On the existence of stationary states in general road networks

Our daily driving experience and empirical observations suggest that traffic patterns in a road network are relatively stationary during peak periods. In numerous transportation network studies, there has been an implicit conjecture that stationary states exist in a network when origin demands, route choice proportions, and destination supplies are constant. In this study, we first rigorously formulate the conjecture within the framework of a network kinematic wave theory with an invariant junction model. After defining stationary states, we derive a system of algebraic equations in 3-tuples of stationary link flow-rates, demands, and supplies. We then introduce a new definition of junction critical demand levels based on effective demands and supplies. With a map in critical demand levels, we show that its fixed points and, therefore, stationary states exist with the help of Brouwer’s fixed point theorem. For two simple road networks, we show that the map is well-defined and can be used to solve stationary states with a brute-force method. Finally we summarize the study and present some future extensions and applications.     

Improving noise assessment at intersections by modeling traffic dynamics

Three families of road noise prediction models can be distinguished. Static noise models only consider free-flow constant-speed traffic with uniformly distributed vehicles. Analytic noise models assume that all vehicles are isolated from one another but account for their mean kinematic profile over the network. Micro-simulation noise models relax the hypothesis of no interaction between vehicles and fully capture traffic flow dynamic effects such as queue evolution. This study compares the noise levels obtained by these three methodologies at signalized intersections and roundabouts. It reveals that micro-simulation noise models outperform the other approaches. Particularly, they are able to capture the effects of stochastic transient queues in under-saturated conditions as well as stop-and-go behaviors in oversaturated regime. Accounting for traffic dynamics is also shown to improve predictions of noise variations due to different junction layouts. In this paper, a roundabout is found to induce a 2.5 dB(A) noise reduction compared to a signalized intersection in under-saturated conditions while the acoustic contributions of both kinds of junctions balance in oversaturated regime.     

Noise level in the vicinity of signalized roundabouts

The analysis, assessment and estimation of noise levels in the vicinity of intersections is a more complex problem than a similar analysis for roads and streets. This is due to the varied geometry of the intersections, differences in the loads of individual movements, participation of heavy vehicles and mass transport vehicles, as well as the various types of traffic management and traffic control. This article analyses the influence of intersection type and traffic characteristics on the noise levels in the vicinity of classic channelized intersections with signalization, roundabouts and signalized roundabouts. Based on the conducted measurements, it has been established that, with comparable traffic parameters and the same distance from the geometric centre of the intersection, the L_Aeq value for signalized roundabouts is 2.5–10.8 dB higher in comparison to classic channelized intersections with signalization and 3.3–6.7 dB higher in relations to the analysed roundabout. Additionally the differences between L_Aeq levels at individual entries at the same signalized roundabouts may reach the value of approximately 4.5 dB. Such situation is influenced by differences in the intersection geometry, diameter of the intersection’s central island, traffic flow type, traffic management at the entries and traffic volume, especially the amount and traffic movements of multiple axle heavy vehicles. These factors have been analysed in detail in relation to signalized roundabouts in this paper.     

Continuous formulations and analytical properties of the link transmission model

The link transmission model (LTM) has great potential for simulating traffic flow in large-scale networks since it is much more efficient and accurate than the Cell Transmission Model (CTM). However, there lack general continuous formulations of LTM, and there has been no systematic study on its analytical properties such as stationary states and stability of network traffic flow. In this study we attempt to fill the gaps. First we apply the Hopf–Lax formula to derive Newell’s simplified kinematic wave model with given boundary cumulative flows and the triangular fundamental diagram. We then apply the Hopf–Lax formula to define link demand and supply functions, as well as link queue and vacancy functions, and present two continuous formulations of LTM, by incorporating boundary demands and supplies as well as invariant macroscopic junction models. With continuous LTM, we define and solve the stationary states in a road network. We also apply LTM to directly derive a Poincaré map to analyze the stability of stationary states in a diverge-merge network. Finally we present an example to show that LTM is not well-defined with non-invariant junction models. We can see that Newell’s model and continuous LTM complement each other and provide an alternative formulation of the network kinematic wave theory. This study paves the way for further extensions, analyses, and applications of LTM in the future.     

Recent developments in traffic flow modeling using macroscopic fundamental diagram

ABSTRACT

This paper presents an overview of the recent developments in traffic flow modelling and analysis using macroscopic fundamental diagram (MFD) as well as their applications. In recent literature, various aggregated traffic models have been proposed and studied to analyse traffic flow while enhancing network efficiency. Many of these studies have focused on models based on MFD that describes the relationship between aggregated flow and aggregated density of transport networks. The analysis of MFD has been carried out based on experimental data collected from sensors and GPS, as well as simulation models. Several factors are found to influence the existence and shape of MFD, including traffic demand, network and signal settings, and route choices. As MFD can well express the traffic dynamics of large urban transport networks, it has been extensively applied to traffic studies, including the development of network-wide control strategies, network partitioning, performance evaluation, and road pricing. This work also presents future extensions and research directions for MFD-based traffic modelling and applications.     

Stability and bifurcation in network traffic flow: A Poincaré map approach

Previous studies have shown that, in a diverge-merge network with two intermediate links (the DM network), the kinematic wave model always admits stationary solutions under constant boundary conditions, but periodic oscillations can develop from empty initial conditions. Such contradictory observations suggest that the stationary states be unstable. In this study we develop a systematic approach to investigate the stability property of stationary states in this and other networks within the framework of network kinematic wave theories. Based on the observation that kinematic waves propagate in a circular path when only one of the two intermediate links is congested, we derive a one-dimensional, discrete Poincaré map in the out-flux at a Poincaré section. We then prove that the fixed points of the Poincaré map correspond to stationary flow-rates on the two links. With Lyapunov’s first method, we demonstrate that the Poincaré map can be finite-time stable, asymptotically stable, or unstable. When unstable, the map is found to have periodical points of period two, but no chaotic solutions. We further analyze the bifurcation in the stability of the Poincaré map caused by varying route choice proportions. We apply the Poincaré map approach to analyzing traffic patterns in more general (DM)ⁿ and beltway networks, which are sufficient and necessary structures for network-induced unstable traffic and gridlock, respectively. This study demonstrates that the Poincaré map approach can be efficiently applied to analyze traffic dynamics in any road networks with circular information propagation and provides new insights into unstable traffic dynamics caused by interactions among network bottlenecks.     

Analysis of Characteristics of the Dynamic Flow-Density Relation and its Application to Traffic Flow Models

Abstract

Online traffic flow modeling is of increasing importance due to intelligent transport systems and technologies. The flow-density relation plays an important role in traffic flow modeling and provides a basic way to illustrate traffic flow behavior under different traffic flow and traffic density conditions. Until now the research effort has focused mainly on the shape of the relation. The time series of the relation has not been identified clearly, even though the time series of the relation reflects the upstream/downstream traffic conditions and should be considered in the traffic flow modeling. In this paper, the dynamic flow-density relation is identified based on the classification of traffic states and is quantified employing fuzzy logic. The quantified dynamic flow-density relation builds the basis for online application of a macroscopic traffic flow model. The new approach to online modeling of traffic flow applying the dynamic flow-density relation alleviates parameter calibration problems stemming from the static flow-density relation.     

Stochastic adaptive control model for traffic signal systems

An adaptive control model of a network of signalized intersections is proposed based on a discrete-time, stationary, Markov decision process. The model incorporates probabilistic forecasts of individual vehicle actuations at downstream inductance loop detectors that are derived from a macroscopic link transfer function. The model is tested both on a typical isolated traffic intersection and a simple network comprised of five four-legged signalized intersections, and compared to full-actuated control. Analyses of simulation results using this approach show significant improvement over traditional full-actuated control, especially for the case of high volume, but not saturated, traffic demand.     

Traffic guidance–perimeter control coupled method for the congestion in a macro network

Macroscopic fundamental diagram (MFD) describes the macro relationship between a network vehicle density and a network space mean flow, without requiring the mastery of complex origin to destination data. Thus, MFD provides an opportunity for the macro control of urban road network. However, most of the existing MFD control methods ignore the active role of traffic guidance in solving congestion problems. This study presents a traffic guidance–perimeter control coupled (TGPCC) method to improve the performance of macroscopic traffic networks. The method considers the optimal cumulative volume of a network as the goal and establishes a programming function according to the network equilibrium rule of traffic flow amongst multiple MFD sub-regions, which regards the minimum delay of network, as the objective. The Logit model for the compliance rate of driver route guidance is established by the stated preference survey. Moreover, the perimeter control (PC) method is proposed for adjusting the phase split of intersections. Finally, three schemes, namely, the TGPCC, PC and the method without PC and guidance are tested on a network with four well-defined MFD sub-regions. Results show that the TGPCC addresses the issue of congestion and decreases the total delay accordingly.     

A three-dimensional macroscopic fundamental diagram for mixed bi-modal urban networks

Recent research has studied the existence and the properties of a macroscopic fundamental diagram (MFD) for large urban networks. The MFD should not be universally expected as high scatter or hysteresis might appear for some type of networks, like heterogeneous networks or freeways. In this paper, we investigate if aggregated relationships can describe the performance of urban bi-modal networks with buses and cars sharing the same road infrastructure and identify how this performance is influenced by the interactions between modes and the effect of bus stops. Based on simulation data, we develop a three-dimensional vehicle MFD (3D-vMFD) relating the accumulation of cars and buses, and the total circulating vehicle flow in the network. This relation experiences low scatter and can be approximated by an exponential-family function. We also propose a parsimonious model to estimate a three-dimensional passenger MFD (3D-pMFD), which provides a different perspective of the flow characteristics in bi-modal networks, by considering that buses carry more passengers. We also show that a constant Bus–Car Unit (BCU) equivalent value cannot describe the influence of buses in the system as congestion develops. We then integrate a partitioning algorithm to cluster the network into a small number of regions with similar mode composition and level of congestion. Our results show that partitioning unveils important traffic properties of flow heterogeneity in the studied network. Interactions between buses and cars are different in the partitioned regions due to higher density of buses. Building on these results, various traffic management strategies in bi-modal multi-region urban networks can then be integrated, such as redistribution of urban space among different modes, perimeter signal control with preferential treatment of buses and bus priority.     

Local online kernel ridge regression for forecasting of urban travel times

Accurate and reliable forecasting of traffic variables is one of the primary functions of Intelligent Transportation Systems. Reliable systems that are able to forecast traffic conditions accurately, multiple time steps into the future, are required for advanced traveller information systems. However, traffic forecasting is a difficult task because of the nonlinear and nonstationary properties of traffic series. Traditional linear models are incapable of modelling such properties, and typically perform poorly, particularly when conditions differ from the norm. Machine learning approaches such as artificial neural networks, nonparametric regression and kernel methods (KMs) have often been shown to outperform linear models in the literature. A bottleneck of the latter approach is that the information pertaining to all previous traffic states must be contained within the kernel, but the computational complexity of KMs usually scales cubically with the number of data points in the kernel. In this paper, a novel kernel-based machine learning (ML) algorithm is developed, namely the local online kernel ridge regression (LOKRR) model. Exploiting the observation that traffic data exhibits strong cyclic patterns characterised by rush hour traffic, LOKRR makes use of local kernels with varying parameters that are defined around each time point. This approach has 3 advantages over the standard single kernel approach: (1) It allows parameters to vary by time of day, capturing the time varying distribution of traffic data; (2) It allows smaller kernels to be defined that contain only the relevant traffic patterns, and; (3) It is online, allowing new traffic data to be incorporated as it arrives. The model is applied to the forecasting of travel times on London’s road network, and is found to outperform three benchmark models in forecasting up to 1 h ahead.     

Improved driver responses at intersections with red signal countdown timers

Traffic Signal Countdown Timers (TSCTs) are innovative, practical and cost effective technologies with the potential to improve efficiency at signalized intersections. The purpose of these devices is to assist motorists in decision-making at signalized intersections with real-time signal duration information. This study focused specifically on driver responses in the presence of a Red Signal Countdown Timer (RSCT). A Linear Mixed Effect (LME) model was developed to predict the effect of RSCT on the headway of the first vehicle waiting on a red signal. The model predicted 0.72 s reduction in the headway of the first queued vehicle resulting from the presence of RSCT, while the observed difference in mean headway was 0.82 s. This result is suggestive of a reduction in start-up lost time at signalized intersections, i.e., an improvement in signalized intersection efficiency when an RSCT is present.     

Mining and correlating traffic events from human sensor observations with official transport data using self-organizing-maps

Cities are complex systems, where related Human activities are increasingly difficult to explore within. In order to understand urban processes and to gain deeper knowledge about cities, the potential of location-based social networks like Twitter could be used a promising example to explore latent relationships of underlying mobility patterns. In this paper, we therefore present an approach using a geographic self-organizing map (Geo-SOM) to uncover and compare previously unseen patterns from social media and authoritative data. The results, which we validated with Live Traffic Disruption (TIMS) feeds from Transport for London, show that the observed geospatial and temporal patterns between special events (r = 0.73), traffic incidents (r = 0.59) and hazard disruptions (r = 0.41) from TIMS, are strongly correlated with traffic-related, georeferenced tweets. Hence, we conclude that tweets can be used as a proxy indicator to detect collective mobility events and may help to provide stakeholders and decision makers with complementary information on complex mobility processes.     

Equilibrium analysis and route guidance in large-scale networks with MFD dynamics

Recent studies have demonstrated that Macroscopic Fundamental Diagram (MFD), which provides an aggregated model of urban traffic dynamics linking network production and density, offers a new generation of real-time traffic management strategies to improve the network performance. However, the effect of route choice behavior on MFD modeling in case of heterogeneous urban networks is still unexplored. The paper advances in this direction by firstly extending two MFD-based traffic models with different granularity of vehicle accumulation state and route choice behavior aggregation. This configuration enables us to address limited traffic state observability and to scrutinize implications of drivers’ route choice in MFD modeling. We consider a city that is partitioned in a small number of large-size regions (aggregated model) where each region consists of medium-size sub-regions (more detailed model) exhibiting a well-defined MFD. This paper proposes a route guidance advisory control system based on the aggregated model as a large-scale traffic management strategy that utilizes aggregated traffic states while sub-regional information is partially known. In addition, we investigate the effect of equilibrium conditions (i.e. user equilibrium and system optimum) on the overall network performance, in particular MFD functions.     

A comparative study of Macroscopic Fundamental Diagrams of arterial road networks governed by adaptive traffic signal systems

Using a stochastic cellular automaton model for urban traffic flow, we study and compare Macroscopic Fundamental Diagrams (MFDs) of arterial road networks governed by different types of adaptive traffic signal systems, under various boundary conditions. In particular, we simulate realistic signal systems that include signal linking and adaptive cycle times, and compare their performance against a highly adaptive system of self-organizing traffic signals which is designed to uniformly distribute the network density. We find that for networks with time-independent boundary conditions, well-defined stationary MFDs are observed, whose shape depends on the particular signal system used, and also on the level of heterogeneity in the system. We find that the spatial heterogeneity of both density and flow provide important indicators of network performance. We also study networks with time-dependent boundary conditions, containing morning and afternoon peaks. In this case, intricate hysteresis loops are observed in the MFDs which are strongly correlated with the density heterogeneity. Our results show that the MFD of the self-organizing traffic signals lies above the MFD for the realistic systems, suggesting that by adaptively homogenizing the network density, overall better performance and higher capacity can be achieved.     

Characterization and prediction of air traffic delays

This paper presents a new class of models for predicting air traffic delays. The proposed models consider both temporal and spatial (that is, network) delay states as explanatory variables, and use Random Forest algorithms to predict departure delays 2–24 h in the future. In addition to local delay variables that describe the arrival or departure delay states of the most influential airports and links (origin–destination pairs) in the network, new network delay variables that characterize the global delay state of the entire National Airspace System at the time of prediction are proposed. The paper analyzes the performance of the proposed prediction models in both classifying delays as above or below a certain threshold, as well as predicting delay values. The models are trained and validated on operational data from 2007 and 2008, and are evaluated using the 100 most-delayed links in the system. The results show that for a 2-h forecast horizon, the average test error over these 100 links is 19% when classifying delays as above or below 60 min. Similarly, the average over these 100 links of the median test error is found to be 21 min when predicting departure delays for a 2-h forecast horizon. The effects of changes in the classification threshold and forecast horizon on prediction performance are studied.     

Network-oriented household activity pattern problem for system optimization

The recently emerging trend of self-driving vehicles and information sharing technologies, made available by private technology vendors, starts creating a revolutionary paradigm shift in the coming years for traveler mobility applications. By considering a deterministic traveler decision making framework at the household level in congested transportation networks, this paper aims to address the challenges of how to optimally schedule individuals’ daily travel patterns under the complex activity constraints and interactions. We reformulate two special cases of household activity pattern problem (HAPP) through a high-dimensional network construct, and offer a systematic comparison with the classical mathematical programming models proposed by Recker (1995). Furthermore, we consider the tight road capacity constraint as another special case of HAPP to model complex interactions between multiple household activity scheduling decisions, and this attempt offers another household-based framework for linking activity-based model (ABM) and dynamic traffic assignment (DTA) tools. Through embedding temporal and spatial relations among household members, vehicles and mandatory/optional activities in an integrated space-time-state network, we develop two 0–1 integer linear programming models that can seamlessly incorporate constraints for a number of key decisions related to vehicle selection, activity performing and ridesharing patterns under congested networks. The well-structured network models can be directly solved by standard optimization solvers, and further converted to a set of time-dependent state-dependent least cost path-finding problems through Lagrangian relaxation, which permit the use of computationally efficient algorithms on large-scale high-fidelity transportation networks.     

Closed-form multiclass cell transmission model enhanced with overtaking,lane-changing,and first-in first-out properties

A novel multiclass macroscopic model is proposed in this article. In order to enhance first-in, first-out property (FIFO) and transmission function in the multiclass traffic modeling, a new multiclass cell transmission model with FIFO property (herein called FM-CTM) is extended from its prior multiclass cell transmission model (M-CTM). Also, to enhance its analytical compactness and resultant computational convenience, FM-CTM is formulated in this paper as a set of closed-form matrix equations. The objective is to improve the accuracy of traffic state estimation by enforcing FIFO property when a fast vehicle cannot overtake a slow vehicle due to a limitation of a single-lane road. Moreover, the proposed model takes into account a different priority for vehicles of each class to move forward through congested road conditions, and that makes the flow calculation independent from their free-flow speeds. Some hypothetical and real-world freeway networks with a constant or varying number of lanes are selected to verify FM-CTM by comparing with M-CTM and the conventional CTM. Observed densities of VISSIM and real-world dataset of I-80 are selected to compare with the simulated densities from the three CTMs. The numerical results show that FM-CTM outperforms the other two models by 15% of accuracy measures in most cases. Therefore, the proposed model is expected to be well applicable to the road network with a mixed traffic and varying number of lanes.     

On the allocation of city space to multiple transport modes

Abstract

This paper analyzes urban multimodal transportation systems in an aggregated way. To describe the aggregate behavior of traffic in cities, use is made of an idea that is now receiving some attention: the macroscopic fundamental diagram (MFD). We demonstrate through simulation how the MFD can be used to monitor and control a real network, in this case a portion of San Francisco, using readily available input data. We then show how different modes interact on the same network and discuss how these interactions might be incorporated into an MFD for multimodal networks. The work unveils two main results: first, it confirms recent results showing that restricting access to a city's congested areas can improve mobility for all travelers, including those who endure the restrictions; and second, that dedicating street space to collective transport modes can improve accessibility for all modes, even those from which space is taken away.     

Cooperative traffic control of a mixed network with two urban regions and a freeway

Currently most optimization methods for urban transport networks (i) are suited for networks with simplified dynamics that are far from real-sized networks or (ii) apply decentralized control, which is not appropriate for heterogeneously loaded networks or (iii) investigate good-quality solutions through micro-simulation models and scenario analysis, which make the problem intractable in real time. In principle, traffic management decisions for different sub-systems of a transport network (urban, freeway) are controlled by operational rules that are network specific and independent from one traffic authority to another. In this paper, the macroscopic traffic modeling and control of a large-scale mixed transportation network consisting of a freeway and an urban network is tackled. The urban network is partitioned into two regions, each one with a well-defined Macroscopic Fundamental Diagram (MFD), i.e. a unimodal and low-scatter relationship between region density and outflow. The freeway is regarded as one alternative commuting route which has one on-ramp and one off-ramp within each urban region. The urban and freeway flow dynamics are formulated with the tool of MFD and asymmetric cell transmission model, respectively. Perimeter controllers on the border of the urban regions operating to manipulate the perimeter interflow between the two regions, and controllers at the on-ramps for ramp metering are considered to control the flow distribution in the mixed network. The optimal traffic control problem is solved by a Model Predictive Control (MPC) approach in order to minimize total delay in the entire network. Several control policies with different levels of urban-freeway control coordination are introduced and tested to scrutinize the characteristics of the proposed controllers. Numerical results demonstrate how different levels of coordination improve the performance once compared with independent control for freeway and urban network. The approach presented in this paper can be extended to implement efficient real-world control strategies for large-scale mixed traffic networks.