Useful statistical distributions in modeling traffic flow

The state of the art of macroscopic vehicle traffic flow models is discussed and the traffic flow stability of these models is analyzed. A nonlinear traffic flow stability criterion is investigated using the wavefront expansion technique. Qualitative relationships between traffic flow stability and model parameters are derived for an entire class of second-order macroscopic traffic flow models. Numerical results axe obtained using the CLAWPACK package for the well-known Payne-Whitham model, in order to illustrate the stability criterion. The newly derived stability results are consistent with previous reported results obtained using both microscopic models and approximate linearization methods. Moreover, the stability criteria derived in the paper can provide more refined information regarding the propagation of traffic flow perturbations and shock waves in second-order models than previously established methodologies.

As the most promising alternative to internal combustion engines (ICEs), electric vehicles (EVs) have an excellent development outlook. The charging route scheduling of EVs can simultaneously affect traffic congestion in the transportation network (TN) and power flow distribution in the power distribution network (PDN). The research on TN and PDN coupling networks based on the static traffic flow model is relatively mature; however, it ignores that the traffic flow will spread across periods in a short scheduling period. In this paper, a semi‐dynamic traffic flow model is proposed to represent the dynamic propagation characteristics of EVs and ICEs flow. Furthermore, the cost of carbon emission and system operation are combined as the overall goal of system optimisation. Since the model has become a more complex non‐linear model, this paper proposes to combine the heuristic sequential boundary tightening and binary expansion method to linearise the model. The study compared four cases and found that a 20% penetration rate of EVs can reduce carbon emissions by 4.2% while reducing the system's total cost by 10%. Moreover, the impact of network congestion on the spatiotemporal distribution of traffic flow and power flow in the coupled network is alleviated.

Most of the models of road traffic flow at fixed-cycle controlled intersection assume stationary distributions and provide steady state results. The assumption that a constant number of vehicles can leave the system during the green phase is unrealistic in real life situations. A discrete time queuing model was developed to describe the operation of traffic flow at a road intersection with fixed-cycle signalized control and to account for the randomness in the number of vehicles that can leave the system. The results show the expected queue size in the system when the traffic is light and for abusy period, respectively. For the light period, when the traffic intensity is less than one, it takes a shorter green cycle time for vehicles to clear up than during high trafficintensity (the road junction is saturated). Increasing the number of cars that can leave the junction at the turn of the green phase reduces the number of cycle times before the queue is cleared.

The prevailing roadway and traffic conditions on expressways in India are vastly different when compared with the other roads in India and also, there is no perfect lane-discipline. The knowledge of roadway capacity is an important basic input required for planning, design, analysis, and operation of roadway systems. Hence, this work aims to model traffic flow on Indian urban expressways with specific reference to Delhi–Gurgaon expressway and estimate its capacity using the micro-simulation model using VISSIM 5·40. For this purpose, the field data collected on traffic-flow characteristics on expressways was used in calibration and validation of the simulation model. The validated simulation model was then used to develop fundamental traffic–flow relationships, namely, speed–flow, speed–area occupancy, and flow–area occupancy for the traffic-flow levels, starting from near-zero until the capacity of the facility. The capacity of an eight-lane divided urban expressway in level terrain with 14·0-m wide road space (one direction of traffic flow) was found to be in the range of 9700–10 000 vehicles/h. Moreover, through sensitivity analysis using simulation model, the following relationships, (i) percentage trucks in the traffic stream and capacity-level flow and (ii) percentage of trucks in the traffic stream and capacity-level traffic-stream speed, were developed. The results and the overall methodology followed in this study for modeling traffic flow on expressways in India to determine the capacity estimates under varying traffic compositions may be very useful for the practitioners and also for the continuing efforts to prepare an Indian Highway Capacity Manual.

Introduction. Problematic sections of the road network are intersections with high traffic intensity of conflicting pedestrian and traffic flow, in particular, right and left turns. At such crossings, there are significant traffic delays. In the case of vehicles turning left or right at an intersection when passing at a traffic light signal that allows traffic, should give way to pedestrians crossing the roadway on the crosswalk. In the case of high intensity of pedestrian traffic, it is impossible to complete the turn of such vehicles, they remain at the intersection, so there are significant traffic delays for returning vehicles.Purpose. Therefore, the work aims to study the interaction of traffic and pedestrian flows with high intensity at regulated intersections to improve their capacity.Methods. To study the parameters of traffic flows, in particular, the length of congestion, we used traffic flow models, which include a psychophysiological model of following a vehicle moving in front, and a model based on traffic rules. To model, pedestrian flows the Wiedemann model was used. The leastsquares method was used to obtain empirical nonlinear dependences of congestion length on the intensities of conflicting pedestrian and traffic flows.Results. The paper uses known methods for solving applied problems in the field of traffic for some unique cases, namely the intersection of intensive -traffic and pedestrian flows. Studies of road and pedestrian traffic parameters at crossings have shown that the length of congestion significantly depends on the intensity of traffic flow, but with increas-ing intensity of pedestrian traffic more than 1000 people/h, the length of congestion changes insignificantly. If there are trams at the intersection, the length of congestion increases by an average of 1.14% and depends significantly on the intensity of traffic and pedestrian flows.It is proposed to introduce three-phase traffic light regulation on such sections when one of the phases allows traffic only for pedestrians. The simulation results showed that the length of congestion in the absence of rail vehicles on the approaches to the intersection decreases by an average of 45.3% and is weakly dependent on the intensity of pedestrian flows. If there are rail vehicles at the crossing, the length of congestion can reduce by an average of 13.7%. But in some cases may increase.Conclusion. The research methodology presented in this paper can be used for intersections with another traffic organization scheme to justify the feasibility of introducing threephase traffic light control when one of the phases allows traffic only to pedestrians.

Several forms of statistical distributions are used in the study of radio-wave propagation. The paper refers to several of the commoner types, including the one-sided normal, exponential, Rayleigh, gamma, Nakagami-m and Weibull distributions, and shows that they are all simple interrelated forms of the Stacy distribution.

A variety of macroscopic traffic flow models have been applied to formulate the link-based system optimal dynamic traffic assignment (SO-DTA) problem in a many-to-one network. It is expected that SO-DTA models based on various traffic flow models usually result in different optimal link traffic evolution patterns, but whether and how traffic flow models affect the minimal system cost and the corresponding optimal arrival pattern at the destination is unclear. Three traffic flow models–point-queue, spatial-queue, and cell-transmission–are examined, and their resulted minimal system cost in many-to-one networks is compared. It is proved that for three simple networks–a linear network with two sequential bottlenecks, a two-in-one-out merge network, and a one-in-two-out diverge network–the minimal system costs for the SO-DTA models based on these three traffic flow models are identical. Numerical experiments show that this property appears to be held for general many-to-one networks. The reason may be that all three traffic flow models propagate the uncongested flows at the same speed and release the congested flows always at the link capacity. In SO-DTA applications where only the minimal system cost or arrival pattern at the destination is of major interest, the findings can be utilized to substantially expedite the solution procedure.

Many mathematical models for the disease transmission dynamics of Ebola have been developed and studied, particularly during and after the 2014 outbreak in West Africa. Most of these models are systems of ordinary differential equations (ODEs). One of the common assumptions made in these ODE models is that the duration of disease stages, such as latent and infectious periods, follows an exponential distribution. Gamma distributions have also been used in some of these models. It has been demonstrated that, when the models are used to evaluate disease control strategies such as quarantine or isolation, the models with exponential and Gamma distribution assumptions may generate contradictory results (Feng et al. in Bull Math Biol 69(5):1511-1536, 2007). Several Ebola models are considered in this paper with various stage distributions, including exponential, Gamma and arbitrary distributions. These models are used to evaluate control strategies such as isolation (or hospitalization) and timely burial and to identify potential discrepancies between the results from models with exponential and Gamma distributions.

In this paper, considering the influence of mixed traffic and overtaking on traffic flow, the formula of viscous resistance was put forth; a new Hydrodynamics model was established. Discrete analysis was carried out on the mechanical equation through the difference method, through which the change in the traffic flows parameters through time and space can be analyzed. Finally, the measured data simulation analysis results show that the new traffic flow model is of certain practical reference.

Hopf bifurcation control for the traffic flow model considering the tail light effect

<p>Most of worldwide population lives in urban areas, demanding for air quality information with a high spatio-temporal resolution. The most promising approaches for estimating urban air quality within the complex urban topography are small sensor networks and simulation models.</p><p>The TRAFAIR project focuses on understanding the role of traffic emissions on urban air quality by the combination of dispersion modelling, space- and time-resolved gas monitoring by lower cost sensors and realistic traffic flow rates by dynamic traffic model based on real time traffic data. Test cities of TRAFAIR are Modena, Florence, Pisa, Livorno, Zaragoza and Santiago de Compostela.</p><p>Depending on the size of the urban area, from 6 to 13 sensors units are deployed across each city since August 2019, providing estimates of NO, NO<sub>2</sub>, CO and O<sub>3</sub>, along with RH and temperature. Metal oxide sensors are deployed in Tuscany (Florence, Pisa, Livorno) and electrochemical cells are used elsewhere. The units are calibrated on a regular basis by co-location at the air quality regulatory stations and subsequently deployed across the town to monitor several representative locations (e.g. Low Emission Zones, hospital surroundings). For each sensor the raw readings (e.g. mV for electrochemical cells) are collected and a regression model (e.g. Random Forest) is applied to derive a calibration function, exploiting the data from the regulatory stations during co-location periods; for instance in Modena, the first short-term calibration provided a model with a Mean Absolute Error between 5 – 6 ppb and 2 – 4 ppb for NO and NO<sub>2</sub> respectively.</p><p>The sensors are used for both real-time urban air quality mapping and to test and validate the 24hr forecast service of NOx by the microscale lagrangian dispersion model GRAL. The simulation domains, covering the urban area of each TRAFAIR city, have a horizontal resolution of 4 m and allow to account for the presence of buildings. The dispersion model mainly focuses on NOx by traffic emissions, although domestic heating will be also included in the analysis. Vehicular emissions are based either upon historical traffic data (e.g. induction loops), or upon previously available traffic flow simulation, or upon traffic pattern reconstruction using a traffic flow model followed by a cluster analysis to group streets with similar pattern.</p><p>The final goal of the project is the development of a tool to support local policymakers and to inform citizenship about the quality of air and the impact of urban emission sources, particularly traffic. A secondary goal of the project is the development of a valuable QA/QC protocol for small sensor units and the optimization of the modelling chain for the forecast of traffic and domestic heating impact on local air quality at the urban scale.</p>

Multi-anticipative bi-directional visual field traffic flow models in the connected vehicle environment

Based on the full velocity difference (FVD) model, with the consideration of the effect of information about the two leading cars to the following car, an improved two_car following model of traffic flow has been deduced. The linear stable judging condition is obtained to the improved model by its stability analysis, which shows the stability range of the improved model is obviously larger than FVD model by comparing them. Numerical simulation shows that our model can avoid the disadvantage of negative velocity occurring at small reaction coefficient in FVD model by adjusting the information of the next-nearest-neighbor leading car. And there is unavoidable effect to traffic flow from the next-nearest-neighbor leading car’s information.

We introduce a new "second order" model of traffic flow. As noted in [C. Daganzo, Requiem for second-order fluid with approximation to traffic flow, Transportation Res. Part B, 29 (1995), pp. 277--286], the previous "second order" models, i.e., models with two equations (mass and "momentum"), lead to nonphysical effects, probably because they try to mimic the gas dynamics equations, with an unrealistic dependence on the acceleration with respect to the space derivative of the "pressure." We simply replace this space derivative with a convective derivative, and we show that this very simple repair completely resolves the inconsistencies of these models. Moreover, our model nicely predicts instabilities near the vacuum, i.e., for very light traffic.

Accurate short‐term traffic flow modeling is an essential prerequisite to analyze and control traffic flow. Canonical data‐driven methods are a large account of parameters that may be underfitted with limited training samples, yet they cannot adaptively boost their understanding of the spatiotemporal dependencies of the traffic flow. The noisy and unstable traffic flow data also prevent the models from effectively learning the underlying patterns for forecasting future traffic flow. To address these issues, we propose an easy‐to‐implement yet effective boosting model based on extreme gradient boosting and enhance it by wavelet denoising for short‐term traffic flow forecasting. The discrete wavelet denoising is employed to preprocess the noisy traffic flow data. Then, the denoised training datasets are reconstructed to train the extreme gradient boosting model. These two components are integrated seamlessly in a unified framework, and the whole framework can retain the features in the data as much as possible. Our model can precisely capture the hidden spatial dependency in the data. Extensive experiments are conducted on four benchmark datasets compared with frequently used models. The results demonstrate that the proposed model can precisely capture the hidden spatial dependency of the traffic flow data and achieve superior performance.