Microscopic Traffic Flow Models Research Articles

Evaluation of Existing Performance and Potential for Optimization of Traffic Signals in Karachi

Traffic streams in most of the urban areas of developing countries are highly heterogeneous with poor lane discipline. Traffic simulation and optimization packages based on microscopic traffic flow models are popular for modeling traffic flow and optimizing traffic controls all around the globe. However, applying microsimulation packages to model undisciplined and heterogeneous traffic streams may not yield perfect results. But, macroscopic models can be easily calibrated for such heterogeneous and undisciplined traffic streams. This research applies the calibrated Cell Transmission Model (CTM)-based optimization tool to determine optimal signal plans and to evaluate the potential of reduction in control delay at signalized intersections. Most of the traffic signals in Karachi are pre-timed with a constant signal plan throughout the day, despite significant changes in traffic dynamics within a day. This study evaluates the performance of existing signal timing plans at two different locations in Karachi. The selected locations include a segment of urban arterial with three consecutive signals in close proximity. The second location was a standalone signalized intersection. Twelve-hour traffic and delay data on typical working days were collected through video recording technique. The data collected from the field were simulated using CTM-based signal optimization software, DISCO. The optimization results show an improvement of 45% in the existing delay at the selected segment of Khayaban-e-Ittehad. The delay at KDA intersection can be reduced by 29% by optimizing signal plans. The study shows that optimum signal timings based on accurate data can reduce delays and improve traffic network performance.

Multi-vehicle tracking with microscopic traffic flow model-based particle filtering

This paper addresses the problem of tracking multiple vehicles on multi-lane roads with consideration for interactions among vehicles. Due to limited lane resources and traffic heterogeneity, vehicles have to interact with neighboring vehicles while moving along roads to improve their navigability and safety, resulting in highly dependent motions. However, multitarget tracking algorithms generally assume that targets move independently of one another. To address this limitation, using the microscopic traffic flow (MTF) model for modeling vehicle dynamics in the presence of interactions with surrounding traffic, an MTF-based tracking algorithm is proposed under the particle filter (PF) framework. The recursive maximum likelihood (RML) method is integrated into the PF to estimate unknown parameters in the MTF model. The posterior Cramer–Rao lower bound (PCRLB) is also derived for this problem. The performance of the proposed MTF-PF algorithm is compared with those of existing algorithms for multi-vehicle tracking on multi-lane roads. Numerical results show that the proposed algorithm requires less prior information while yielding more accurate and consistent tracks.

Pedestrian-vehicle interference at a signalized crossing based on detailed microscopic traffic flow models

Interference between pedestrians and motor vehicles at signalized intersections not only leads the traffic to delay and traffic efficiency to decrease, but also induces traffic crashes to happen frequently. In this paper, a microscopic discrete model for traffic flow is adopted to study the mutual interference mechanism between pedestrians and vehicles at signalized intersection. The vehicular traffic flow model is based on the refined NaSch model, and traffic lights are introduced to consider the driver anticipating in traffic signal switching. Based on the multi-step lattice gas model, the pedestrian flow model considers the fact that the pedestrians’ speed increases gradually during pedestrian cross-street green time. Both models reflect real features of movement of vehicles (pedestrians) in daily life. When the traffic light signal switches, the vehicles (pedestrians) staying in the conflict area result in the delay of pedestrians (vehicles). It is assumed that pedestrians and vehicles cannot coexist in the conflict area at the same time. In the simulation, the periodic boundary condition is applied to the lane, and the open boundary condition is applied to the crosswalk. The arrival rate of pedestrian is assumed to satisfy the Poisson distribution. Both the fundamental diagram of vehicular traffic flow and the pedestrian waiting time are calculated, and the phase diagram revealing the global nature of the presented model is obtained accordingly. The quantitative characteristics of vehicle (pedestrian) delay time caused by pedestrians (vehicles) staying in the conflict area are given as well. Simulation results show that there is a critical split. When the split is less than the critical value, three kinds of traffic phases, i.e., free flow phase, saturated flow phase, and jamming flow phase, appear with the increase of density. When the split is larger than the critical value, four kinds of traffic phases, i.e., free flow phase, coexisting phase, saturated flow phase, and jamming flow phase are distinguished. The delay caused by the mutual interference between pedestrians and motor vehicles is closely related to the state of vehicle flow and the state of pedestrian flow. When the arrival rate of pedestrians is quite large and the split is large enough, these pedestrians in the waiting area cannot be emptied once in a single pedestrian cross-street cycle. The qualitative and quantitative characteristics of mutual interference between pedestrians and vehicles are discussed in more detail. The setting of a reasonable split not only ensures the efficiency of traffic flow, but also reduces the waiting time of pedestrians to cross the street.

Traffic flow models

Traffic flow is the study of the movement of individual drivers and vehicles between two points and the interactions they make with one another.Traffic flow models can be used to simulate traffic, for instance to evaluate ex-ante the use of a new part of the infrastructure. Models can be categorized based on, firstly, representation of the traffic flow in terms of flows (macroscopic), groups of drivers (macroscopic) or individual drivers (microscopic) and, secondly, underlying behavioral theory, which can be based on characteristics of the flow (macroscopic) or individual drivers (microscopic behavior). Microscopic traffic flow variables focus on individual drivers. Macroscopic traffic flow variables reflect the average state of the traffic flow. A macroscopic traffic flow model is a mathematical traffic model that formulates the relationships among traffic flow characteristics like density, flow, mean speed of a traffic stream etc. such models are conventionally arrived at by integrating microscopic traffic flow models and converting the single-entity level characteristics to comparable system level characteristics.

Efficient calibration of microscopic car-following models for large-scale stochastic network simulators

This paper proposes a simulation-based optimization methodology for the efficient calibration of microscopic traffic flow models (i.e., car-following models) of large-scale stochastic network simulators. The approach is a metamodel simulation-based optimization (SO) method. To improve computational efficiency of the SO algorithm, problem-specific and simulator-specific structural information is embedded into a metamodel. As a closed-form expression is sought, we propose adopting the steady-state solution of the car-following model as an approximation of its simulation-based input-output mapping. This general approach is applied for the calibration of the Gipps car-following model embedded in a microscopic traffic network simulator, on a large network. To this end, a novel formulation for the traffic stream models corresponding to the Gipps car-following law is provided.The proposed approach identifies points with good performance within few simulation runs. Comparing its performances to that of a traditional approach, which does not take advantage of the structural information, the objective function is improved by two orders of magnitude in most experiments. Moreover, this is achieved within tight computational budgets, i.e., few simulation runs. The solutions identified improve the fit to the field measurements by one order of magnitude, on average. The structural information provided to the metamodel is shown to enable the SO algorithm to become robust to both the quality of the initial points and the simulator stochasticity.

Modelling of car exhaust emission on the basis of data obtained from microscopic traffic flow model

In the paper the procedure for car exhaust emission calculation along the road network has been presented. Input parameters for an emission model were obtained from the microscopic traffic flow model. Traffic simulations have been performed in Vissim software. To analyse emission in a road sections whole network has been discretized into fixed length segments. The examples of traffic flow emission modelling for selected lanes at intersection where the traffic flow is controlled by traffic lights are also presented.

A generic data assimilation framework for vehicle trajectory reconstruction on signalized urban arterials using particle filters

With trajectory data, a complete microscopic and macroscopic picture of traffic flow operations can be obtained. However, trajectory data are difficult to observe over large spatiotemporal regions—particularly in urban contexts—due to practical, technical and financial constraints. The next best thing is to estimate plausible trajectories from whatever data are available. This paper presents a generic data assimilation framework to reconstruct such plausible trajectories on signalized urban arterials using microscopic traffic flow models and data from loops (individual vehicle passages and thus vehicle counts); traffic control data; and (sparse) travel time measurements from whatever source available. The key problem we address is that loops suffer from miss- and over-counts, which result in unbounded errors in vehicle accumulations, rendering trajectory reconstruction highly problematic. Our framework solves this problem in two ways. First, we correct the systematic error in vehicle accumulation by fusing the counts with sparsely available travel times. Second, the proposed framework uses particle filtering and an innovative hierarchical resampling scheme, which effectively integrates over the remaining error distribution, resulting in plausible trajectories. The proposed data assimilation framework is tested and validated using simulated data. Experiments and an extensive sensitivity analysis show that the proposed method is robust to errors both in the model and in the measurements, and provides good estimations for vehicle accumulation and vehicle trajectories with moderate sensor quality. The framework does not impose restrictions on the type of microscopic models used and can be naturally extended to include and estimate additional trajectory attributes such as destination and path, given data are available for assimilation.

Carrot and stick: A game-theoretic approach to motivate cooperative driving through social interaction

This driving-simulator study aimed to motivate cooperative lane-change maneuvers in automated freeway driving under human supervision. Two interaction concepts were designed based on game theory. These concepts supported drivers’ cooperation by applying both rewards and sanctions as the proverbial carrot and stick. The social-status interaction rewards gap creation by revealing a driver’s prior cooperative behavior to other road users. The trade-off interaction introduces a system in which points compensate time loss and gain. Both concepts were evaluated from the left- and right-lane perspective, framing 39 participants to “be fast.” Drivers in the right lane asked those in the left lane to open a gap to overtake, mediated through a vehicle-to-vehicle connection and an augmented-reality user interface.Only 67% of the merging requests were accepted by left-lane drivers due to time pressure in the baseline condition. The social-status interaction enhanced acceptance to 86% on average and even to 97% for requests made by drivers marked as cooperative. The trade-off interaction enhanced acceptance to 87% as drivers gained a virtual benefit for losing one second. The subjective evaluation was positive for all conditions, and the social concepts were rated significantly higher on items associated with social relationships. Both social interaction concepts motivate cooperation and shape drivers’ behavior even under time pressure. Social mechanisms power maneuver-based local cooperation between traffic participants.It is expected that involving drivers in cooperative maneuvers has a beneficial effect on traffic performance, which microscopic traffic flow modeling should validate next. Gamified interaction and interface elements involve drivers of automated vehicles into strategic decisions and could help to mitigate automation effects. Since they don’t “drive” any more, cooperative interaction concepts now make them “play driving” and formulate pleasing strategies.

Simulation of Traffic Flow to Analyze Lane Changes on Multi-lane Highways under Non-lane Discipline

The present study uses the microscopic traffic simulation flow model VISSIM for generating traffic flow data to obtain the essential parameters. Study calibrated and validated the VISSIM model based on the field data. Further, lane change behaviour is analyzed with homogeneous vehicle type traffic on four-lane, six-lane and eight-lane divided highways sections through VISSIM simulation model. The study finds the number of lane changes depends on traffic volume as well as on a number of lanes provided for a direction of travel. Lane change data was correlated with traffic volume, and the third-degree polynomial trend was found to be fitted on each type of simulated highway sections. A maximum number of lane changes and lane change at the capacity level of the volume are also quantified on simulated sections of four-lane, six-lane and eight-lane divided highways.

Traveling waves for a microscopic model of traffic flow

We consider the follow-the-leader model for traffic flow. The position of each car $z_i(t)$ satisfies an ordinary differential equation, whose speed depends only on the relative position $z_{i+1}(t)$ of the car ahead. Each car perceives a local density $ρ_i(t)$. We study a discrete traveling wave profile $W(x)$ along which the trajectory $(ρ_i(t), z_i(t))$ traces such that $W(z_i(t)) = ρ_i(t)$ for all $i$ and $t>0$; see definition 2.2. We derive a delay differential equation satisfied by such profiles. Existence and uniqueness of solutions are proved, for the two-point boundary value problem where the car densities at $x\to±∞$ are given. Furthermore, we show that such profiles are locally stable, attracting nearby monotone solutions of the follow-the-leader model.

Feedback Traffic Control at Highway Work Zones using Variable Speed Limits

This paper presents a novel real-time merging traffic control approach for throughput maximization at highway work zones using Variable Speed Limits (VSL). A Proportional-Integral (PI) feedback regulator is employed for control which is simpler and potentially more robust compared to heuristic or optimal control procedures. Practical VSL implementation aspects have been taken into account. The proposed concept is demonstrated and evaluated using a validated microscopic traffic flow model for a real motorway work zone in Germany. Remarkable improvements can be observed for all performance indexes considered and for all replications simulated. Investigations have been carried out for different compliance rates, different set points utilized by the feedback regulator, as well as for different values of the lower admissible bound of the VSL. The proposed approach is deemed suitable for field implementation.

Stability analysis on a dynamical model of route choice in a connected vehicle environment

Research on connected vehicle environment has been growing rapidly to investigate the effects of real-time exchange of kinetic information between vehicles and road condition information from the infrastructure through radio communication technologies. A fully connected vehicle environment can substantially reduce the latency in response caused by human perception-reaction time with the prospect of improving both safety and comfort. This study presents a dynamical model of route choice under a connected vehicle environment. We analyze the stability of headways by perturbing various factors in the microscopic traffic flow model and traffic flow dynamics in the car-following model and dynamical model of route choice. The advantage of this approach is that it complements the macroscopic traffic assignment model of route choice with microscopic elements that represent the important features of connected vehicles. The gaps between cars can be decreased and stabilized even in the presence of perturbations caused by incidents. The reduction in gaps will be helpful to optimize the traffic flow dynamics more easily with safe and stable conditions. The results show that the dynamics under the connected vehicle environment have equilibria. The approach presented in this study will be helpful to identify the important properties of a connected vehicle environment and to evaluate its benefits.

Theoretical analysis of bifurcations in a microscopic traffic model accounting for optimal velocity

In this paper, a modified microscopic traffic flow model accounting for the optimal velocity has been proposed. Different with previous models, drivers’ response ability and the maximum of accelerations are considered in the term of the optimal velocity. The effect of parameters in the term of the optimal velocity on bifurcations in the rotary traffic is studied here. Besides, the evolvement of bifurcations in the system is calculated by performing numerical simulation experiments. Moreover, the linear stability analysis of the proposed model is presented.

Simple synchronization protocols for heterogeneous networks: beyond passivity

Synchronization among autonomous agents via local interactions is one of the benchmark problems in multi-agent control. Whereas synchronization algorithms for identical agents have been thoroughly studied, synchronization of heterogeneous networks still remains a challenging problem. The existing algorithms primarily use the internal model principle, assigning to each agent a local copy of some dynamical system (internal model). Synchronization of heterogeneous agents thus reduces to global synchronization of identical generators and local synchronization between the agents and their internal models. The internal model approach imposes a number of restrictions and leads to sophisticated dynamical (and, in general, nonlinear) controllers. At the same time, passive heterogeneous agents can be synchronized by a very simple linear protocol, which is used for consensus of first-order integrators. A natural question arises whether analogous algorithms are applicable to synchronization of agents that do not satisfy the passivity condition. In this paper, we study the synchronization problem for heterogeneous agents that are not passive but satisfy a weaker input feedforward passivity (IFP) condition. We show that such agents can also be synchronized by a simple linear protocol, provided that the interaction graph is strongly connected and the couplings are sufficiently weak. We demonstrate how stability of cooperative adaptive cruise control algorithms and some microscopic traffic flow models reduce to synchronization of heterogeneous IFP agents.

Modelling vehicular interactions for heterogeneous traffic flow using cellular automata with position preference

This paper proposes and validates a modified cellular automata model for determining interaction rate (i.e. number of car-following/overtaking instances) using traffic flow data measured in the field. The proposed model considers lateral position preference by each vehicle type and introduces a position preference parameter β in the model which facilitates gradual drifting towards preferred position on road, even if the gap in front is sufficient. Additionally, the model also improves upon the conventional model by calculating safe front and back gap dynamically based on speed and deceleration properties of leader and follower vehicles. Sensitivity analysis was carried out to determine the effect of β on vehicular interactions and the model was calibrated and validated using interaction rates observed in the field. Paired tests were conducted to determine the validity of the model in determining interaction rates. Results of the simulations show that there is a parabolic relationship between area occupancy and interaction rate of different vehicle types. The model performed satisfactorily as the simulated interaction rate between different vehicle types were found to be statistically similar to those observed in field. Also, as expected, the interaction rate between light motor vehicles (LMVs) and heavy motor vehicles (HMVs) were found to be higher than that between LMVs and three wheelers because LMVs and HMVs share the same lane. This could not be done using conventional CA models as lateral movement rules were dictated by only speeds and gaps. So, in conventional models, the vehicles would end up in positions which are not realistic. The position preference parameter introduced in this model motivates vehicles to stay in their preferred positions. This study demonstrates the use of interaction rate as a measure to validate microscopic traffic flow models.

An extended microscopic traffic flow model based on the spring-mass system theory

This study proposes a new microscopic traffic flow model based on the spring-mass system theory. In particular, considering the similarity between the acceleration or deceleration behavior in traffic flow and the scaling properties of a spring, a car-following (CF) model is proposed based on the fundamental physical law of the spring-mass system. Stability of the proposed model is analyzed using the perturbation method to obtain the stability condition. Numerical experiments are performed through simulation. The results demonstrate the proposed model can capture the characteristic of propagation backwards of disturbance in traffic flow. In addition, the findings of this study provide insights in modeling traffic flow from the mechanical system theory perspective.

Fine-tuning ADAS algorithm parameters for optimizing traffic safety and mobility in connected vehicle environment

Under the Connected Vehicle environment where vehicles and road-side infrastructure can communicate wirelessly, the Advanced Driver Assistance Systems (ADAS) can be adopted as an actuator for achieving traffic safety and mobility optimization at highway facilities. In this regard, the traffic management centers need to identify the optimal ADAS algorithm parameter set that leads to the optimization of the traffic safety and mobility performance, and broadcast the optimal parameter set wirelessly to individual ADAS-equipped vehicles. Once the ADAS-equipped drivers implement the optimal parameter set, they become active agents that work cooperatively to prevent traffic conflicts, and suppress the development of traffic oscillations into heavy traffic jams. Measuring systematic effectiveness of this traffic management requires am analytic capability to capture the quantified impact of the ADAS on individual drivers’ behaviors and the aggregated traffic safety and mobility improvement due to such an impact. To this end, this research proposes a synthetic methodology that incorporates the ADAS-affected driving behavior modeling and state-of-the-art microscopic traffic flow modeling into a virtually simulated environment. Building on such an environment, the optimal ADAS algorithm parameter set is identified through a multi-objective optimization approach that uses the Genetic Algorithm. The developed methodology is tested at a freeway facility under low, medium and high ADAS market penetration rate scenarios. The case study reveals that fine-tuning the ADAS algorithm parameter can significantly improve the throughput and reduce the traffic delay and conflicts at the study site in the medium and high penetration scenarios. In these scenarios, the ADAS algorithm parameter optimization is necessary. Otherwise the ADAS will intensify the behavior heterogeneity among drivers, resulting in little traffic safety improvement and negative mobility impact. In the high penetration rate scenario, the identified optimal ADAS algorithm parameter set can be used to support different control objectives (e.g., safety improvement has priority vs. mobility improvement has priority).

An improved car-following model with multiple preceding cars’ velocity fluctuation feedback

In order to explore and evaluate the effects of velocity variation trend of multiple preceding cars used in the Cooperative Adaptive Cruise Control (CACC) strategy on the dynamic characteristic, fuel economy and emission of the corresponding traffic flow, we conduct a study as follows: firstly, with the real-time car-following (CF) data, the close relationship between multiple preceding cars’ velocity fluctuation feedback and the host car’s behaviors is explored, the evaluation results clearly show that multiple preceding cars’ velocity fluctuation with different time window-width are highly correlated to the host car’s acceleration/deceleration. Then, a microscopic traffic flow model is proposed to evaluate the effects of multiple preceding cars’ velocity fluctuation feedback in the CACC strategy on the traffic flow evolution process. Finally, numerical simulations on fuel economy and exhaust emission of the traffic flow are also implemented by utilizing VT-micro model. Simulation results prove that considering multiple preceding cars’ velocity fluctuation feedback in the control strategy of the CACC system can improve roadway traffic mobility, fuel economy and exhaust emission performance.

Modelling and controlling of car-following behavior in real traffic flow using ARMAX identification and Model Predictive Control

Nowadays, car following models, as the most popular microscopic traffic flow modeling, are increasingly being used by transportation experts to evaluate new Intelligent Transportation System (ITS) and Advanced Driver Assistance Systems (ADAS) applications. The control of car following is essential due to its safety and its operational efficiency. For this purpose, this paper builds a model of car following behavior based on ARMAX structure from a real traffic data set and presents a Model Predictive Control (MPC) controller. An important advantage of this type of control is its ability to cope with constraints on controls. Since safety and operational efficiency are constraints for car following, therefore we have recruited this type of controller in this study to deal with these constraints. Based on the relative distance and relative acceleration of each instant, the MPC predicts the future behavior of the leader vehicle (LV) and according to this behavior, the acceleration of the follower vehicle (FV) is controlled. The MPC tries to control this acceleration in a way to keep the relative distance at a safe region. To investigate the performance of the designed controller, the result of the system is compared with the behavior of human drivers with similar initial conditions. Also, some other test performances were accomplished to investigate other features such as robustness and the stability of the designed MPC. The simulation results show that the MPC controller has a behavior much safer than that of real drivers and it can provide a pleasant trip for passengers.

Challenges in Applying Calibration Methods to Stochastic Traffic Models

This paper evaluates calibration and validation as a means to understand traffic flow models better. The paper concentrates on the car-following part of these models and demonstrates that the calibration of stochastic models under certain circumstances can become difficult. Three types of stochasticity are distinguished for microscopic traffic flow models: the stochasticity coming from noisy data, the stochasticity coming from the distribution of the parameters describing the driver’s behavior, and the stochasticity coming from the model itself when a noise component is added to a deterministic differential equation governing the vehicle’s movements. By using four submodels with four noise terms and an identical deterministic part, this paper shows that a calibration with synthetic and, therefore, reproducible data can lead to results that are awry. The parameters fitted by the calibration procedure were significantly different for the deterministic and stochastic models. It was concluded that stochasticity was the reason why the parameter estimation of stochastic models sometimes failed. Up to now, the authors have not been able to propose a solution to cope with this intrinsic pitfall of genuine stochastic models.