empirical data of I-210W. Both the SCTM and the MCS of the MCTM are tested. A discussion of the computational efficiency and the accuracy issues of the two methods is provided based on the empirical results. Both the numerical simulation results and the empirical results confirm that the SCTM is capable of accurately estimating the means and SDs of the freeway densities as compared to the MCS.     

Exploring the issue of integrating logistics and traffic control in urban areas

This paper proposes an optimization framework for urban transportation networks’ (re-)design which explicitly takes into account the specific decision-making processes of ordinary users and logistic operators. Ordinary users are typically commuters whose travels consist of well-defined pairs of origin and destination points, while logistic operators make deliveries at multiple locations. Obviously, these two user classes have different objectives and scopes of action. These differences are seldom considered in traffic research since most models aggregate the flow demand in OD matrices and use assignment models to predict the response of all users as if the dynamics of their optimization processes were of the same nature. This work demonstrates that better results can be achieved if the particular features of each user class are included in the models. It potentially improves the estimation of the responses and allows managers to shape their control measures to address specific user needs.     

Short-term traffic flow rate forecasting based on identifying similar traffic patterns

The ability to timely and accurately forecast the evolution of traffic is very important in traffic management and control applications. This paper proposes a non-parametric and data-driven methodology for short-term traffic forecasting based on identifying similar traffic patterns using an enhanced K-nearest neighbor (K-NN) algorithm. Weighted Euclidean distance, which gives more weight to recent measurements, is used as a similarity measure for K-NN. Moreover, winsorization of the neighbors is implemented to dampen the effects of dominant candidates, and rank exponent is used to aggregate the candidate values. Robustness of the proposed method is demonstrated by implementing it on large datasets collected from different regions and by comparing it with advanced time series models, such as SARIMA and adaptive Kalman Filter models proposed by others. It is demonstrated that the proposed method reduces the mean absolute percent error by more than 25%. In addition, the effectiveness of the proposed enhanced K-NN algorithm is evaluated for multiple forecast steps and also its performance is tested under data with missing values. This research provides strong evidence suggesting that the proposed non-parametric and data-driven approach for short-term traffic forecasting provides promising results. Given the simplicity, accuracy, and robustness of the proposed approach, it can be easily incorporated with real-time traffic control for proactive freeway traffic management.     

Validation of traffic flow models with respect to the spatiotemporal evolution of congested traffic patterns

We propose a quantitative approach for calibrating and validating key features of traffic instabilities based on speed time series obtained from aggregated data of a series of neighboring stationary detectors. The approach can be used to validate models that are calibrated by other criteria with respect to their collective dynamics. We apply the proposed criteria to historic traffic databases of several freeways in Germany containing about 400 occurrences of congestions thereby providing a reference for model calibration and quality assessment with respect to the spatiotemporal dynamics. First tests with microscopic and macroscopic models indicate that the criteria are both robust and discriminative, i.e., clearly distinguishes between models of higher and lower predictive power.     

Optimization method of alternate traffic restriction scheme based on elastic demand and mode choice behavior

As a countermeasure to urban traffic congestion, alternate traffic restriction (ATR) involves a certain proportion of automobiles being prohibited from entering pre-determined ATR districts during specific time periods. The present study introduces an optimization method for ATR schemes in terms of both their restriction districts and the proportion of restricted automobiles. As a Stackelberg game between traffic policy makers and road users, the ATR scheme optimization problem is established using a bi-level programming model, with the upper-level examining an ATR scheme aimed at consumers’ surplus maximization under the condition of overload flow minimization, and the lower-level synthetically optimizing elastic demand, mode choice (private car, public transit and park-and-ride) and multi-class user equilibrium assignment. A genetic algorithm based on the graph theory is also proposed to solve the bi-level programming model with a gradient project algorithm for solving the lower-level model. To our knowledge, this study represents the first attempt to theoretically optimize an ATR scheme using a systematic approach with mathematical model specification.     

Dynamics of heterogeneity in urban networks: aggregated traffic modeling and hierarchical control

Real traffic data and simulation analysis reveal that for some urban networks a well-defined Macroscopic Fundamental Diagram (MFD) exists, which provides a unimodal and low-scatter relationship between the network vehicle density and outflow. Recent studies demonstrate that link density heterogeneity plays a significant role in the shape and scatter level of MFD and can cause hysteresis loops that influence the network performance. Evidently, a more homogeneous network in terms of link density can result in higher network outflow, which implies a network performance improvement. In this article, we introduce two aggregated models, region- and subregion-based MFDs, to study the dynamics of heterogeneity and how they can affect the accuracy scatter and hysteresis of a multi-subregion MFD model. We also introduce a hierarchical perimeter flow control problem by integrating the MFD heterogeneous modeling. The perimeter flow controllers operate on the border between urban regions, and manipulate the percentages of flows that transfer between the regions such that the network delay is minimized and the distribution of congestion is more homogeneous. The first level of the hierarchical control problem can be solved by a model predictive control approach, where the prediction model is the aggregated parsimonious region-based MFD and the plant (reality) is formulated by the subregion-based MFDs, which is a more detailed model. At the lower level, a feedback controller of the hierarchical structure, tries to maximize the outflow of critical regions, by increasing their homogeneity. With inputs that can be observed with existing monitoring techniques and without the need for detailed traffic state information, the proposed framework succeeds to increase network flows and decrease the hysteresis loop of the MFD. Comparison with existing perimeter controllers without considering the more advanced heterogeneity modeling of MFD highlights the importance of such approach for traffic modeling and control.     

Privacy protection method for fine-grained urban traffic modeling using mobile sensors

With the ubiquitous nature of mobile sensing technologies, privacy issues are becoming increasingly important, and need to be carefully addressed. Data needs for transportation modeling and privacy protection should be deliberately balanced for different applications. This paper focuses on developing privacy mechanisms that would simultaneously satisfy privacy protection and data needs for fine-grained urban traffic modeling applications using mobile sensors. To accomplish this, a virtual trip lines (VTLs) zone-based system and related filtering approaches are developed. Traffic-knowledge-based adversary models are proposed and tested to evaluate the effectiveness of such a privacy protection system by making privacy attacks. The results show that in addition to ensuring an acceptable level of privacy, the released datasets from the privacy-enhancing system can also be applied to urban traffic modeling with satisfactory results. Albeit application-specific, such a “Privacy-by-Design” approach would hopefully shed some light on other transportation applications using mobile sensors.     

The impact of road traffic noise on urban protected areas: A landscape modeling approach

We modeled the propagation of traffic noise over the landscape and analyzed its impact on the structure and configuration of protected areas of the Twin Cities Metro Region, Minnesota. Using four noise thresholds, we found that at low and medium noise levels, 19% and 11% of the protected areas are within the road-effect zone. Using mean patch area and patch shape index, we measured the acoustic fragmentation of habitats. We found that at higher levels of noise patch shape index increased, while mean patch size decreased. The acoustic diversity of a patch is also found to be correlated with land cover type, patch area, and patch shape.     

Heterogeneous traffic flow modelling for an arterial using grid based approach

A grid based modelling approach akin to cellular automata (CA) is adopted for heterogeneous traffic flow simulation. The road space is divided into a grid of equally sized cells. Moreover, each vehicle type occupies one or more cell as per its size unlike CA traffic flow model where each vehicle is represented by a single cell. Model needs inputs such as vehicle size, its maximum speed, acceleration, deceleration, probability constants, and arrival pattern. The position and speed of the vehicles are assumed to be discrete. The speed of each vehicle changes according to its interactions with other vehicles, following some stochastic rules depending on the circumstances. The model is calibrated and validated using real data and VISSIM. The results indicate that grid based model can reasonably well simulate complex heterogeneous traffic as well as offers higher computational efficiency needed for real time application.     

Construction of traffic state vector using mutual information for short-term traffic flow prediction

Short-term traffic flow prediction is an integral part in most of Intelligent Transportation Systems (ITS) research and applications. Many researchers have already developed various methods that predict the future traffic condition from the historical database. Nevertheless, there has not been sufficient effort made to study how to identify and utilize the different factors that affect the traffic flow. In order to improve the performance of short-term traffic flow prediction, it is necessary to consider sufficient information related to the road section to be predicted. In this paper, we propose a method of constructing traffic state vectors by using mutual information (MI). First, the variables with different time delays are generated from the historical traffic time series, and the spatio-temporal correlations between the road sections in urban road network are evaluated by the MI. Then, the variables with the highest correlation related to the target traffic flow are selected by using a greedy search algorithm to construct the traffic state vector. The K-Nearest Neighbor (KNN) model is adapted for the application of the proposed state vector. Experimental results on real-world traffic data show that the proposed method of constructing traffic state vector provides good prediction accuracy in short-term traffic prediction.