A probabilistic stationary speed–density relation based on Newell’s simplified car-following model

Probabilistic models describing macroscopic traffic flow have proven useful both in practice and in theory. In theoretical investigations of wide-scatter in flow–density data, the statistical features of flow density relations have played a central role. In real-time estimation and traffic forecasting applications, probabilistic extensions of macroscopic relations are widely used. However, how to obtain such relations, in a manner that results in physically reasonable behavior has not been addressed. This paper presents the derivation of probabilistic macroscopic traffic flow relations from Newell’s simplified car-following model. The probabilistic nature of the model allows for investigating the impact of driver heterogeneity on macroscopic relations of traffic flow. The physical features of the model are verified analytically and shown to produce behavior which is consistent with well-established traffic flow principles. An empirical investigation is carried out using trajectory data from the New Generation SIMulation (NGSIM) program and the model’s ability to reproduce real-world traffic data is validated.     

Macroscopic traffic flow propagation stability for adaptive cruise controlled vehicles

Traffic flow propagation stability is concerned about whether a traffic flow perturbation will propagate and form a traffic shockwave. In this paper, we discuss a general approach to the macroscopic traffic flow propagation stability for adaptive cruise controlled (ACC) vehicles. We present a macroscopic model with velocity saturation for traffic flow in which each individual vehicle is controlled by an adaptive cruise control spacing policy. A nonlinear traffic flow stability criterion is investigated using a wavefront expansion technique. Quantitative relationships between traffic flow stability and model parameters (such as traffic flow and speed, etc.) are derived for a generalized ACC traffic flow model. The newly derived stability results are in agreement with previously derived results that were obtained using both microscopic and macroscopic models with a constant time headway (CTH) policy. Moreover, the stability results derived in this paper provide sufficient and necessary conditions for ACC traffic flow stability and can be used to design other ACC spacing policies.     

A phenomenological model for dynamic traffic flow in networks

A macroscopic model for dynamic traffic flow is presented. The main goal of the model is the real time simulation of large freeway networks with multiple sources and sinks. First, we introduce the model in its discrete formulation and consider some of its properties. It turns out, that our non-hydrodynamical ansatz for the flows results in a very advantageous behavior of the model. Next the fitting conditions at junctions of a traffic network are discussed. In the following sections we carry out a continuous approximation of our discrete model in order to derive stationary solutions and to consider the stability of the homogeneous one. It turns out, that for certain conditions unstable traffic flow occurs. In a subsequent section, we compare the stability of the discrete model and the corresponding continuous approximation. This confirms in retrospection the close similarities of both model versions. Finally we compare the results of our model with the results of another macroscopic model, that was recently suggested by Kerner and Konhäuser [Phys. Rev. E 48, 2335–2338 (1993)].     

Network traffic control based on a mesoscopic dynamic flow model

The paper focuses on Network Traffic Control based on aggregate traffic flow variables, aiming at signal settings which are consistent with within-day traffic flow dynamics. The proposed optimisation strategy is based on two successive steps: the first step refers to each single junction optimisation (green timings), the second to network coordination (offsets). Both of the optimisation problems are solved through meta-heuristic algorithms: the optimisation of green timings is carried out through a multi-criteria Genetic Algorithm whereas offset optimisation is achieved with the mono-criterion Hill Climbing algorithm. To guarantee proper queuing and spillback simulation, an advanced mesoscopic traffic flow model is embedded within the network optimisation method. The adopted mesoscopic traffic flow model also includes link horizontal queue modelling. The results attained through the proposed optimisation framework are compared with those obtained through benchmark tools.     

Visco‐elastic traffic flow model

To increase our understanding of the operations of traffic system, a visco‐elastic traffic model was proposed in analogy of non‐Newtonian fluid mechanics. The traffic model is based on mass and momentum conservations, and includes a constitutive relation similar to that of linear visco‐elastic fluids. The further inclusion of the elastic effect allows us to describe a high‐order traffic model more comprehensively because the use of relaxation time indicates that vehicle drivers adjust their time headway in a reasonable and safe range. The self‐organizing behaviour is described by introducing the effects of pressure and visco‐elasticity from the point of view in fluid mechanics. Both the viscosity and elasticity can be determined by using the relaxation time and the traffic sound speed. The sound speed can be approximately represented by the road operational parameters including the free‐flow speed, the jam density, and the density of saturation if the jam pressure in traffic flows is identical to the total pressure at the flow saturation point. A linear stability analysis showed that the traffic flow should be absolutely unstable for disturbances with short spatial wavelengths. There are two critical points of regime transition in traffic flows. The first point happens at the density of saturation, and the second point occurs at a density relating on the sound speed and the fundamental diagram of traffic flows. By using a triangular form flow–density relation, a numerical test based on the new model is carried out for congested traffic flows on a loop road without ramp effect. The numerical results are discussed and compared with the result of theoretical analysis and observation data of traffic flows. Copyright © 2011 John Wiley & Sons, Ltd.     

A macro model for traffic flow on road networks with varying road conditions

In this paper, we develop a macro traffic flow model with consideration of varying road conditions. Our analytical and numerical results illustrate that good road condition can enhance the speed and flow of uniform traffic flow whereas bad road condition will reduce the speed and flow. The numerical results also show that good road condition can smooth shock wave and improve the stability of traffic flow whereas bad road condition will lead to steeper shock wave and reduce the stability of traffic flow. Our results are also qualitatively accordant with empirical results, which implies that the proposed model can qualitatively describe the effects of road conditions on traffic flow. These results can guide traffic engineers to improve the road quality in traffic engineering. Copyright © 2012 John Wiley & Sons, Ltd.     

A novel traffic signal control formulation

A novel traffic signal control formulation is developed through a mixed integer programming technique. The formulation considers dynamic traffic, uses dynamic traffic demand as input, and takes advantage of a convergent numerical approximation to the hydrodynamic model of traffic flow. As inherent from the underlying hydrodynamic model, this formulation covers the whole range of the fundamental relationships between speed, flow, and density. Kinematic waves of the stop-and-go traffic associated with traffic signals are also captured. Because of this property, one does not need to tune or switch the model for the different traffic conditions. It “automatically” adjusts to the different traffic conditions. We applied the model to three demand scenarios in a simple network. The results seemed promising. This model produced timing plans that are consistent with models that work for unsaturated conditions. In gridlock conditions, it produced a timing plan that was better than conventional queue management practices.     

A hybrid deep learning based traffic flow prediction method and its understanding

Deep neural networks (DNNs) have recently demonstrated the capability to predict traffic flow with big data. While existing DNN models can provide better performance than shallow models, it is still an open issue of making full use of spatial-temporal characteristics of the traffic flow to improve their performance. In addition, our understanding of them on traffic data remains limited. This paper proposes a DNN based traffic flow prediction model (DNN-BTF) to improve the prediction accuracy. The DNN-BTF model makes full use of weekly/daily periodicity and spatial-temporal characteristics of traffic flow. Inspired by recent work in machine learning, an attention based model was introduced that automatically learns to determine the importance of past traffic flow. The convolutional neural network was also used to mine the spatial features and the recurrent neural network to mine the temporal features of traffic flow. We also showed through visualization how DNN-BTF model understands traffic flow data and presents a challenge to conventional thinking about neural networks in the transportation field that neural networks is purely a “black-box” model. Data from open-access database PeMS was used to validate the proposed DNN-BTF model on a long-term horizon prediction task. Experimental results demonstrated that our method outperforms the state-of-the-art approaches.     

RENAISSANCE – A unified macroscopic model-based approach to real-time freeway network traffic surveillance

The paper presents a unified macroscopic model-based approach to real-time freeway network traffic surveillance as well as a software tool RENAISSANCE that has been recently developed to implement this approach for field applications. RENAISSANCE is designed on the basis of stochastic macroscopic freeway network traffic flow modeling, extended Kalman filtering, and a number of traffic surveillance algorithms. Fed with a limited amount of real-time traffic measurements, RENAISSANCE enables a number of freeway network traffic surveillance tasks, including traffic state estimation and short-term traffic state prediction, travel time estimation and prediction, queue tail/head/length estimation and prediction, and incident alarm. The traffic state estimation and prediction lay the operating foundation of RENAISSANCE since RENAISSANCE bases the other traffic surveillance tasks on its traffic state estimation or prediction results. The paper first introduces the utilized stochastic macroscopic freeway network traffic flow model and a real-time traffic measurement model, upon which the complete dynamic system model of RENAISSANCE is established with special attention to the handling of some important model parameters. The algorithms for the various traffic surveillance tasks addressed are described along with the functional architecture of the tool. A simulation test was conducted via application of RENAISSANCE to a hypothetical freeway network example with a sparse detector configuration, and the testing results are presented in some detail. Final conclusions and future work are outlined.     

Short‐term traffic flow prediction with linear conditional Gaussian Bayesian network

Traffic flow prediction is an essential part of intelligent transportation systems (ITS). Most of the previous traffic flow prediction work treated traffic flow as a time series process only, ignoring the spatial relationship from the upstream flows or the correlation with other traffic attributes like speed and density. In this paper, we utilize a linear conditional Gaussian (LCG) Bayesian network (BN) model to consider both spatial and temporal dimensions of traffic as well as speed information for short‐term traffic flow prediction. The LCG BN allows both continuous and discrete variables, which enables the consideration of categorical variables in traffic flow prediction. A microscopic traffic simulation dataset is used to test the performance of the proposed model compared to other popular approaches under different predicting time intervals. In addition, the authors investigate the importance of spatial data and speed data in flow prediction by comparing models with different levels of information. The results indicate that the prediction accuracy will increase significantly when both spatial data and speed data are included. Copyright © 2016 John Wiley & Sons, Ltd.     

Automatic calibration of fundamental diagram for first‐order macroscopic freeway traffic models

Despite its importance in macroscopic traffic flow modeling, comprehensive method for the calibration of fundamental diagram is very limited. Conventional empirical methods adopt a steady state analysis of the aggregate traffic data collected from measurement devices installed on a particular site without considering the traffic dynamics, which renders the simulation may not be adaptive to the variability of data. Nonetheless, determining the fundamental diagram for each detection site is often infeasible. To remedy these, this study presents an automatic calibration method to estimate the parameters of a fundamental diagram through a dynamic approach. Simulated flow from the cell transmission model is compared against the measured flow wherein an optimization merit is conducted to minimize the discrepancy between model‐generated data and real data. The empirical results prove that the proposed automatic calibration algorithm can significantly improve the accuracy of traffic state estimation by adapting to the variability of traffic data when compared with several existing methods under both recurrent and abnormal traffic conditions. Results also highlight the robustness of the proposed algorithm. The automatic calibration algorithm provides a powerful tool for model calibration when freeways are equipped with sparse detectors, new traffic surveillance systems lack of comprehensive traffic data, or the case that lots of detectors lose their effectiveness for aging systems. Furthermore, the proposed method is useful for off‐line model calibration under abnormal traffic conditions, for example, incident scenarios. Copyright © 2015 John Wiley & Sons, Ltd.     

Hybrid artificial neural network and locally weighted regression models for lane-based short-term urban traffic flow forecasting

ABSTRACT

In recent years, there has been considerable research interest in short-term traffic flow forecasting. However, forecasting models offering a high accuracy at a fine temporal resolution (e.g. 1 or 5?min) and lane level are still rare. In this study, a combination of genetic algorithm, neural network and locally weighted regression is used to achieve optimal prediction under various input and traffic settings. The genetically optimized artificial neural network (GA-ANN) and locally weighted regression (GA-LWR) models are developed and tested, with the former forecasting traffic flow every 5-min within a 30-min period and the latter for forecasting traffic flow of a particular 5-min period of each for four lanes of an urban arterial road in Beijing, China. In particular, for morning peak and off-peak traffic flow prediction, the GA-ANN 5-min traffic flow model results in average errors of 3–5% and most 95th percentile errors of 7–14% for each of the four lanes; for the peak and off-peak time traffic flow predictions, the GA-LWR 5-min traffic flow model results in average errors of 2–4% and most 95th percentile errors are lower than 10% for each of the four lanes. When compared to previous models that usually offer average errors greater than 6–15%, such empirical findings should be of interest to and instrumental for transportation authorities to incorporate in their city- or state-wide Advanced Traveller Information Systems (ATIS).     

Bayesian inference of channelized section spillover via Markov Chain Monte Carlo sampling

Channelized section spillover (CSS) is usually referred to the phenomenon of a traffic flow being blocked upstream and not being able to enter the downstream channelized section. CSS leads to extra delays, longer queues, and a biased detection of the flow rate. An estimation of CSS, including its occurrence and duration, is helpful for analysis of the state of traffic flow, as a basis for traffic evaluation and management. This has not been studied or reported in prior literature. A Bayesian model is developed through this research to estimate CSS, with its occurrence and duration formulated as a posterior distribution of given travel time and flow rate data. Basic properties of CSS are discussed initially, followed by a macroscopic model that explicitly models the CSS and encapsulates first-in-first-out (FIFO) behavior at an upstream section, with a goal of generating the prior distribution of CSS duration. Posterior distribution is then constructed using the detected flow rate and travel time vehicles samples. The Markov Chain Monte Carlo (MCMC) sampling method is used to solve this Bayesian model. The proposed model is implemented and tested in a channelized intersection and its modeling results are compared with Vissim simulation outputs, which demonstrated satisfactory results.     

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.     

A network‐based dynamic air traffic flow model for short‐term en route traffic prediction

This paper presents a dynamic network‐based approach for short‐term air traffic flow prediction in en route airspace. A dynamic network characterizing both the topological structure of airspace and the dynamics of air traffic flow is developed, based on which the continuity equation in fluid mechanics is adopted to describe the continuous behaviour of the en route traffic. Building on the network‐based continuity equation, the space division concept in cell transmission model is introduced to discretize the proposed model both in space and time. The model parameters are sequentially updated based on the statistical properties of the recent radar data and the new predicting results. The proposed method is applied to a real data set from Shanghai Area Control Center for the short‐term air traffic flow prediction both at flight path and en route sector level. The analysis of the case study shows that the developed method can characterize well the dynamics of the en route traffic flow, thereby providing satisfactory prediction results with appropriate uncertainty limits. The mean relative prediction errors are less than 0.10 and 0.14, and the absolute errors fall in the range of 0 to 1 and 0 to 3 in more than 95% time intervals respectively, for the flight path and en route sector level. Copyright © 2017 John Wiley & Sons, Ltd.     

A macroscopic traffic model for highway work zones: Formulations and numerical results

This study presents a multilane model for analyzing the dynamic traffic properties of a highway segment under a lane‐closure operation that often incurs complex interactions between mandatory lane‐changing vehicles and traffic at unblocked lanes. The proposed traffic flow formulations employ the hyperbolic model used in the non‐Newtonian fluid dynamics, and assume the lane‐changing intensity between neighboring lanes as a function of their difference in density. The results of extensive simulation experiments indicate that the proposed model is capable of realistically replicating the impacts of lane‐changing maneuvers from the blocked lanes on the overall traffic conditions, including the interrelations between the approaching flow density, the resulting congestion level, and the exiting flow rate from the lane‐closure zone. Our extensive experimental analyses also confirm that traffic conditions will deteriorate dramatically and evolve to the state of traffic jam if the density has exceeded its critical level that varies with the type of lane‐closure operations. This study also provides a convenient way for computing such a critical density under various lane‐closure conditions, and offers a theoretical basis for understanding the formation as well as dissipation of traffic jam.     

Exploring the effects of cooperative adaptive cruise control on highway traffic flow using microscopic traffic simulation

This paper examines the impact of having cooperative adaptive cruise control (CACC) embedded vehicles on traffic flow characteristics of a multilane highway system. The study identifies how CACC vehicles affect the dynamics of traffic flow on a complex network and reduce traffic congestion resulting from the acceleration/deceleration of the operating vehicles. An agent-based microscopic traffic simulation model (Flexible Agent-based Simulator of Traffic) is designed specifically to examine the impact of these intelligent vehicles on traffic flow. The flow rate of cars, the travel time spent, and other metrics indicating the evolution of traffic congestion throughout the lifecycle of the model are analyzed. Different CACC penetration levels are studied. The results indicate a better traffic flow performance and higher capacity in the case of CACC penetration compared to the scenario without CACC-embedded vehicles.     

Logistic modeling of the equilibrium speed-density relationship

The fundamental diagram, as the graphical representation of the relationships among traffic flow, speed, and density, has been the foundation of traffic flow theory and transportation engineering. Seventy-five years after the seminal Greenshields model, a variety of models have been proposed to mathematically represent the speed-density relationship which underlies the fundamental diagram. Observed in these models was a clear path toward two competing goals: mathematical elegance and empirical accuracy. As the latest development of such a pursuit, this paper presents a family of speed-density models with varying numbers of parameters. All of these models perform satisfactorily and have physically meaningful parameters. In addition, speed variation with traffic density is accounted for; this enables statistical approaches to traffic flow analysis. The results of this paper not only improve our understanding of traffic flow but also provide a sound basis for transportation engineering studies.     

A platoon based cooperative eco-driving model for mixed automated and human-driven vehicles at a signalised intersection

The advancements in communication and sensing technologies can be exploited to assist the drivers in making better decisions. In this paper, we consider the design of a real-time cooperative eco-driving strategy for a group of vehicles with mixed automated vehicles (AVs) and human-driven vehicles (HVs). The lead vehicles in the platoon can receive the signal phase and timing information via vehicle-to-infrastructure (V2I) communication and the traffic states of both the preceding vehicle and current platoon via vehicle-to-vehicle (V2V) communication. We propose a receding horizon model predictive control (MPC) method to minimise the fuel consumption for platoons and drive the platoons to pass the intersection on a green phase. The method is then extended to dynamic platoon splitting and merging rules for cooperation among AVs and HVs in response to the high variation in urban traffic flow. Extensive simulation tests are also conducted to demonstrate the performance of the model in various conditions in the mixed traffic flow and different penetration rates of AVs. Our model shows that the cooperation between AVs and HVs can further smooth out the trajectory of the latter and reduce the fuel consumption of the entire traffic system, especially for the low penetration of AVs. It is noteworthy that the proposed model does not compromise the traffic efficiency and the driving comfort while achieving the eco-driving strategy.