Macroscopic Traffic Model Research Articles

Investigating the relationship between freeway rear-end crash rates and macroscopically modeled reaction time

This study tests the hypothesis that an analytically estimated driver reaction time required for asymptotic stability, based on the macroscopic Gazis-Herman-Rothery (GHR) model, serves as an indicator of the impact of traffic oscillations on rear-end crashes. If separate GHR models are fit discontinuously for different traffic regimes, the local drop in required reaction time between these regimes can also be estimated. This study evaluates the relationship between rear-end crash rates and that drop in required reaction time. Traffic data from 28 sensors were used to fit the GHR model. Rear-end crash rates, estimated from four years of crash data, exhibited a positive correlation with the drop in required reaction time at the congested regime’s density-breakpoint. A linear relationship provided the best fit. These results motivate follow-on research to incorporate macroscopically derived reaction time in road-safety planning. More generally, the study demonstrates a useful application of a discontinuous macroscopic traffic model.

A coupled macroscopic traffic and pollutant emission modelling system for Barcelona

We present a coupled macroscopic traffic and emission modelling system tailored to the Barcelona metropolitan area that allows estimating hourly road transport emissions at road link level. We use the developed system to perform an emission sensitivity analysis of typically high uncertainty emission features and assess their impact. We also explore the uncertainties of our system compared to a microscopic approach in a representative area of Barcelona. The developed macroscopic system shows a high sensitivity to spatially-resolved vehicle fleet composition inputs, meteorological effects on diesel engines (+19% in NOx) and non-exhaust sources (80% of total PM emissions). The comparison with the microscopic system shows that discrepancies grow as a function of the congestion level, up to +65% in NOx. The resulting coupled system will be used in further steps of the research to evaluate the impact of traffic management strategies upon urban emissions and air quality levels in Barcelona.

A generic work zone evaluation tool driven by a macroscopic traffic simulation model

A generic work zone evaluation tool driven by a macroscopic traffic simulation model

Multiscale Control of Generic Second Order Traffic Models by Driver-Assist Vehicles

We study the derivation of generic high order macroscopic traffic models from a follow-the-leader particle description via a kinetic approach. First, we recover a third order traffic model as the hydrodynamic limit of an Enskog-type kinetic equation. Next, we introduce in the vehicle interactions a binary control modelling the automatic feedback provided by driver-assist vehicles and we upscale such a new particle description by means of another Enskog-based hydrodynamic limit. The resulting macroscopic model is now a Generic Second Order Model (GSOM), which contains in turn a control term inherited from the microscopic interactions. We show that such a control may be chosen so as to optimise global traffic trends, such as the vehicle flux or the road congestion, constrained by the GSOM dynamics. By means of numerical simulations, we investigate the effect of this control hierarchy in some specific case studies, which exemplify the multiscale path from the vehicle-wise implementation of a driver-assist control to its optimal hydrodynamic design.

A two-dimensional multi-class traffic flow model

The aim of this work is to introduce a two-dimensional macroscopic traffic model for multiple populations of vehicles. Starting from the paper [ 21 ], where a two-dimensional model for a single class of vehicles is proposed, we extend the dynamics to a multi-class model leading to a coupled system of conservation laws in two space dimensions. Besides the study of the Riemann problems we also present a Lax-Friedrichs type discretization scheme recovering the theoretical results by means of numerical tests. We calibrate the multi-class model with real data and compare the fitted model to the real trajectories. Finally, we test the ability of the model to simulate the overtaking of vehicles.

A Fast Lax–Hopf Algorithm to Solve the Lighthill–Whitham–Richards Traffic Flow Model on Networks

Efficient and exact algorithms are important for performing fast and accurate traffic network simulations with macroscopic traffic models. In this paper, we extend the semianalytical Lax–Hopf algorithm in order to compute link inflows and outflows with the Lighthill–Whitham–Richards (LWR) model. Our proposed fast Lax–Hopf algorithm has a very low computational complexity. We demonstrate that some of the original algorithm’s operations (associated with the initial conditions) can be discarded, leading to a faster computation of boundary demands/supplies in network simulation problems for general concave fundamental diagrams (FDs). Moreover, the computational cost can be further reduced for triangular FDs and specific space–time discretizations. The resulting formulation has a performance comparable to the link transmission model and because it solves the original LWR model for a wide range of FD shapes, with any initial configuration, it is suitable to solve a broad range of traffic operations problems. As part of the analysis, we compare the performance of the proposed scheme with that of other well-known computational methods.

Sustainable traffic management and control system for arterial with contraflow left-turn lanes

Nowadays, air pollution caused by traffic congestion has progressively drawn more and more attention. This paper proposes a traffic management and control platform from the perspective of sustainable development to reduce both vehicle emission and delay along arterial with contraflow left-turn lane (CLL). Unlike the traditional intersection layout and the control strategy, the existence of the contraflow left-turn lanes at intersections brings difficulties in setting phase sequences due to the complex interactions among upstream and downstream lanes. Furthermore, the queueing conditions are totally different from traditional intersections due to the complex queueing phenomenon between pre-signals and main signals. A macroscopic traffic model is proposed to model the intersection along arterial with CLL and is established on the basis of finite capacity queueing models. The optimization framework derives fixed-time traffic signal control plans, in which the green splits of the main signal and the pre-signal are explicitly considered. The nondominated sorting genetic algorithm II (NSGA-II) is employed to solve problem. A case study based on the field data of four intersections along the West Yan’an Road in the city of Shanghai is carried out to investigate the performance of the proposed framework. The microscopic simulator AIMSUN is used to evaluate and compare the travel delay and vehicle emissions obtained by the newly proposed signal plans and the signal plans derived by using traditional traffic control method. The simulation results indicate that the proposed framework successfully reduce travel delay and vehicle emission at intersections along arterial road with CLL.

Parking pricing vs. congestion pricing: a macroscopic analysis of their impact on traffic

This paper focuses on parking pricing and congestion pricing and their short-term effects not only on traffic congestion but also on the potential revenue for a city. We develop a multimodal macroscopic traffic and parking search model based on aggregated data at the network level. Our methodology allows us to analyze how introducing parking pricing inside a network, or a congestion toll combined with a park and ride (P+R) scheme can affect the drivers’ decision between entering the network by car or using P+R. This decision directly influences the number of drivers using P+R, and this impacts, in turn, the traffic performance. We illustrate our proposed framework in a case study of an area with a high parking demand for public parking spaces within the city of Zurich, Switzerland. Results show that parking pricing combined with P+R is indeed a viable option compared to congestion pricing for improving traffic performance.

Mixed Vehicular Traffic Flow Model on an Inclined Multilane Road

This study outlines the Kerner’s 3 phase traffic flow theory, which states that traffic flow occurs in three phases and these are free flow, synchronized flow and wide moving jam phase. A macroscopic traffic model that is factoring road inclination is developed and its features discussed. By construction of the solution to the Rienmann problem, the model is written in conservative form and solved numerically. Using the Lax-Friedrichs method and going ahead to simulate traffic flow on an inclined multi lane road. The dynamics of traffic flow involving cars(fast moving) and trucks(slow moving) on a multi-lane inclined road is studied. Generally, trucks move slower than cars and their speed is significantly reduced when they are moving uphill on an in- clined road, which leads to emergence of a moving bottleneck. If the inclined road is multi-lane then the cars will tend to change lanes with the aim of overtaking the slow moving bottleneck to achieve free flow. The moving bottleneck and lanechange ma- noeuvres affect the dynamics of flow of traffic on the multi-lane road, leading to traffic phase transitions between free flow (F) and synchronised flow(S). Therefore, in order to adequately describe this kind of traffic flow, a model should incorporate the effect of road inclination. This study proposes to account for the road inclination through the fundamental diagram, which relates traffic flow rate to traffic density and ultimately through the anticipation term in the velocity dynamics equation of macroscopic traffic flow model. The features of this model shows how the moving bottleneck and an incline multilane road affects traffic transistions from Free flow(F) to Synchronised flow(S). For a better traffic management and control, proper understanding of traffic congestion is needed. This will help road designers and traffic engineers to verify whether traffic properties and characteristics such as speed(velocity), density and flow among others determines the effectiveness of traffic flow.

A macroscopic traffic flow model considering the velocity difference between adjacent vehicles on uphill and downhill slopes

In this paper, we deduced a macroscopic traffic model on the uphill and downhill slopes by employing the transformation relation from microscopic variables to macroscopic ones based on a microscopic car-following model considering the velocity difference between adjacent vehicles. The angle [Formula: see text] of the uphill and downhill and the gravitational force have a great impact upon the stability of traffic flow. The linear stability analysis for macroscopic traffic model yielded the stability condition. The Korteweg–de Vries (KdV) equation is derived by nonlinear analysis and the corresponding solution to the density wave near the neutral stability line is obtained. By using the upwind finite difference scheme for simulation, the spatiotemporal evolution patterns of traffic flow on the uphill and downhill are attained. The unstable region is shrunken with slope of the gradient increasing and backward-traveling density waves gradually decrease and even disappear on uphill. Conversely, the unstable region on downhill is extended and density waves propagate quickly backward to the whole road with slope of the gradient increasing.

A macroscopic traffic model based on transition velocities

In this paper, a new traffic model is presented which characterizes spatial changes in traffic density to smoothly align the traffic flow with forward conditions. This alignment is a function of the difference in velocities so there is no change in flow when the velocities are the same. The commonly employed Payne-Witham (PW) model aligns traffic with a constant speed (velocity) regardless of the transitions on a road. Thus, the distance covered during alignment and driver behavior are ignored. As a consequence, the resulting speeds can exceed the maximum or go below zero. With the proposed model, the speed during alignment is a function of the traffic density. In particular, traffic adapts quicker for a smaller forward density and vice versa. Results are presented for discontinuous traffic densities caused by a bottleneck along both straight and circular roads which show that this model provides more realistic behavior than the PW and Zhang models.

A Generic Work Zone Evaluation Tool Driven by Macroscopic Traffic Simulation Model

This study proposed a generic work zone evaluation tool driven by a dynamic macroscopic traffic model. The tool can investigate the effects of a work zone on freeway conditions. The classical freeway traffic network model METANET was extended to better capture typical work zone characteristics in terms of speed and capacity reductions through modifying its speed-density relationship functions. The tool can present profiles of traffic state variables, system-level performance indices, and annotated traffic conditions maps. It was used to develop a prototype computer-aided decision support system and applied in two simulation-based case studies. Case studies show that it is effective and useful for understanding complicated work zone impacts and can aid in better design and assessment of work zone plans. It can be integrated in a dynamic transportation management system for better communication between road operator and travellers.

Implications of different road pricing schemes in urban areas: a case study for Budapest

Road pricing is an efficient instrument to regulate use of roads. In Budapest, Hungary, only cordon pricing has been investigated in detail. This paper reports on a study of the implications of applying different road pricing schemes in the city using a macroscopic traffic model. Firstly, the functional relationship between pricing schemes and road transport demand was investigated. Secondly, the implications of applying road pricing schemes on travel demand, travel time, delay time, average speed and carbon dioxide emissions of road users inside and outside of the pricing area, as well as revenues generated by applying the schemes, were studied. The results revealed that a time-based system showed the best performance inside the pricing area. However, it generated heavy congestion on non-priced roads bordering the pricing area, which would increase travel times, delay times and carbon dioxide emissions and would decrease average travel speeds on the entire network. The cordon-based system was the least effective pricing system for most of the studied parameters, while the distance-based system showed good performance both inside and outside the pricing area. Regarding the revenues generated, variable-toll systems (time-based and distance-based systems) showed the potential to generate higher revenues than the fixed-toll system (cordon-based system).

Hybrid Dynamic Traffic Model for Freeway Flow Analysis Using a Switched Reduced-Order Unknown-Input State Observer.

This paper introduces a new methodology for reconstructing vehicle densities of freeway segments by utilizing the limited data collected by traffic-counting sensors and developing a macroscopic traffic stream model formulated as a switched reduced-order state observer design problem with unknown or partially known inputs. Specifically, the traffic network is modeled as a hybrid dynamic system in a state space that incorporates unknown inputs. For freeway segments with traffic-counting sensors installed, vehicle densities are directly computed using field traffic count data. A reduced-order state observer is designed to analyze traffic state transitions for freeway segments without field traffic count data to indirectly estimate the vehicle densities for each freeway segment. A simulation-based experiment is performed applying the methodology and using data of a segment of Beijing Jingtong freeway in Beijing, China. The model execution results are compared with the field data associated with the same freeway segment, and highly consistent results are achieved. The proposed methodology is expected to be adopted by traffic engineers to evaluate freeway operations and develop effective management strategies.

Modeling heterogeneous traffic with cooperative adaptive cruise control vehicles: A first-order macroscopic perspective

ABSTRACTThis paper proposes a modeling framework to characterize steady-state traffic flow relations for heterogeneous traffic composed of both standard (S) and Cooperative Adaptive Cruise Control (CACC, labeled C here) vehicles, capturing the impact of C market penetration and vehicle sequence within a lane. The resulting parameterized fundamental diagram is then integrated with a first-order macroscopic traffic model, allowing us to characterize the operational performance on a network for heterogeneous traffic with varying C market penetration rates. This approach is demonstrated through an illustrative case study which considers a small freeway section with time-varying demand, merging traffic from an entrance ramp, and C market penetration ranging from 0.0–1.0. The results indicate that maximum throughput does not change appreciably as C traffic is first introduced, but eventually increases significantly for mid-to-high C penetration rates. Additionally, it shows that increasing C market penetration and separating vehicle classes slows upstream congestion propagation.

Development of a binary logistic lane change model and its validation using empirical freeway data

An effective macroscopic lane change (LC) model is required to facilitate active and dynamic lane management to develop cell-based multilane macroscopic traffic models. Existing logistic regression LC models do not undertake model classification of lane change; do not consider performance measures in the validation of field data and ignore movement between lanes during time-varying traffic. Models that consider the direction of LC are, however, biased in their prediction of left LC (LLC) and right LC (RLC) direction. This study proposed a simplified macroscopic cell-based binary logistic LC (BLLC) model describing the LC probability using fewer explanatory variables; in this model, the direction of LC is considered as a new variable. Considering the model performance measures, the results show that there exists substantial difference in LC behaviour in both directions. The present model also achieved a smaller difference in the percentage of accurate prediction (0.9%) between the LLC and RLC.

Cyber-physical Optimal Traffic Signal Control Based on a Macroscopic Traffic Model and Its Verification Using Microscopic Traffic Simulator

Cyber-physical Optimal Traffic Signal Control Based on a Macroscopic Traffic Model and Its Verification Using Microscopic Traffic Simulator

Modelling multi-class disordered traffic streams using traversable distance: a concept analogous to fluid permeability

In multi-class disordered traffic conditions, the presence of numerous classes of vehicles having different size and operational characteristics invalidates the behaviour of lane discipline. Each vehicle traverses through a series of both viable as well as accessible gaps created by other vehicles, thus defining a permeable medium. In this paper, a plausible way to incorporate the disordered behaviour on macroscopic traffic stream modelling is discussed. A new metric termed as traversable distance has been formulated for characterising this behaviour, based on field observations. Based on class-specific traversable distances that correspond to a set of incommensurate density measures, equilibrium speed functions have been redefined. Disordered stream behaviour significantly affects the scatter in the equilibrium speed–density relationship which is a key input to macroscopic traffic flow models. Results from the modified speed functions based on traversable distance proved that the proposed methodology could considerably explain the scatter observed in the fundamental diagram.

Vehicular Traffic Management Based on Traffic Engineering for Vehicular Ad Hoc Networks

Urbanization causes many problems to human mobility, since people living in the cities tend to increase the vehicular traffic flow. City road infrastructure does not increase faster than the number of vehicles, thus causing traffic congestion in dense urban centers. Besides travel delay, vehicular traffic congestion results in serious problems to human beings (e.g., health problems due to stress), to the planet (e.g., increase in pollution) and to the economy (e.g., waste of a large amount of money due to time spent in traffic jams). In order to improve vehicular traffic flow in dense urban areas, this paper presents a new Vehicular Traffic Management Service based on Traffic Engineering theory, called Re-RouTE. The Re-RouTE service relies on the density of vehicles in roads and applies the flow-density macroscopic traffic engineering model to identify congested routes. Roads are represented by a weighted graph, which is then used to discover routes without traffic jams and with a small increase in the travel distance. The main goal of Re-RouTE is to reduce traffic jams while increasing the global vehicular traffic flow of the road network. Moreover, the service was designed to reduce traffic jams instead of moving them to a different road/area. Simulation results show the ability of Re-RouTE to improve travel time, travel distance, speed and the number of messages transmitted when compared to a literature solution.

Traffic Control on Freeways Using Variable Speed Limits

A new practical oriented feedback control structure for traffic control on freeways using variable speed limits is presented. Therefore, a simple controller structure which satisfies legal and operator demands for a single road is derived from system analysis of a macroscopic traffic model. Furthermore, this road-controller is accompanied with a sequence control and a road-network-controller. In contrast to existing work, novel control variables are used within controller design and tuning guidelines for non-control-engineers are given. The proposed control structure is investigated in simulations, which have been validated using experimental data from the German autobahn.