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Macroscopic traffic flow modeling is essential for describing and forecasting the characteristics of traffic flow. However, the classic Lighthill–Whitham–Richards (LWR) model only provides equilibrium values for steady‐state conditions and fails to capture common stochastic variabilities, which are a necessary component of accurate modeling of real‐time traffic management and control. In this paper, a stochastic LWR (SLWR) model that randomizes free‐flow speed is developed to account for the stochasticity incurred by the heterogeneity of drivers, while holding individual drivers' behavior constant. The SLWR model follows a conservation law of stochastic traffic density and flow and is formulated as a time‐dependent stochastic partial differential equation. The model is solved using a dynamically bi‐orthogonal (DyBO) method based on a spatial basis and stochastic basis. Various scenarios are simulated and compared with the Monte Carlo (MC) method, and the results show that the SLWR model can effectively describe dynamic traffic evolutions and reproduce some commonly observed traffic phenomena. Furthermore, the DyBO method shows significant computational advantages over the MC method. [ABSTRACT FROM AUTHOR]

In this work, a conserved higher-order (CHO) macroscopic traffic flow model is extended to road networks. We first introduce the Riemann problem at a junction for the CHO model and then provide a general framework to solve it, considering the compatibility between the CHO and Lighthill-Whitham-Richards (LWR) models. Through the presented framework, Riemann solvers for the LWR model can be extended to the CHO model. Specifically, a kind of Riemann solver for the LWR model is extended to derive the Riemann solver for the CHO model, in which the total actual flow at the junction is maximized. The Riemann solvers for three typical junctions (one-in-two-out junction, two-in-one-out junction, and two-in-two-out junction) are discussed. The first-order finite-volume method is adopted to solve the extended model. Numerical examples are given to validate the extended model and the numerical algorithm. [ABSTRACT FROM AUTHOR]

Intelligent traffic control and guidance system is an effective way to solve urban traffic congestion, improve road capacity and guarantee drivers' travel safety, while short-term traffic flow prediction is the core of intelligent traffic control and guidance system. To investigate the long-term memory and the dynamic feature of short-time traffic flow time series, a hybrid model was proposed by integrating autoregressive fractionally integrated moving average (ARFIMA) model and nonlinear autoregressive (NAR) neural network model to predict short-time traffic flow, in which ARFIMA model can address the long-term memory of linear component and NAR neural network can accommodate the dynamic feature of nonlinear residual component. First, the ARFIMA model was employed to predict the linear component of traffic flow, and the results were compared with those of autoregressive integrated moving average (ARIMA) model. Next, the NAR neural network model was adopted to forecast the nonlinear residual components, and the weighted results were considered as the predicted flow of the hybrid model. The proposed hybrid model was validated by using the cross-sectional traffic flow data in California freeways obtained from the open-access PeMS database. The results showed that the ARFIMA model considering the long-term memory can effectively predict the short-term traffic flow, and the prediction accuracy of the hybrid model is better than that of the singular models. The findings provide an alternative for the short-term traffic flow prediction with lower error and higher accuracy. [ABSTRACT FROM AUTHOR]

Network topologies are considered to be the fundamental factors that govern the network's macroscopic fundamental diagram (MFD) and performance. Despite its significance, this domain remains underexplored. This study employed empirical data as evidence to examine the explicit connections between network topologies and the parameters of a specific MFD, in the form of a macroscopic Underwood's model. Sixty-three 1 × 1 km dense urban networks were sampled in Hong Kong. The macroscopic Underwood's models of the sampled networks were estimated based on taxi Global Positioning System (GPS) data. The results reveal that the network free-flow speed decreased with the average number of junctions per unit distance, which captures the frequency of network-induced stop-and-go vehicle motion. The network optimal density decreased with the degree density normalized by the trafficable area, which represents the intensity of the conflicts between traffic streams. A spatially variable macroscopic Underwood's model was subsequently established. [ABSTRACT FROM AUTHOR]

Linear data projection is widely used for unbiased traffic data estimation. Nevertheless, recent studies have proven that direct model estimation based on linearly projected data that ignores the scaling factor variability may lead to systematically biased parameters. Adjustment factors were derived for a generalised multivariate polynomial (GMP) function with fixed exponents to remove such biases. However, the methods have not been extended to generic nonlinear transport models necessitating nonlinear regressions. This paper scrutinises the mechanism of systematic data point distortion resulting from linear data projection and identifies the practical difficulties of the adjustment factor approach to other nonlinear models. To reduce such biases in nonlinear transport models, a generic mean value restoration (MVR) method, requiring only the first two moments of the scaling factor, and an extended MVR (EMVR) method, further incorporating higher-order moments by assuming a scaling factor distribution, are proposed. Simulation studies are conducted for both GMP functions with relaxed exponents and multivariate exponential decay functions, which are the most commonly adopted nonlinear functions for modeling traffic flow, to examine the effectiveness and robustness of the proposed methods for recovering the assumed true model parameters. Results reveal that the EMVR method generally can achieve higher level of accuracy. [ABSTRACT FROM AUTHOR]

This study develops a predictive continuum dynamic user-optimal model for the simultaneous departure time and route choice problem through a variational inequality (VI) approach. A polycentric urban city with multiple central business districts (CBDs) is considered, and travelers are classified into different classes according to their destinations (i.e., CBDs). The road network within the modeling city is assumed to be sufficiently dense and can be viewed as a continuum. A predictive dynamic user-optimal (PDUO) model has been previously used to model traffic flow with a given traffic demand distribution, in which travelers choose the routes that minimize the actual travel cost to the CBD. In this work, we combine the departure time choice with the PDUO model to study the simultaneous departure time and route choice problem. The user-optimal departure time principle is satisfied, which states that for each origin–destination pair, the total costs incurred by travelers departing at any time are equal and minimized. We then present an equivalent VI and solve it using the projection method after discretization based on unstructured meshes. A numerical experiment for an urban city with two CBDs is presented to demonstrate the effectiveness of the numerical algorithm. [ABSTRACT FROM AUTHOR]

This paper establishes a mathematical model that can represent the conflicting effects of two pedestrian streams that have an oblique intersecting angle in a large crowd. In a previous paper, a controlled experiment in which two streams of pedestrians were asked to walk in designated directions was used to model the bidirectional pedestrian stream of certain intersecting angles. In this paper, the writers revisit that problem and apply the Bayesian inference method to calibrate an improved model with the controlled experiment data. Pedestrian movement data are also collected from a busy crosswalk by using a video observation approach. The two sets of data are used separately to calibrate the proposed model. With the calibrated model, the relationship between speed, density, and flow is studied in both the reference and conflicting streams, and a prediction is made regarding how these factors affected the interactions of moving pedestrian streams. It is found that the speed of one stream not only decreases with its total density, but also decreases with the ratio of its flow relative to the total flow, i.e., the speed of the pedestrians decreases if their stream changes from the major to minor stream. It is also observed that the maximum disruption that was induced by pedestrian flow from an intersecting angle occurs when the angle is approximately 135°. [ABSTRACT FROM AUTHOR]

The goals of this paper are to (1) provide a review of the recently developed measures for assessing the quality of origin-destination (O-D) trip tables estimated from traffic counts and (2) propose a new generalized demand scale (GDS) measure. This GDS quality measure generalizes the total demand scale (TDS) quality measure by allowing the assessment of the intrinsic underdeterminant problem of O-D estimation from traffic counts at various spatial levels. Numerical examples are provided to compare the proposed GDS measure with the TDS measure, the maximal possible relative error, and the expected relative error and to illustrate the features of the GDS measure. [ABSTRACT FROM AUTHOR]

This study reviews and compares two heuristic algorithms: methods of successive averages and route swapping, which are commonly used in simulation-based dynamic traffic assignment models. A new hybrid algorithm that has the advantages of both algorithms is introduced. As finding a unique solution cannot be guaranteed, the concept of solution reliability is suggested for the formulation of convergence criterion. An example network is used to illustrate the method. [ABSTRACT FROM AUTHOR]

In this paper, we develop a model of bidirectional pedestrian streams with an oblique intersecting angle that represents the crossing interaction of pedestrians moving in different directions on a walking facility. We formulate the model based on Drake’s model in the traffic flow literature, and calibrate it using results from a set of controlled experiments in which two groups of pedestrians were asked to walk in different directions and cross on designated walkways with different levels of pedestrian flow and different intersecting angles. Their movements were video recorded, and macroscopic quantities such as speed, density, and flow were extracted to calibrate the model of bidirectional pedestrian streams. All of the parameters of the calibrated model are statistically significant at the 0.1% level. [ABSTRACT FROM AUTHOR]

In a recent paper, the weighted essentially non-oscillatory (WENO) numerical scheme was applied to solve a multi-class Lighthill–Whitham–Richards (MCLWR) traffic flow model (J. Comput. Phys. 2003; 191:639–659). We discuss and present an enhanced WENO scheme with Lax–Friedrichs flux splitting by improving the estimation of the minimal characteristic speed of the MCLWR model, which is based on a set of inequalities of eigenvalues. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We propose a macroscopic model of lane-changing that is consistent with car-following behavior on a two-lane highway. Using linear stability theory, we find that lane-changing affects the stable region and the propagation speeds of the first-order and second-order waves. In analyzing a small disturbance, our model effectively reproduces certain non-equilibrium traffic-flow phenomena-small disturbance instability, stop-and-go waves, and local clusters that are affected by lane-changing. The model also gives the flow-density relationships in terms of the actual flow rate, the lane-changing rate, and the difference between the potential flow rate (the flow rate that would have occurred without lane-changing) and the actual flow rate. The relationships between the actual flow rate and traffic density and between the lane-changing rate and traffic density follow a reverse-lambda shape, which is largely consistent with observed traffic phenomena. [ABSTRACT FROM AUTHOR]

This paper deals with the effects of traffic bottlenecks using an extended Lighthill-Whitham-Richards (LWR) model. The solution structure is analytically indicated by the study of the Riemann problem characterized by a discontinuous flux. This leads to a typical solution describing a queue upstream of the bottleneck and its width and height, and informs the design of a δ-mapping algorithm. More significantly, it is found that the kinetic model is able to reproduce stop-and-go waves for a triangular fundamental diagram. Some simulation examples, which are in agreement with the analytical solutions, are given to support these conclusions. [ABSTRACT FROM AUTHOR]

In this paper, we present a new car-following model by taking into account the effects of the traffic interruption probability on the car-following behaviour of the following vehicle. The stability condition of the model is obtained by using the linear stability theory. The modified Korteweg-de Vries (KdV) equation is constructed and solved, and three types of traffic flows in the headway sensitivity space-stable, metastable, and unstable-are classified. Both the analytical and simulation results show that the traffic interruption probability indeed has an influence on driving behaviour, and the consideration of traffic interruption probability in the car-following model could stabilize traffic flow. [ABSTRACT FROM AUTHOR]

We analytically investigate a wide cluster solution and show that it is not admitted in some of the traffic flow models in the literature. For those traffic flow models that admit the wide cluster solution, the relationship between two important control parameters and the critical densities that divide an equilibrium solution into stable and unstable regions is thoroughly discussed in detail. We find that such wide clusters exist with a free traffic density in an unstable region, and with one or three critical densities. These results are different from the cases in the well-known higher-order traffic flow models of Payne and Whitham [H. J. Payne, "Models of freeway traffic and control," in Mathematical Models of Public Systems, A. G. Bekey, ed., Simulation Council Proc. Ser. 1, La Jolla, CA, 1971, pp. 51-61], [G. B. Whitham, Linear and Nonlinear Waves, John Wiley and Sons, New York, 1974], Kühne [R. D. Kühne, "Macroscopic freeway model for dense traffic-stop-start waves and incident detection," in Proceedings of the 9th International Symposium on Transportation and Traffic Theory, J. Volmuller and R. Hamerslag, eds., VNU Science Press, Utrecht, 1984, pp. 21-42], and Kerner and Konhäuser [B. S. Kerner and P. Konhäuser, Phys. Rev. E (3), 50 (1994), pp. 54-83]. [ABSTRACT FROM AUTHOR]

This paper presents a reliability-based network design problem. A network reliability concept is embedded into the continuous network design problem in which travelers' route choice behavior follows the stochastic user equilibrium assumption. A new capacity-reliability index is introduced to measure the probability that all of the network links are operated below their capacities when serving different traffic patterns deviating from the average condition. The reliability-based network design problem is formulated as a bi-level program in which the lower level sub-program is the probit-based stochastic user equilibrium problem and the upper level sub-program is the maximization of the new capacity reliability index. The lower level sub-program is solved by a variant of the method of successive averages using the exponential average to represent the learning process of network users on a daily basis that results in the daily variation of traffic-flow pattern, and Monte Carlo stochastic loading. The upper level sub-program is tackled by means of genetic algorithms. A numerical example is used to demonstrate the concept of the proposed framework. [ABSTRACT FROM AUTHOR]

In this paper, a wavelet-Galerkin formulation with domain transformation is applied to solve the kinematic wave model of traffic flow. A domain transformation method is employed to resolve the constraints imposed on the solution variables. This avoids the problem of generating invalid solution of traffic states as with conventional numerical schemes for the wave model. With the localized scaling function or wavelet, the method is also capable of capturing the shock wave in the traffic model. Moreover, due to the localized characteristics of wavelets, the bandwidths of matrices are usually very small. Therefore, a robust band-matrix solver can be employed to enhance computational efficiency. Numerical examples are given to demonstrate the effectiveness of the proposed method. Copyright © John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

An introduction to topics discussed within the special issue "Recent Advances in Traffic Control and Management" is presented, including an article which evaluated the capacity of multi-lane roundabout while taking into consideration the unequal traffic distribution between the circulating lanes, another article which proposed a new risk-averse user equilibrium model to estimate the distribution of traffic flows, and another article on the risk factors in air traffic control.

Provides an overview of the articles contained in the 2004 issue of the "Journal of Intelligent Transportation Systems" regarding advanced algorithms in traffic signal control for urban road systems. Discussion of the signal control for road traffic within the framework of optimal control theory; Presentation of a genetic algorithm to generate optimized signal timings; Adoption of a two-stage heuristic model, which is formulated as a mixed integer linear program.