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.     

Evidence of convective instability in congested traffic flow: A systematic empirical and theoretical investigation

An extended open system such as traffic flow is said to be convectively unstable if perturbations of the stationary state grow but propagate in only one direction, so they eventually leave the system. By means of data analysis, simulations, and analytical calculations, we give evidence that this concept is relevant for instabilities of congested traffic flow. We analyze detector data from several hundred traffic jams and propose estimates for the linear growth rate, the wavelength, the propagation velocity, and the severity of the associated bottleneck that can be evaluated semi-automatically. Scatter plots of these quantities reveal systematic dependencies. On the theoretical side, we derive, for a wide class of microscopic and macroscopic traffic models, analytical criteria for convective and absolute linear instabilities. Based on the relative positions of the stability limits in the fundamental diagram, we divide these models into five stability classes which uniquely determine the set of possible elementary spatiotemporal patterns in open systems with a bottleneck. Only two classes, both dominated by convective instabilities, are compatible with observations. By means of approximate solutions of convectively unstable systems with sustained localized noise, we show that the observed spatiotemporal phenomena can also be described analytically. The parameters of the analytical expressions can be inferred from observations, and also (analytically) derived from the model equations.     

Spatial-temporal traffic flow pattern identification and anomaly detection with dictionary-based compression theory in a large-scale urban network

Traffic flow pattern identification, as well as anomaly detection, is an important component for traffic operations and control. To reveal the characteristics of regional traffic flow patterns in large road networks, this paper employs dictionary-based compression theory to identify the features of both spatial and temporal patterns by analyzing the multi-dimensional traffic-related data. An anomaly index is derived to quantify the network traffic in both spatial and temporal perspectives. Both pattern identifications are conducted in three different geographic levels: detector, intersection, and sub-region. From different geographic levels, this study finds several important features of traffic flow patterns, including the geographic distribution of traffic flow patterns, pattern shifts at different times-of-day, pattern fluctuations over different days, etc. Both spatial and temporal traffic flow patterns defined in this study can jointly characterize pattern changes and provide a good performance measure of traffic operations and management. The proposed method is further implemented in a case study for the impact of a newly constructed subway line. The before-and-after study identifies the major changes of surrounding road traffic near the subway stations. It is found that new metro stations attract more commute traffic in weekdays as well as entertaining traffic during weekends.     

Short-term traffic flow prediction using time-varying Vasicek model

This paper provides a two-step approach based on the stochastic differential equations (SDEs) to improve short-term prediction. In the first step of this framework, a Hull-White (HW) model is applied to obtain a baseline prediction model from previous days. Then, the extended Vasicek model (EV) is employed for modeling the difference between observations and baseline predictions (residuals) during an individual day. The parameters of this time-varying model are estimated at each sample using the residuals in a short duration of time before the time point of prediction; so it provides a real time prediction. The extracted model recovers the valuable local variation information during each day. The performance of our method in comparison with other methods improves significantly in terms of root mean squared error (RMSE), mean absolute error (MAE) and mean relative error (MRE) for real data from Tehran’s highways and the open-access PeMS database. We also demonstrate that the proposed model is appropriate for imputing the missing data in traffic dataset and it is more efficient than the probabilistic principal component analysis (PPCA) and k-Nearest neighbors (k-NN) methods.     

Algorithms to find shortest and alternative paths in free flow and congested traffic regimes

Location-based systems can be very helpful to mobile users if they are able to suggest shortest paths to destination taking into account the actual traffic conditions. This would allow to inform the drivers not only about the current shortest paths to destination but also about alternative, timely computed paths to avoid being trapped in the traffic jams signaled by cyber-physical-social systems. To this aim, the paper proposes a set of algorithms that solve very fast the All Pair Shortest Paths problem in both the free flow and congested traffic regimes, for road networks of medium-large size, thus enabling location-based systems to deal with emergencies and critical traffic conditions in city and metropolitan areas, whose transport networks typically range from some hundreds to many thousands of nodes, respectively. The paths to avoid being trapped in the traffic jams are computed by using a simulation of the shockwave propagation, instead of historical data. A parallel version of the algorithms is also proposed to solve the All Pair Shortest Paths problem for metropolitan areas with very large road networks. A time performance analysis of the proposed algorithms for transport networks of various size is carried out.     

A flexible traffic stream model and its three representations of traffic flow

To connect microscopic driving behaviors with the macro-correspondence (i.e., the fundamental diagram), this study proposes a flexible traffic stream model, which is derived from a novel car-following model under steady-state conditions. Its four driving behavior-related parameters, i.e., reaction time, calmness parameter, speed- and spacing-related sensitivities, have an apparent effect in shaping the fundamental diagram. Its boundary conditions and homogenous case are also analyzed in detail and compared with other two models (i.e., Longitudinal Control Model and Intelligent Driver Model). Especially, these model formulations and properties under Lagrangian coordinates provide a new perspective to revisit the traffic flow and complement with those under Eulerian coordinate. One calibration methodology that incorporates the monkey algorithm with dynamic adaptation is employed to calibrate this model, based on real-field data from a wide range of locations. Results show that this model exhibits the well flexibility to fit these traffic data and performs better than other nine models. Finally, a concrete example of transportation application is designed, in which the impact of three critical parameters on vehicle trajectories and shock waves with three representations (i.e., respectively defined in x-t, n-t and x-n coordinates) is tested, and macro- and micro-solutions on shock waves well agree with each other. In summary, this traffic stream model with the advantages of flexibility and efficiency has the good potential in level of service analysis and transportation planning.     

A new probability statistical model for traffic noise prediction on free flow roads and control flow roads

A new traffic noise prediction approach based on a probability distribution model of vehicle noise emissions and achieved by Monte Carlo simulation is proposed in this paper. The probability distributions of the noise emissions of three types of vehicles are obtained using an experimental method. On this basis, a new probability statistical model for traffic noise prediction on free flow roads and control flow roads is established. The accuracy of the probability statistical model is verified by means of a comparison with the measured data, which has shown that the calculated results of L_eq, L₁₀, L₅₀, L₉₀, and the probability distribution of noise level occurrence agree well with the measurements. The results demonstrate that the new method can avoid the complicated process of traffic flow simulation but still maintain high accuracy for the traffic noise prediction.     

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.     

Analytical and grid-free solutions to the Lighthill-Whitham-Richards traffic flow model

In this article, we propose a computational method for solving the Lighthill-Whitham-Richards (LWR) partial differential equation (PDE) semi-analytically for arbitrary piecewise-constant initial and boundary conditions, and for arbitrary concave fundamental diagrams. With these assumptions, we show that the solution to the LWR PDE at any location and time can be computed exactly and semi-analytically for a very low computational cost using the cumulative number of vehicles formulation of the problem. We implement the proposed computational method on a representative traffic flow scenario to illustrate the exactness of the analytical solution. We also show that the proposed scheme can handle more complex scenarios including traffic lights or moving bottlenecks. The computational cost of the method is very favorable, and is compared with existing algorithms. A toolbox implementation available for public download is briefly described, and posted at http://traffic.berkeley.edu/project/downloads/lwrsolver.     

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).     

A path-based flow formulation for the traffic assignment problem

In order to improve cooperation between traffic management and travelers, traffic assignment is the key component to achieve the objectives of both traffic management and route choice decisions for travelers. Traffic assignment can be classified into two models based on the behavioral assumptions governing route choices: User Equilibrium (UE) and System Optimum (SO) traffic assignment. According to UE and SO traffic assignment, travelers usually compete to choose the least cost routes to minimize their own travel costs, while SO traffic assignment requires travelers to work cooperatively to minimize overall cost in the road network. Thus, the paradox of benefits between UE and SO indicates that both are not practical. Thus, a solution technique needs to be proposed to balance UE and SO models, which can compromise both sides and give more feasible traffic assignments. In this paper, Stackelberg game theory is introduced to the traffic assignment problem, which can achieve the trade-off process between traffic management and travelers. Since traditional traffic assignments have low convergence rates, the gradient projection algorithm is proposed to improve efficiency.     

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.     

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.     

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.     

On the fundamental diagram for freeway traffic: A novel calibration approach for single-regime models

The speed-density or flow-density relationship has been considered as the foundation of traffic flow theory. Existing single-regime models calibrated by the least square method (LSM) could not fit the empirical data consistently well both in light-traffic/free-flow conditions and congested/jam conditions. In this paper, first, we point out that the inaccuracy of single-regime models is not caused solely by their functional forms, but also by the sample selection bias. Second, we apply a weighted least square method (WLSM) that addresses the sample selection bias problem. The calibration results for six well-known single-regime models using the WLSM fit the empirical data reasonably well both in light-traffic/free-flow conditions and congested/jam conditions. Third, we conduct a theoretical investigation that reveals the deficiency associated with the LSM is because the expected value of speed (or a function of it) is nonlinear with regard to the density (or a function of it).     

A dual decomposition method for sector capacity constrained traffic flow optimization

An aggregate air traffic flow model based on a multicommodity network is used for traffic flow management in the National Airspace System. The problem of minimizing the total travel time of flights in the National Airspace System of the United States, subject to sector capacity constraints, is formulated as an Integer Program. The resulting solution achieves optimal delay control. The Integer Program implemented for the scenarios investigated has billions of variables and constraints. It is relaxed to a Linear Program for computational efficiency. A dual decomposition method is applied to solve the large scale Linear Program in a computationally tractable manner. A rounding algorithm is developed to map the Linear Program solution to a physically acceptable result, and is implemented for the entire continental United States. A 2-h traffic flow management problem is solved with the method.     

A variational formulation for higher order macroscopic traffic flow models of the GSOM family

The GSOM (Generic second order modelling) family of traffic flow models combines the LWR model with dynamics of driver-specific attributes and can be expressed as a system of conservation laws. The object of the paper is to show that a proper Lagrangian formulation of the GSOM model can be recast as a Hamilton–Jacobi equation, the solution of which can be expressed as the value function of an optimal control problem. This value function is interpreted as the position of vehicles, and the optimal trajectories of the optimal control formulation can be identified with the characteristics. Further the paper analyzes the initial and boundary conditions, proposes a generalization of the inf-morphism and the Lax–Hopf formulas to the GSOM model, and considers numerical aspects.     

The prigogine-herman kinetic model predicts widely scattered traffic flow data at high concentrations

The classical derivation of a traffic stream model (e.g. speed/concentration relation) from the equilibrium solutions of the Prigogine–Herman kinetic equation invokes the nontrivial assumption that the underlying distribution of desired speeds is nonzero for vanishingly small speeds. In this paper we investigate the situation when this assumption does not hold. It is found that the Prigogine–Herman kinetic equation has a one-parameter family of equilibrium solutions, and hence an associated traffic stream model, only for traffic concentrations below some critical value; at higher concentrations there is a two-parameter family of solutions, and hence a continuum of mean velocities for each concentration. This result holds for both constant values of the passing probability and the relaxation time, and for values that depend on concentration in the manner assumed by Prigogine and Herman. It is hypothesized that this result reflects the well-known tendency toward substantial scatter in observational data of traffic flow at high concentrations.     

Efficient missing data imputing for traffic flow by considering temporal and spatial dependence

The missing data problem remains as a difficulty in a diverse variety of transportation applications, e.g. traffic flow prediction and traffic pattern recognition. To solve this problem, numerous algorithms had been proposed in the last decade to impute the missed data. However, few existing studies had fully used the traffic flow information of neighboring detecting points to improve imputing performance. In this paper, probabilistic principle component analysis (PPCA) based imputing method, which had been proven to be one of the most effective imputing methods without using temporal or spatial dependence, is extended to utilize the information of multiple points. We systematically examine the potential benefits of multi-point data fusion and study the possible influence of measurement time lags. Tests indicate that the hidden temporal–spatial dependence is nonlinear and could be better retrieved by kernel probabilistic principle component analysis (KPPCA) based method rather than PPCA method. Comparison proves that imputing errors can be notably reduced, if temporal–spatial dependence has been appropriately considered.     

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.