Microscopic Traffic Flow Models Research Articles

Do We Really Need to Calibrate All the Parameters? Variance-Based Sensitivity Analysis to Simplify Microscopic Traffic Flow Models

Automated calibration of microscopic traffic flow models is all but simple for a number of reasons, including the computational complexity of black-box optimization and the asymmetric importance of parameters in influencing model performances. The main objective of this paper is therefore to provide a robust methodology to simplify car-following models, that is, to reduce the number of parameters (to calibrate) without sensibly affecting the capability of reproducing reality. To this aim, variance-based sensitivity analysis is proposed and formulated in a “factor fixing” setting. Among the novel contributions are a robust design of the Monte Carlo framework that also includes, as an analysis factor, the main nonparametric input of car-following models, i.e., the leader's trajectory, and a set of criteria for “data assimilation” in car-following models. The methodology was applied to the intelligent driver model (IDM) and to all the trajectories in the “reconstructed” Next Generation SIMulation (NGSIM) I80-1 data set. The analysis unveiled that the leader's trajectory is considerably more important than the parameters in affecting the variability of model performances. Sensitivity analysis also returned the importance ranking of the IDM parameters. Basing on this, a simplified model version with three (out of six) parameters is proposed. After calibrations, the full model and the simplified model show comparable performances, in face of a sensibly faster convergence of the simplified version.

Does traffic-related calibration of car-following models provide accurate estimations of vehicle emissions?

Fuel consumption or pollutant emissions can be assessed by coupling a microscopic traffic flow model with an instantaneous emission model. Traffic models are usually calibrated using goodness of fit indicators related to the traffic behavior. Thus, this paper investigates how such a calibration influences the accuracy of fuel consumption and NOx and PM estimations. Two traffic models are investigated: Newell and Gipps. It appears that the Gipps model provides the closest simulated trajectories when compared to real ones. Interestingly, a reverse ranking is observed for fuel consumption, NOx and PM emissions. For both models, the emissions of single vehicles are very sensitive to the calibration. This is confirmed by a global sensitivity analysis of the Gipps model that shows that non-optimal parameters significantly increase the variance of the outputs. Fortunately, this is no longer the case when emissions are calculated for a group of many vehicles. Indeed, the mean errors for platoons are close to 10% for the Gipps model and always lower than 4% for the Newell model. Another interesting property is that optimal parameters for each vehicle can be replaced by the mean values with no discrepancy for the Newell model and low discrepancies for the Gipps model when calculating the different emission outputs. Finally, this study presents preliminary results that show that multi-objective calibration methods are certainly the best direction for future works on the Gipps model. Indeed, the accuracy of vehicle emissions can be highly improved with negligible counterparts on the traffic model accuracy.

Исследование интегральных характеристик перекрестков при помощи микроскопических моделей транспортных потоков

Рассматривается проблема применимости микроскопического моделирования транспортных потоков к анализу достаточно больших фрагментов сетей на примере модели дискретного потока с безопасной дистанцией. Вводится понятие интегральных характеристик перекрестков и предлагается методика получения интегральных характеристик на основе данных численных экспериментов по моделированию потоков на заданном перекрестке. Методика применяется к кольцевому коммутатору с Т-образными перекрестками, анализируются полученные характеристики.

Platform for Two-Dimensional Cellular Automata Models Implemented by Living Cells of Electrically Controlled Green Paramecia Designed for Transport of Micro-Particles

Microscopic traffic flow models are a class of scientific models of vehicular traffic dynamics. Here, we attempted to establish an experimental platform for mimicking microscopic traffic flow models at microscopic dimensions. We achieved this, by monitoring the flow of micro-sized particles transported by the motile cells of living microorganisms. Some researchers have described the cells of protozoan species as “swimming neurons” or “swimming sensory cells” applicable to biological micro-electro-mechanical systems or micro-biorobotics. Therefore these cells, in a controlled environment, may form a good model system for bio-implementable cellular automata for traffic simulation. The living cells of theParameciumspecies including those of green paramecia (Paramecium bursaria), actively migrate towards a negatively charged electrode when exposed to an electric field. This type of cellular movement is known as galvanotaxis.P. bursariawas chosen as amodel organismsince the ideal micro-vehicles required for micro-particle transport must have a particular particle packing capacity within the cells. The present study establishes that the movement of cells with or without the loading of microspheres (Φ, 9.75 µm) can be controlled on a two-dimensional plane under strict electrical controls. Lastly, implementation of microchips equipped with optimally sized micro-flow channels that allow the single-cell traffic of swimmingP. bursariawas proposed for further studies and mathematical modeling.

Multiscale Traffic Flow Modeling in Mixed Networks

Multiscale traffic flow modeling, which combines traffic models of different scales (e.g., of network and traffic representation), offers many opportunities for the simulation and evaluation of traffic measures and policies in large networks. For example, macroscopic continuum models of traffic flow could be used to simulate the propagation of traffic on large freeway corridors and networks efficiently and parsimoniously, whereas microscopic models of traffic flow could be used to simulate those parts of the network where more detail (e.g., lateral behavior) is required, such as at intersections and toll plazas. One key requirement of such a multiscale framework is related to the interface between models of different scales. This interface should ensure consistency in (a) vehicle conservation and (b) vehicle and traveler properties that must be transported over this interface (e.g., vehicle type, occupancy, and destination). In the approach presented, both types of consistency problems can be solved simultaneously, and this approach is illustrated with an integrated example. This multiscale modeling framework enables the coupling of any macroscopic model with any microscopic model (and vice versa) without putting constraints on the internal structure or parameterization in either model.

Three-phase theory of city traffic: Moving synchronized flow patterns in under-saturated city traffic at signals

Three-phase traffic flow theory of city traffic has been developed. Based on simulations of a stochastic microscopic traffic flow model, features of moving synchronized flow patterns (MSP) have been studied, which are responsible for a random time-delayed breakdown of a green-wave (GW) organized in a city. A possibility of GW control leading to the prevention of GW breakdown has been demonstrated. A diagram of traffic breakdown in under-saturated traffic (transition from under- to over-saturated city traffic) at the signal has been found; the diagram presents regions of the average arrival flow rate, within which traffic breakdown can occur, in dependence of parameters of the time-function of the arrival flow rate or/and signal parameters. Physical reasons for a crucial difference between results of classical theory of city traffic and three-phase theory are explained. In particular, we have found that under-saturated traffic at the signal can exist during a long time interval, when the average arrival flow rate is larger than the capacity of the classical theory; the classical capacity is equal to a minimum capacity in three-phase theory. Within a range of the average arrival flow rate between the minimum and maximum signal capacities, under-saturated traffic is in a metastable state with respect to traffic breakdown. We have distinguished the following possible causes for the metastability of under-saturated traffic: (i) The arrival flow rate during the green phase is larger than the saturation flow rate. (ii) The length of the upstream front of a queue at the signal is a finite value. (iii) The outflow rate from a MSP (the rate of MSP discharge) is larger than the saturation flow rate.

Invariance and homogenization of an adaptive time gap car-following model

In this paper we consider a microscopic model of traffic flow called the adaptive time gap car-following model. This is a system of ODEs which describes the interactions between cars moving on a single line. The time gap is the time that a car needs to reach the position of the car in front of it (if the car in front of it would not move and if the moving car would not change its velocity). In this model, both the velocity of the car and the time gap satisfy an ODE. We study this model and show that under certain assumptions, there is an invariant set for which the dynamics is defined for all times and for which we have a comparison principle. As a consequence, we show rigorously that after rescaling, this microscopic model converges to a macroscopic model that can be identified as the classical LWR model for traffic.

The Analysis of Traffic Flow Model

With worsening traffic condition in large and medium-sized cities, it has become one of the most important steps for the urban traffic strategy to solve the traffic problems. Since the urban traffic is a complex system in various factors and huge scale, to establish related mathematical model through computer numerical simulation is a significant solution to the comprehensive problems of complex analysis, decision and planning. At present researches on the problems have been achieved in many foreign countries, but domestic research is not enough, especially in the practical application. The macroscopic traffic flow model and microscopic traffic flow model are described and cellular automaton model, dual channel decision model and car-following model are analyzed in this paper, prediction of the ideal traffic flow and trip distribution is consequently concluded, which deepen the understanding to the traffic flow of various phenomenon intrinsic mechanism and predict most closely to the actual situation of traffic flow, which can make fundamental work for traffic flow simulation and for real-time traffic control[1-3].

Phases of scaling and cross-correlation behavior in traffic

While many microscopic models of traffic flow describe transitions between different traffic phases, such transitions are difficult to quantify in measured traffic data. Here we study long-term traffic recordings consisting of ≈2900 days of flow, density, and velocity time series with minute resolution from a Spanish motorway. We calculate fluctuations, cross-correlations, and long-term persistence properties of these quantities in the flow–density diagram. This leads to a data-driven definition of (local) traffic states based on the dynamical properties of the data, which differ from those given in standard guidelines. We find that detrending techniques must be used for persistence analysis because of non-stationary daily and weekly traffic flow patterns. We compare our results for the measured data with analysis results for a microscopic traffic model, finding good agreement in most quantities. However, the simulations cannot easily reproduce the congested traffic states observed in the data. We show how fluctuations and cross-correlations in traffic data may be used for prediction, i.e., as indications of increasing or decreasing velocities.

Are vehicle trajectories simulated by dynamic traffic models relevant for estimating fuel consumption?

This paper questions the relevance of microscopic traffic models for estimating the impact of traffic strategies on fuel consumption. Urban driving cycles from the ARTEMIS database are simplified into piecewise linear speed profiles to mimic the classical outputs of microscopic traffic flow models. Fuel consumption is estimated for real and simplified trajectories and links between kinematics and the fuel consumption errors are investigated. Simplifying trajectories causes fuel consumption underestimation, from −1.2 to −5.2% on average according to the level of simplification; errors can approach −20% for some cycles. A focus on kinematic phases indicates that the maximum speed reached and the time decelerating are the main influences on fuel consumption. Finally, in the case where maximum speeds are estimated correctly, it is shown that errors committed at each kinematic phase when acceleration distributions are approximated by their mean values, converge towards small errors over complete cycles. A method is developed to quantify and reduce these errors.

Intelligent driving in traffic systems with partial lane discipline

It is a most common notion in traffic theory that driving in lanes and keeping lane changes to a minimum leads to smooth and laminar traffic flow, and hence to increased traffic capacity. On the other hand, there exist persistent vehicular traffic systems that are characterised by habitual disregarding of lane markings, and partial or complete loss of laminar traffic flow. Here, we explore the stability of such systems through a microscopic traffic flow model, where the degree of lane-discipline is taken as a variable, represented by the fraction of drivers that disregard lane markings completely. The results show that lane-free traffic may win over completely ordered traffic at high densities, and that partially ordered traffic leads to the poorest overall flow, while not considering the crash probability. Partial order in a lane-free system is similar to partial disorder in a lane-disciplined system in that both lead to decreased traffic capacity. This could explain the reason why standard enforcement methods, which rely on continuous increase of order, often fail to incur order to lane-free traffic systems. The results also provide an insight into the cooperative phenomena in open systems with self-driven particles.

Speed Synchronization Process of Merging Vehicles from the Entrance Ramp

This paper explores the “lane-changing preparation process,” defined as the synchronization process, from a new, integrated perspective. A comprehensive study was conducted to analyze the behavioral characteristics of the speed synchronization process of merging vehicles from entrance ramps by tracking their trajectories in the merge lanes. On the basis of gap selection, merging vehicles were classified as either original gap type or overtaking type, and the existence of speed synchronization was proved by comparing the speed differences of merging vehicles in relation to the putative leader (PL) and the putative follower (PF) vehicles. Several rules of merging vehicles during speed synchronization were established in the behavioral study. The merging vehicles tended to maintain a speed 5 to 7 m/s higher than the speed of the PL so as to overtake unsatisfied gaps in the adjacent through lane. When those vehicles intended to accept a gap, they first adjusted their speeds to be within a 2-m/s difference from their PL and PF vehicles and then merged into the targeted gap within 2 to 3 s. Factors affecting drivers' tolerance of their speed with PL and PF vehicles were modeled with the multiregression method. Significant effects in speed synchronization include the number of rejected gaps, acceleration or deceleration, the speed difference between the PL and the PF, the time headway, the remaining distance in the auxiliary lane, and whether the PL is a merged vehicle. Results from this study may contribute to the understanding of the complex lane-changing behavior in microscopic traffic flow modeling.

A Modified Car-Following Model Based on a Neural Network Model of the Human Driver Effects

Nowadays, among the microscopic traffic flow modeling approaches, the car-following models are increasingly used by transportation experts to utilize appropriate intelligent transportation systems. Unlike previous works, where the reaction delay is considered to be fixed, in this paper, a modified neural network approach is proposed to simulate and predict the car-following behavior based on the instantaneous reaction delay of the driver-vehicle unit as the human effects. This reaction delay is calculated based on a proposed idea, and the model is developed based on this feature as an input. In this modeling, the inputs and outputs are chosen with respect to the reaction delay to train the neural network model. Using the field data, the performance of the model is calculated and compared with the responses of some existing neural network car-following models. Considering the difference between the responses of the actual plant and the predicted model as the error, comparison shows that the error in the proposed model is significantly smaller than that that in the other models.

Modeling and Distribution of Link Travel Times: An Analysis on Istanbul Freeways

Travel times can be directly estimated by measurements including probe vehicles, Bluetooth detectors, and etc. Route and network wide travel times can be alternatively specified employing indirect estimation methods. These methods can be classified into two those are trajectory based and traffic flow model based. Considering the latter class, an approach to reconstruct travel times is to employ models commonly used in dynamic traffic assignment, where the travel time on a link is a treated as a function of the number of vehicles on the link. In the presented research, we concentrate on the reconstruction performance of two traffic flow models on freeway link/path travel times. A link performance function based macroscopic traffic flow model is employed and compared with a microscopic traffic flow model. Performances of selected methods are evaluated with the actual measurements on travel time. Actual travel times have been collected on weekdays by using a global positioning system (GPS) module equipped probe vehicle. Following reconstruction of link/path travel times employing macroscopic and microscopic models, an evaluation on the distribution of model calculations with the corresponding to GPS measurements presented.

How Simplifying Urban Driving Cycles Influence Fuel Consumption Estimation?

Optimizing traffic management systems requires the development of dynamic traffic flow models capable of estimating environmental externalities. However, such models only produce simplified trajectories. Therefore they cannot be directly coupled with traditional emission models based on real trajectories, i.e. observed experimentally. The main objective of this research is to evaluate the impacts of using simplified instead of real trajectories as an input for a fuel consumption model, Vehlib library, developed at IFSTTAR/LTE.Driving cycles were selected from 37 ARTEMIS urban driving cycles and processed. The resulting driving cycles were then simplified to make them correspond to the classical outputs of microscopic traffic flow models, i.e. piecewise linear speed profiles. The simplification method used is based on a genetic algorithm with a given number of break points. Reducing the number of such points leads to several levels of simplification. The fuel consumption is then estimated for each simplified driving cycle and its original.A deeper analysis is finally provided to evaluate the error between fuel consumption estimations for original and simplified sub-cycles. The first results show average error equal to -1.27% for simplified sub-cycles with average RMSE equals to 0.90km/h. According to the level of simplification, the average error is equal to -0.13% at fine level, -0.77% at intermediary level and -2.42% at coarse level. A complementary analysis is also provided studying individually several sub-cycles to figure out which kinds of simplification have the main influence on fuel consumption.

A study of the emergence of kinematic waves in targeted state car-following models of traffic

We propose to study the emergence of kinematic waves in microscopic models of traffic flow. The vehicles motion is given by car-following differential systems that incorporate a targeted state function and a strictly positive reaction time. Through simulations, we observe two types of stationary state for a line of vehicle evolving on a ring: a homogeneous state in which vehicle speed and gap are constant and equal and a heterogeneous state in which kinematic waves spread out. The reaction time and the form of the targeted state function seem to be the determining microscopic factors of the macroscopic stationary state stability. A stability linear analysis of the homogeneous state is done with a basic car-following model. The results indicate an explicit condition between the reaction time, the form of the targeted state function and the stationary state nature of the vehicle line.

Calibration of microscopic traffic-flow models using multiple data sources

Parameter identification of microscopic driving models is a difficult task. This is caused by the fact that parameters--such as reaction time, sensitivity to stimuli, etc.--are generally not directly observable from common traffic data, but also due to the lack of reliable statistical estimation techniques. This contribution puts forward a new approach to identifying parameters of car-following models. One of the main contributions of this article is that the proposed approach allows for joint estimation of parameters using different data sources, including prior information on parameter values (or the valid range of values). This is achieved by generalizing the maximum-likelihood estimation approach proposed by the authors in previous work. The approach allows for statistical analysis of the parameter estimates, including the standard error of the parameter estimates and the correlation of the estimates. Using the likelihood-ratio test, models of different complexity (defined by the number of model parameters) can be cross-compared. A nice property of this test is that it takes into account the number of parameters of a model as well as the performance. To illustrate the workings, the approach is applied to two car-following models using vehicle trajectories of a Dutch freeway collected from a helicopter, in combination with data collected with a driving simulator.

How Parameters of Microscopic Traffic Flow Models Relate to Traffic Dynamics in Simulation

Several methodological issues in setting up a calibration process for traffic microsimulation models are still unresolved. The influence of individual parameters of microscopic models on simulated traffic dynamics is also far from clear. To address those issues, the paper sets up a methodology based on the sensitivity analysis of traffic flow models (the one used here is AIMSUN). Sensitivity analysis was performed by means of a series of 30 analyses of variance. These were designed to evaluate the effect of parameters on the variance of the simulated outputs and to draw a general inference about ( a) the proper interval for the aggregation of measurements, ( b) the proper measure of performance (e.g., traffic counts versus speeds), ( c) the proper traffic measurement locations, and ( d) the subset of parameters to calibrate. The analysis allowed quantification of the effect of the single parameters on different traffic phases. For example, it was possible to quantify the extent of the influence of the parameter reaction time on simulated outputs in locations in which free flow, rather than congested conditions, occurs. The great differences between parameters in affecting the different traffic phases suggested that parameters are likely to be calibrated independently, that is, using data from different locations. The first evidence of the possibility of breaking the calibration problem into two subproblems is given. This entails great benefits in regard to computational time, given the exponential computational complexity of the calibration problem.

Comparing traffic flow models with different number of “phases”

By comparing microscopic traffic flow models with a different number of phases in the context of a simple scenario, the similarities as well as the differences of the various traffic flow models can be discussed. It turns out that there is a certain range of traffic flow conditions, where it is difficult to discern the space-time patterns produced by the different models. However, there are some other regions in the parameter space, where clear differences can be detected. Although the results obtained here cannot directly transformed into a real test with real-world data, they may help to finally define realistic scenarios which would result in a clear decision about which model describes reality best.

Comparison of Simulation-Based and Model-Based Calibrations of Traffic-Flow Microsimulation Models

Parameter calibration of traffic microsimulation models usually takes the form of a simulation-based optimization problem, that is, an optimization in which every objective function evaluation calls for a simulation. It is recognized that such a problem is computationally intractable. Running time grows exponentially both in the number of parameters and in the digits accuracy. In addition, considerable computing time is required by each objective function evaluation. This means that only heuristic techniques can be applied. Accordingly, results of the application of the OptQuest/Multistart algorithm to the calibration of AIMSUN microsimulation model parameters on a freeway network are presented. Furthermore, it is claimed that the search for an effective solution to the calibration problem cannot be exhausted by the choice of the most efficient optimization algorithm. The use of available information concerning the phenomenon could allow calibration performance to be enhanced, for example, by reducing dimensions of the domain of feasible solutions. It is argued that this goal could be achieved by using information from the stationary counterpart of microscopic traffic-flow models that depict the aggregate variables of traffic flows as a function of drivers’ microscopic parameters. Because they have a closed analytical formulation, they are well suited for faster calibrations. Results show that values of parameters from stationary model-based calibrations are not far from the optimal ones. Thus the integration of the two approaches cannot be excluded but is worth investigating.