Logistic modeling of the equilibrium speed-density relationship

The fundamental diagram, as the graphical representation of the relationships among traffic flow, speed, and density, has been the foundation of traffic flow theory and transportation engineering. Seventy-five years after the seminal Greenshields model, a variety of models have been proposed to mathematically represent the speed-density relationship which underlies the fundamental diagram. Observed in these models was a clear path toward two competing goals: mathematical elegance and empirical accuracy. As the latest development of such a pursuit, this paper presents a family of speed-density models with varying numbers of parameters. All of these models perform satisfactorily and have physically meaningful parameters. In addition, speed variation with traffic density is accounted for; this enables statistical approaches to traffic flow analysis. The results of this paper not only improve our understanding of traffic flow but also provide a sound basis for transportation engineering studies.     

Data mining using regularized adaptive B‐splines regression with penalization for multi‐regime traffic stream models

This paper presents a new data mining method that integrates adaptive B‐spline regression and traffic flow theory to develop multi‐regime traffic stream models (TSMs). Parameter estimation is implemented adaptively and optimally through a constrained bi‐level programming method. The slave programming determines positions of knots and coefficients of the B‐spline by minimizing the error of B‐spline regression. The master programming model determines the number of knots through a regularized function, which balances model accuracy and model complexity. This bi‐level programming method produces the best fitting to speed–density observations under specific order of splines and possesses great flexibility to accommodate the exhibited nonlinearity in speed–density relationships. Jam density can be estimated naturally using spline TSM, which is sometimes hardly obtainable in many other TSM. Derivative continuity up to one order lower than the highest spline degree can be preserved, a desirable property in some application. A five‐regime B‐spline model is found to exist for generalized speed–density relationships to accommodate five traffic operating conditions: free flow, transition, synchronized flow, stop and go traffic, and jam condition. A typical two‐regime B‐spline form is also explicitly given, depending only on free‐flow speed, optimal speed, optimal density, and jam density. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

Walking infrastructure design assessment by continuous space dynamic assignment modeling

For the planning and design of walking infrastructure, characterized by the fact that the pedestrians can choose their paths freely in two‐dimensional space, applicability of traditional discrete network models is limited. This contribution puts forward an approach for user‐optimal dynamic assignment in continuous time and space for analyzing for instance walking infrastructure in a two‐dimensional space. Contrary to network‐based approaches, the theory allows the traffic units to choose from an infinite non‐countable set of paths through the considered space. The approach first determines the continuous paths using a path choice model. Then, origin‐destination flows are assigned and traffic conditions are calculated. The approach to determine a user‐optimal assignment is heuristic and consists of a sequence of all‐or‐nothing assignments. An application example is presented, showing dynamic user equilibrium traffic flows through a realistic transfer station. The example is aimed at illustrating the dynamic aspects of the modeling approach, such as anticipation on expected flow conditions, and predicted behavior upon catching or missing a connection.     

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.     

Microscopic modeling of large‐scale pedestrian–vehicle conflicts in the city of Madinah,Saudi Arabia

This paper presents a micro‐simulation modeling framework for evaluating pedestrian–vehicle conflicts in crowded crossing areas. The framework adopts a simulation approach that models vehicles and pedestrians at the microscopic level while satisfying two sets of constraints: (1) flow constraints and (2) non‐collision constraints. Pedestrians move across two‐directional cells as opposed to one‐dimensional lanes as in the case of vehicles; therefore, extra caution is considered when modeling the shared space between vehicles and pedestrians. The framework is used to assess large‐scale pedestrian–vehicle conflicts in a highly congested ring road in the City of Madinah that carries 20 000 vehicles/hour and crossed by 140 000 pedestrians/hour after a major congregational prayer. The quantitative and visual results of the simulation exhibits serious conflicts between pedestrians and vehicles, resulting in considerable delays for pedestrians crossing the road (9 minutes average delay) and slow traffic conditions (average speed <10 km/hour). The model is then used to evaluate the following three mitigating strategies: (1) pedestrian‐only phase; (2) grade separation; and (3) pedestrian mall. A matrix of operational measures of effectiveness for network‐wide performance (e.g., average travel time, average speed) and for pedestrian‐specific performance (e.g., mean speed, mean density, mean delay, mean moving time) is used to assess the effectiveness of the proposed strategies. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

Short‐term traffic flow prediction with linear conditional Gaussian Bayesian network

Traffic flow prediction is an essential part of intelligent transportation systems (ITS). Most of the previous traffic flow prediction work treated traffic flow as a time series process only, ignoring the spatial relationship from the upstream flows or the correlation with other traffic attributes like speed and density. In this paper, we utilize a linear conditional Gaussian (LCG) Bayesian network (BN) model to consider both spatial and temporal dimensions of traffic as well as speed information for short‐term traffic flow prediction. The LCG BN allows both continuous and discrete variables, which enables the consideration of categorical variables in traffic flow prediction. A microscopic traffic simulation dataset is used to test the performance of the proposed model compared to other popular approaches under different predicting time intervals. In addition, the authors investigate the importance of spatial data and speed data in flow prediction by comparing models with different levels of information. The results indicate that the prediction accuracy will increase significantly when both spatial data and speed data are included. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

Inhomogeneous cellular automata modeling for mixed traffic with cars and motorcycles

This paper develops inhomogeneous cellular automata models to elucidate the interacting movements of cars and motorcycles in mixed traffic contexts. The car and motorcycle are represented by non‐identical particle sizes that respectively occupy 6×2 and 2×1 cell units, each of which is 1.25×1.25 meters. Based on the field survey, we establish deterministic cellular automata (CA) rules to govern the particle movements in a two‐dimensional space. The instantaneous positions and speeds for all particles are updated in parallel per second accordingly. The deterministic CA models have been validated by another set of field observed data. To account for the deviations of particles' maximum speeds, we further modify the models with stochastic CA rules. The relationships between flow, cell occupancy (a proxy of density) and speed under different traffic mixtures and road (lane) widths are then elaborated.     

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.     

A novel traffic signal control formulation

A novel traffic signal control formulation is developed through a mixed integer programming technique. The formulation considers dynamic traffic, uses dynamic traffic demand as input, and takes advantage of a convergent numerical approximation to the hydrodynamic model of traffic flow. As inherent from the underlying hydrodynamic model, this formulation covers the whole range of the fundamental relationships between speed, flow, and density. Kinematic waves of the stop-and-go traffic associated with traffic signals are also captured. Because of this property, one does not need to tune or switch the model for the different traffic conditions. It “automatically” adjusts to the different traffic conditions. We applied the model to three demand scenarios in a simple network. The results seemed promising. This model produced timing plans that are consistent with models that work for unsaturated conditions. In gridlock conditions, it produced a timing plan that was better than conventional queue management practices.     

Probe vehicle-based traffic state estimation method with spacing information and conservation law

This paper proposes a method of estimating a traffic state based on probe vehicle data that contain spacing and position of probe vehicles. The probe vehicles were assumed to observe spacing by utilizing an advanced driver assistance system, that has been implemented in practice and is expected to spread in the near future. The proposed method relies on the conservation law of the traffic flow but is independent of a fundamental diagram. The conservation law is utilized for reasonable aggregation of the spacing data to acquire the traffic state, i.e., a flow, density and speed. Its independence from a fundamental diagram means that the proposed method does not require predetermined nor exogenous assumptions with regard to the traffic flow model parameters. The proposed method was validated through a simulation experiment under ideal conditions and a field experiment conducted under actual traffic conditions; and empirical characteristics of the proposed method were investigated.     

The Aw–Rascle and Zhang’s model: Vacuum problems,existence and regularity of the solutions of the Riemann problem

In this paper we will discuss some aspects of the recent macroscopic models of the second-order proposed by [Aw, A., Rascle, M., 2000. Resurrection of second order models of traffic flow. SIAM Journal of Applied Mathematics 60 (3), 916–938] and [Zhang, H.M., 2002. A non-equilibrium traffic model devoid of gas-like behavior. Transportation Research Part B 36, 275–290]. These models were suggested after the publication of an article written by [Daganzo, C.F., 1995. Requiem for second-order fluid approximations of traffic flow. Transportation Research Part B 29, 277–286] showing that some classical second-order models can exhibit non-physical solutions. It is shown in this note that the ARZ (Aw–Rascle–Zhang) model respects the anisotropic character of traffic flow, that it yields physical solutions, and that vacuum problems can be solved satisfactorily, provided that the fundamental diagram (equilibrium speed–density relationship) is extended in a suitable fashion. It follows that the Riemann problem for the ARZ model with extended fundamental diagram always admits a solution, and that this solution depends continuously on the initial conditions.     

The speed control effect of highway tunnel sidewall markings based on color and temporal frequency

The low‐luminance monotonous environment in the middle section of highway tunnels offers few reference points and is prone to cause severe visual illusion. Thus, drivers tend to underestimate their driving speed, which can induce speeding behaviors that result in rear‐end collisions. Therefore, discovering low‐cost methods of traffic engineering that reduce this visual illusion and ensure a steady driving speed is an important challenge for current highway tunnel operations. This study analyzes the effects of sidewall markings in typical highway tunnels, specifically observing how their colors and temporal frequencies affect the driver's speed perception in a low‐luminance condition. A three‐dimensional model of the middle section of highway tunnels was built in a driving simulator. Psychophysical tests of speed perception were carried out by the method of limits. The precision of the simulation model was then checked by comparing the results to field test data. The simulation tests studied the stimulus of subjectively equal speed and reaction time in relation to sidewall markings in different colors (red–white combined, yellow–white combined, and blue–white combined). Furthermore, based on the optimal color, the effects of sidewall marking with different temporal frequencies (0.4, 0.8, 1.2, 2, 4, 8, 12, 16, and 32 Hz) on the speed perception of drivers were also analyzed. The test results reveal that the color and temporal frequency of sidewall marking have a significant impact on the driver's stimulus of subjectively equal speed and reaction time. The subjects have the highest speed overestimation and an easy speed judgment with the red–white combined sidewall marking. Within the temporal frequency range of 4.45–7.01 Hz, the subjects have a certain degree of speed overestimation (less than 20%), and the speed perception is sensitive to the temporal frequency changes. Copyright © 2016 John Wiley & Sons, Ltd.     

Microscopic driving theory with oscillatory congested states: Model and empirical verification

The essential distinction between the Fundamental Diagram Approach (FDA) and Kerner’s three-phase theory (KTPT) is the existence of a unique gap–speed (or flow–density) relationship in the former class. In order to verify this relationship, empirical data are analyzed with the following findings: (1) linear relationship between the actual space gap and speed can be identified when the speed difference between vehicles approximates zero; (2) vehicles accelerate or decelerate around the desired space gap most of the time. To explain these phenomena, we propose that, in congested traffic flow, the space gap between two vehicles will oscillate around the desired space gap in the deterministic limit. This assumption is formulated in terms of a cellular automaton. In contrast to FDA and KTPT, the new model does not have any congested steady-state solution. Simulations under periodic and open boundary conditions reproduce the empirical findings of KTPT. Calibrating and validating the model to detector data produces results that are better than that of previous studies.     

Analytical model for information flow propagation wave under an information relay control strategy in a congested vehicle-to-vehicle communication environment

Vehicular traffic congestion in a vehicle-to-vehicle (V2V) communication environment can lead to congestion effects for information flow propagation. Such congestion effects can impact whether a specific information packet of interest can reach a desired location, and if so, in a timely manner to influence the traffic system performance. Motivated by the usefulness and timeliness of information propagation, this paper aims to characterize the information flow propagation wave (IFPW) for an information packet in a congested V2V communication environment under an information relay control strategy. This strategy seeks to exclude information that is dated in the communication buffer under a first-in, first-out queue discipline, from being relayed if the information flow regime is congested. It trades off the need to enable the dissemination of every information packet as far as possible, against the congestion effects that accrue because of the presence of multiple information packets. A macroscopic two-layer model is proposed to characterize the IFPW. The upper layer is formulated as integro-differential equations to characterize the information dissemination in space and time under this control strategy. The lower layer adopts the Lighthill-Whitham-Richards model to capture the traffic flow dynamics. Based on the upper layer model, a necessary condition is derived which quantifies the expected time length that needs to be reserved for broadcasting the information packet of interest so as to ensure the formation of an IFPW under a given density of V2V-equipped vehicles. When the necessary condition is satisfied under homogeneous conditions, it is shown that the information packet can be propagated at an asymptotic speed whose value can be derived analytically. Besides, under the proposed control strategy, only a proportion of vehicles (labeled asymptotic density of informed vehicles) can receive the specific information packet, which can be estimated by solving a nonlinear equation. The asymptotic IFPW speed, the asymptotic density of informed vehicles, and the necessary condition for the IFPW, help in evaluating the timeliness of information propagation and the influence of traffic dynamics on information propagation. In addition, the proposed model can be used to numerically estimate the IFPW speed for heterogeneous conditions, which can aid in the design of traffic management strategies built upon the timely propagation of information through V2V communication.     

Empirical analysis of heterogeneous traffic flow and calibration of porous flow model

Heterogeneous traffic flow, characterized by a free inter-lane exchange, has become an important issue in addressing congestion in urban areas. It is of particular interest in many developing countries, that experience a strong increase in motorcycle use. New approaches to the heterogeneous non-lane-based flow have been proposed. However insufficient empirical verification has been made to estimate vehicle interaction, that is necessary for an accurate representation of mixed-flow conditions. In this paper, we focus on the porous flow approach to capture the complex interactions. The parameters from this approach are estimated from empirical observations. Video data was recorded and processed to capture vehicle interactions at a number of road sections in Surabaya City, Indonesia. The specific behavior of each vehicle in the traffic flow was captured by developing the pore size–density distributions, analyzing the class-specific critical pore sizes, and producing the class specific speed–density and flow–density diagrams. The results reveal how critical pore sizes are based on pore size–density distributions, the flow diagram for each vehicle class, and how traffic flow relationships for motorcyclists and the other vehicles exhibit significant differences. It is concluded that the proposed approach can represent the specific behavior of the motorcyclist in heterogeneous traffic flow, in both the situations of with- and without an exclusive lane for motorcycles, can clarify motorcyclist’s behavior in terms of passenger car unit of motorcycle, and can therefore support policy making on the improvement of urban transport.     

Incorporating work zone configuration factors into speed‐flow and capacity models

This study aims to develop work zone speed‐flow and capacity models, which incorporate work zone configuration factors including the number of work zones, geometrical alignment, work zone speed limit, and work zone length. On the basis of the traffic data from six work zone sites with various work zone configurations, two nonlinear traffic speed and flow models including work zone configuration factors are developed for the uncongested and congested traffic conditions, respectively. A work zone capacity model is proposed on the basis of the two models. The three models can further be used to examine the effects of work zone configuration factors on the speed‐flow relationship and capacity at work zones. Results show that traffic speed, traffic flow, and work zone capacity increase with the posted speed limit. Traffic speed under uncongested conditions decreases with the geometric alignment, the number of work zones, work zone length, and heavy vehicle percentage. Under congested conditions, the increase of the number of work zones is found to exhibit a larger negative impact on the traffic flow than the increase of geometric alignment. The number of work zones is also found to have the largest negative impacts on work zone capacity, followed by the geometric alignment. Short work zone length exhibits a relatively minor contribution to increasing work zone capacity. Copyright © 2014 John Wiley & Sons, Ltd.     

Urban traffic flow prediction: a spatio‐temporal variable selection‐based approach

Short‐term traffic flow prediction in urban area remains a difficult yet important problem in intelligent transportation systems. Current spatio‐temporal‐based urban traffic flow prediction techniques trend aims to discover the relationship between adjacent upstream and downstream road segments using specific models, while in this paper, we advocate to exploit the spatial and temporal information from all available road segments in a partial road network. However, the available traffic states can be high dimensional for high‐density road networks. Therefore, we propose a spatio‐temporal variable selection‐based support vector regression (VS‐SVR) model fed with the high‐dimensional traffic data collected from all available road segments. Our prediction model can be presented as a two‐stage framework. In the first stage, we employ the multivariate adaptive regression splines model to select a set of predictors most related to the target one from the high‐dimensional spatio‐temporal variables, and different weights are assigned to the selected predictors. In the second stage, the kernel learning method, support vector regression, is trained on the weighted variables. The experimental results on the real‐world traffic volume collected from a sub‐area of Shanghai, China, demonstrate that the proposed spatio‐temporal VS‐SVR model outperforms the state‐of‐the‐art. Copyright © 2015 John Wiley & Sons, Ltd.