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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]

Abstract: This article proposes a novel methodology that uses the bi‐level programming formulation to calibrate the expected total demand and the corresponding demand variability of traffic networks. In the bi‐level formulation the upper‐level is either a new maximum likelihood estimation method or a least squares method and the lower‐level is the strategic user equilibrium assignment model (StrUE) which accounts for the day‐to‐day demand volatility. The maximum likelihood method proposed in this article has the ability to utilize information from day‐to‐day observed link flows to provide a unique estimation of the total demand distribution, whereas the least squares method is capable of capturing link flow variations. The lower‐level StrUE model can take the total demand distribution as input, and output a set of link flow distributions which can then be compared to the link‐level observations. The mathematical proof demonstrates the convexity of the model, and the sensitivity to the prediction error is analytically derived. Numerical analysis is conducted to illustrate the efficiency and sensitivity of the proposed model. Some possible future research is discussed in the conclusion. [ABSTRACT FROM AUTHOR]

Abstract: This article proposes an extension of the strategic user equilibrium proposed by Waller and colleagues and Dixit and colleagues. The proposed model relaxes the assumption of proportional Origin‐Destination (O‐D) demand, as it accounts for users’ strategic link choice under independently distributed O‐D demands. The convexity of the mathematical formulation is proved when each O‐D demand is assumed to follow a Poisson distribution independently; link flow distributions and users’ strategic link choice are also proved to be unique. Network performance measures are given analytically. A numerical analysis is conducted on the Sioux Falls network. A Monte Carlo method is used to simulate network performance measures, which are then compared to the results computed from the analytical expression. It is illustrated that the model is capable of accounting for demand volatility while maintaining computation efficiency. [ABSTRACT FROM AUTHOR]

Abstract: The prediction of bus arrival time is important for passengers who want to determine their departure time and reduce anxiety at bus stops that lack timetables. The random forests based on the near neighbor (RFNN) method is proposed in this article to predict bus travel time, which has been calibrated and validated with real‐world data. A case study with two bus routes is conducted, and the proposed RFNN is compared with four methods: linear regression (LR), k‐nearest neighbors (KNN), support vector machine (SVM), and classic random forest (RF). The results indicate that the proposed model achieves high accuracy. That is, one bus route has the results of 13.65 mean absolute error (MAE), 6.90% mean absolute percentage error (MAPE), 26.37 root mean squared error (RMSE) and 13.77 (MAE), 7.58% (MAPE), 29.01 (RMSE), respectively. RFNN has a longer computation time of 44,301 seconds for a data set with 14,182 data. The proposed method can be optimized by the technology of parallel computing and can be applied to real‐time prediction. [ABSTRACT FROM AUTHOR]

Abstract: Connected vehicles are able to proactively change speed to adapt to the prevailing traffic condition. Even in the mixed traffic environment, connected vehicles may function as leading vehicles, hence influencing the driving pattern of following nonconnected vehicles. This article proposes a cell‐based simulation approach to model the proactive driving behavior of connected vehicles. First, a state variable of connected vehicles is introduced to track the trajectory of connected vehicles. Then the exit flow of cells containing connected vehicles is adjusted to simulate the proactive driving behavior, such that the traffic light is green when the connected vehicle arrives at the signalized intersection. The second part of the article conducts numerical tests to examine the effect of the proactive driving behavior of connected vehicles. Extensive test results consistently show that the presence of connected vehicles contributes significantly to the smoothing of traffic flow and vehicular emission reductions in the network. [ABSTRACT FROM AUTHOR]