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.     

Establishing speed–flow–density relationships for exclusive motorcycle lanes

Abstract

The motorcycle is a popular mode of transport in Malaysia and developing Asian countries, but its significant representation in the traffic mix results in high rates of motorcycle accidents. As a result, the Malaysian Government decided to segregate motorcycle traffic along its new federal roads as an engineering approach to reduce accidents. However, traffic engineers needed to know the maximum traffic a motorcycle lane could accommodate. Despite substantial literature related to speed–flow–density relationships and capacities of various transport facilities, there is a knowledge gap regarding motorcycle lanes. This paper establishes motorcycle speed–flow–density relationships and capacities of exclusive motorcycle lanes in Malaysia. Observations of motorcycle flows and speeds were conducted along existing and experimental motorcycle lanes. Motorcycle speed–density data were aggregated and plotted for two types of observable motorcycle riding behaviour patterns that were influenced by the widths of a motorcycle lane: the headway pattern (lane width ≤ 1.7 m) and the space pattern (lane width > 1.7 m). For both riding patterns, regression analysis of motorcycle speed–density data best fits the logarithmic model and consequently the motorcycle flow–density and speed–flow models are derived. Motorcycle lane capacities for headway and space riding patterns are estimated as 3300 mc/hr/lane and 2200 mc/hr/m, respectively.     

Collecting ambient vehicle trajectories from an instrumented probe vehicle: High quality data for microscopic traffic flow studies

This paper presents the methodology and results from a study to extract empirical microscopic vehicular interactions from a probe vehicle instrumented with sensors to monitor the ambient vehicles as it traverses a 28 mi long freeway corridor. The contributions of this paper are two fold: first, the general method and approach to seek a cost-effective balance between automation and manual data reduction that transcends the specific application. Second, the resulting empirical data set is intended to help advance traffic flow theory in general and car following models in particular. Generally the collection of empirical microscopic vehicle interaction data is either too computationally intensive or labor intensive. Historically automatic data extraction does not provide the precision necessary to advance traffic flow theory, while the labor demands of manual data extraction have limited past efforts to small scales. Key to the present study is striking the right balance between automatic and manual processing. Recognizing that any empirical microscopic data for traffic flow theory has to be manually validated anyway, the present study uses a “pretty good” automated processing algorithm followed by detailed manual cleanup using an efficient user interface to rapidly process the data. The study spans roughly two hours of data collected on a freeway during the afternoon peak of a typical weekday that includes recurring congestion. The corresponding data are being made available to the research community to help advance traffic flow theory in general and car following models in particular.     

The identification and empirical characterization of vehicular (Lagrangian) fundamental diagrams in multilane traffic flow

Traditional macroscopic traffic flow modeling framework adopts the spatial–temporal coordinate system to analyze traffic flow dynamics. With such modeling and analysis paradigm, complications arise for traffic flow data collected from mobile sensors such as probe vehicles equipped with mobile phones, Bluetooth, and Global Positioning System devices. The vehicle‐based measurement technologies call for new modeling thoughts that address the unique features of moving measurements and explore their full potential. In this paper, we look into the concept of vehicular fundamental diagram (VFD) and discuss its engineering implications. VFD corresponds to a conventional fundamental diagram (FD) in the kinematic wave (KW) theory that adopts space–time coordinates. Similar to the regular FD in the KW theory, VFD encapsulates all traffic flow dynamics. In this paper, to demonstrate the full potential of VFD in interpreting multilane traffic flow dynamics, we generalize the classical Edie's formula and propose a direct approach of reconstructing VFD from traffic measurements in the vehicular coordinates. A smoothing algorithm is proposed to effectively reduce the nonphysical fluctuation of traffic states calculated from multilane vehicle trajectories. As an example, we apply the proposed methodology to explore the next‐generation simulation datasets and identify the existence and forms of shock waves in different coordinate systems. Our findings provide empirical justifications and further insight for the Lagrangian traffic flow theory and models when applied in practice. Copyright © 2015 John Wiley & Sons, Ltd.     

A kinematic wave theory of lane-changing traffic flow

Frequent lane-changes in highway merging, diverging, and weaving areas could disrupt traffic flow and, even worse, lead to accidents. In this paper, we propose a simple model for studying bottleneck effects of lane-changing traffic and aggregate traffic dynamics of a roadway with lane-changing areas. Based on the observation that, when changing its lane, a vehicle affects traffic on both its current and target lanes, we propose to capture such lateral interactions by introducing a new lane-changing intensity variable. With a modified fundamental diagram, we are able to study the impacts of lane-changing traffic on overall traffic flow. In addition, the corresponding traffic dynamics can be described with a simple kinematic wave model. For a location-dependent lane-changing intensity variable, we discuss kinematic wave solutions of the Riemann problem of the new model and introduce a supply–demand method for its numerical solutions. With both theoretical and empirical analysis, we demonstrate that lane-changes could have significant bottleneck effects on overall traffic flow. In the future, we will be interested in studying lane-changing intensities for different road geometries, locations, on-ramp/off-ramp flows, as well as traffic conditions. The new modeling framework could be helpful for developing ramp-metering and other lane management strategies to mitigate the bottleneck effects of lane-changes.     

A porous flow approach to modeling heterogeneous traffic in disordered systems

A continuum model that describes a disordered, heterogeneous traffic stream is presented. Such systems are widely prevalent in developing countries where classical traffic models cannot be readily applied. The characteristics of such systems are unique since drivers of smaller vehicles exploit their maneuverability to move ahead through lateral gaps at lower speeds. At higher speeds, larger vehicles press their advantage of greater motive power. The traffic stream at the microscopic level is disordered and defines a porous medium. Each vehicle is considered to move through a series of pores defined by other vehicles. A speed-density relationship that explicitly considers the pore space distribution is presented. This captures the considerable dynamics between vehicle classes that are overlooked when all classes are converted to a reference class (usually Passenger Car Equivalents) as is traditionally done. Using a finite difference approximation scheme, traffic evolution for a two-class traffic stream is shown.     

A stochastic model of traffic flow: Theoretical foundations

In a variety of applications of traffic flow, including traffic simulation, real-time estimation and prediction, one requires a probabilistic model of traffic flow. The usual approach to constructing such models involves the addition of random noise terms to deterministic equations, which could lead to negative traffic densities and mean dynamics that are inconsistent with the original deterministic dynamics. This paper offers a new stochastic model of traffic flow that addresses these issues. The source of randomness in the proposed model is the uncertainty inherent in driver gap choice, which is represented by random state dependent vehicle time headways. A wide range of time headway distributions is allowed. From the random time headways, counting processes are defined, which represent cumulative flows across cell boundaries in a discrete space and continuous time conservation framework. We show that our construction implicitly ensures non-negativity of traffic densities and that the fluid limit of the stochastic model is consistent with cell transmission model (CTM) based deterministic dynamics.     

Experimental and empirical investigations of traffic flow instability

Traffic instability is an important but undesirable feature of traffic flow. This paper reports our experimental and empirical studies on traffic flow instability. We have carried out a large scale experiment to study the car-following behavior in a 51-car-platoon. The experiment has reproduced the phenomena and confirmed the findings in our previous 25-car-platoon experiment, i.e., standard deviation of vehicle speeds increases in a concave way along the platoon. Based on our experimental results, we argue that traffic speed rather than vehicle spacing (or density) might be a better indicator of traffic instability, because vehicles can have different spacing under the same speed. For these drivers, there exists a critical speed between 30 km/h and 40 km/h, above which the standard deviation of car velocity is almost saturated (flat) along the 51-car-platoon, indicating that the traffic flow is likely to be stable. In contrast, below this critical speed, traffic flow is unstable and can lead to the formation of traffic jams. Traffic data from the Nanjing Airport Highway support the experimental observation of existence of a critical speed. Based on these findings, we propose an alternative mechanism of traffic instability: the competition between stochastic factors and the so-called speed adaptation effect, which can better explain the concave growth of speed standard deviation in traffic flow.     

Modeling and analysis of mixed flow of cars and powered two wheelers

In modern cities, a rapid increase of motorcycles and other types of Powered Two-Wheelers (PTWs) is observed as an answer to long commuting in traffic jams and complex urban navigation. Such increasing penetration rate of PTWs creates mixed traffic flow conditions with unique characteristics that are not well understood at present. Our objective is to develop an analytical traffic flow model that reflects the mutual impacts of PTWs and Cars. Unlike cars, PTWs filter between cars, have unique dynamics, and do not respect lane discipline, therefore requiring a different modeling approach than traditional “Passenger Car Equivalent” or “Follow the Leader”. Instead, this work follows an approach that models the flow of PTWs similarly to a fluid in a porous medium, where PTWs “percolate” between cars depending on the gap between them.Our contributions are as follows: (I) a characterization of the distribution of the spacing between vehicles by the densities of PTWs and cars; (II) a definition of the equilibrium speed of each class as a function of the densities of PTWs and cars; (III) a mathematical analysis of the model’s properties (IV) an impact analysis of the gradual penetration of PTWs on cars and on heterogeneous traffic flow characteristics.The proposed model could contribute as an enabler for ‘PTW-aware’ future Cooperative Intelligent Transport Systems technologies and traffic regulations.     

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 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.     

Modeling the information flow propagation wave under vehicle-to-vehicle communications

Vehicle-to-vehicle (V2V) communications under the connected vehicle context have the potential to provide new paradigms to enhance the safety, mobility and environmental sustainability of surface transportation. Understanding the information propagation characteristics in space and time is a key enabler for V2V-based traffic systems. Most existing analytical models assume instantaneous propagation of information flow through multi-hop communications. Such an assumption ignores the spatiotemporal relationships between the traffic flow dynamics and V2V communication constraints. This study proposes a macroscopic two-layer model to characterize the information flow propagation wave (IFPW). The traffic flow propagation is formulated in the lower layer as a system of partial differential equations based on the Lighthill-Whitham-Richards model. Due to their conceptual similarities, the upper layer adapts and modifies a spatial Susceptible-Infected epidemic model to describe information dissemination between V2V-equipped vehicles using integro-differential equations. A closed-form solution is derived for the IFPW speed under homogeneous conditions. The IFPW speed is numerically determined for heterogeneous conditions. Numerical experiments illustrate the impact of traffic density and market penetration of V2V-equipped vehicles on the IFPW speed. The proposed model can capture the spatiotemporal relationships between the traffic and V2V communication layers, and aid in the design of novel information propagation strategies to manage traffic conditions under V2V-based traffic systems.     

Empirical flow-density and speed-spacing relationships: Evidence of vehicle length dependency

Traffic flow theory has come to a point where conventional, fixed time averaged data are limiting our insight into critical behavior both at the macroscopic and microscopic scales. This paper develops a methodology to measure relationships of density and vehicle spacing on freeways. These relationships are central to most traffic flow theories but have historically been difficult to measure empirically. The work leads to macroscopic flow-density and microscopic speed-spacing relationships in the congested regime derived entirely from dual loop detector data and then verified against the NGSIM data set. The methodology eliminates the need to seek out stationary conditions and yields clean relationships that do not depend on prior assumptions of the curve shape before fitting the data. Upon review of the clean empirical relationships a key finding of this work is the fact that many of the critical parameters of the macroscopic flow-density and microscopic speed-spacing relationships depend on vehicle length, e.g., upstream moving waves should travel through long vehicles faster than through short vehicles. Thus, the commonly used assumption of a homogeneous vehicle fleet likely obscures these important phenomena. More broadly, if waves travel faster or slower depending on the length of the vehicles through which the waves pass, then the way traffic is modeled should be updated to explicitly account for inhomogeneous vehicle lengths.     

Modeling the impacts of mandatory and discretionary lane-changing maneuvers

In this paper, a novel mesoscopic multilane model is proposed to enable simultaneous simulation of mandatory and discretionary lane-changing behaviors to realistically capture multilane traffic dynamics. The model considers lane specific fundamental diagrams to simulate dynamic heterogeneous lane flow distributions on expressways. Moreover, different priority levels are identified according to different lane-changing motivations and the corresponding levels of urgency. Then, an algorithm is proposed to estimate the dynamic mandatory and discretionary lane-changing demands. Finally, the lane flow propagation is defined by the reaction law of the demand–supply functions, which can be regarded as an extension of the Incremental-Transfer and/or Priority Incremental-Transfer principles. The proposed mesoscopic multilane cell transmission model is calibrated and validated on a complex weaving section of the State Route 241 freeway in Orange County, California, showing both the positive and negative impact of lane changing maneuvers, e.g., balancing effect and capacity drop, respectively. Moreover, the empirical study verifies that the model requires no additional data other than the cell transmission model does. Thus, the proposed model can be deployed as a simple simulation tool for accessing dynamic mesoscopic multilane traffic state from data available to most management centers, and also the potential application in predicting the impact of traffic incident or lane control strategy.     

Estimation of flow and density using probe vehicles with spacing measurement equipment

Probe vehicles provide some of the most useful data for road traffic monitoring because they can acquire wide-ranging and spatiotemporally detailed information at a relatively low cost compared with traditional fixed-point observation. However, current GPS-equipped probe vehicles cannot directly provide us volume-related variables such as flow and density. In this paper, we propose a new probe vehicle-based estimation method for obtaining volume-related variables by assuming that a probe vehicle can measure the spacing to its leading one. This assumption can be realized by utilizing key technologies in advanced driver assistance systems that are expected to spread in the near future. We developed a method of estimating the flow, density, and speed from the probe vehicle data without exogenous assumptions on traffic flow characteristics, such as a fundamental diagram. In order to quantify the characteristics of the method, we performed a field experiment at a real-world urban expressway by employing prototypes of the probe vehicles with spacing measurement equipment. The result showed that the proposed method could accurately estimate the 5 min and hourly traffic volumes with probe vehicle penetration rate of 3.5% and 0.2%, respectively.     

Modeling traffic's flow-density relation: Accommodation of multiple flow regimes and traveler types

This research investigates freeway-flow impacts of different traveler types by specifying and applying a latent-segmentation model of congested and uncongested driving behaviors. Drivers in uncongested conditions are assumed to drive at self-chosen speeds, while drivers in congested conditions are assumed to take speed as given and choose a spacing (between their vehicle and the previous vehicle). Several classes of driver-vehicle combinations are distinguished in a data set based on double-loop-detector pulses and a household travel survey. These classifications are made on the basis of vehicle type and gender, leading to class estimates of speeds and spacings. The segmentation model is specified as a logit function of density, weather, and vehicle type, leading to estimates of congested-condition probabilities. Unobserved heterogeneity is incorporated in all models via common error assumptions.Results indicate that segmentation models are promising tools for traffic data analysis and that information on travelers, their vehicles, and weather conditions explains significant variation in flow data. By clarifying a greater understanding of traffic conditions and traveler behavior explains much scatter in the fundamental relation between flow, speed, and density, can assist regions in their traffic-management efforts and engineers in their design of roadway facilities. Ultimately, such improvements to travel networks should enhance quality of life.     

Including heavy vehicles in a car‐following model: modelling,calibrating and validating

Heavy vehicles influence general traffic in many different ways compared with passenger vehicles, and this may result in different levels of traffic instability. Increases in the number and proportion of heavy vehicles in the traffic stream will therefore result in different traffic flow conditions. This research initially outlines the different car‐following behaviour of drivers in congested heterogeneous traffic conditions indicating the necessity for developing a car‐following model, which includes these differences. A psychophysical car‐following model, similar in form to Weideman's car‐following model, was developed. Due to the complexity of the developed model, the calibration of the model was undertaken using a particle swarm optimisation algorithm with the data recorded under congested traffic conditions. This was then incorporated into a traffic microsimulation model. The results showed that the car‐following perceptual thresholds and thus action points of drivers differ based on their vehicle and the lead vehicle types. The inclusion of the heavy vehicles in the model showed significant impacts on the traffic dynamic and interactions amongst different vehicles. Copyright © 2016 John Wiley & Sons, Ltd.     

Optimizing signals for arterials experiencing heavy mixed scooter-vehicle flows

Recognizing the increasing popularity of scooters among urban commuters in developing countries and the significant impacts of their dynamic maneuverability on the progression of mixed traffic, this study presents a simulation-based signal optimization model for arterials experiencing heavy scooter-vehicle flows. The proposed model consists of a macroscopic simulation and a signal optimization module, where the former functions to capture the interactions between scooter and passenger-car flows over the process of discharging, propagation, and formation of intersection queues. The latter offers a specially-designed algorithm to search for the optimal signal plan and arterial offsets, based on the complex departure and arrival patterns of mixed flows estimated with the simulation module. To account for scooters’ unique parallel moving and queue patterns in a travel lane, the proposed signal module has adopted the sub-lane concept in estimating the mixed-flow queue distribution across lanes and their discharging flow rates. The results of extensive experimental analyses with various mixed-flow scenarios confirm that the proposed model offers the potential for signal design for arterials plagued by heavy scooter-vehicle mixed flows.     

Recent developments in traffic flow modeling using macroscopic fundamental diagram

ABSTRACT

This paper presents an overview of the recent developments in traffic flow modelling and analysis using macroscopic fundamental diagram (MFD) as well as their applications. In recent literature, various aggregated traffic models have been proposed and studied to analyse traffic flow while enhancing network efficiency. Many of these studies have focused on models based on MFD that describes the relationship between aggregated flow and aggregated density of transport networks. The analysis of MFD has been carried out based on experimental data collected from sensors and GPS, as well as simulation models. Several factors are found to influence the existence and shape of MFD, including traffic demand, network and signal settings, and route choices. As MFD can well express the traffic dynamics of large urban transport networks, it has been extensively applied to traffic studies, including the development of network-wide control strategies, network partitioning, performance evaluation, and road pricing. This work also presents future extensions and research directions for MFD-based traffic modelling and applications.