Calibration of traffic flow models using a memetic algorithm

A Memetic Algorithm (MA) for the calibration of microscopic traffic flow simulation models is proposed in this study. The proposed MA includes a combination of genetic and simulated annealing algorithms. The genetic algorithm performs the exploration of the search space and identifies a zone where a possible global solution could be located. After this zone has been found, the simulated annealing algorithm refines the search and locates an optimal set of parameters within that zone. The design and implementation of this methodology seeks to enable the generalized calibration of microscopic traffic flow models. Two different Corridor Simulation (CORSIM) vehicular traffic systems were calibrated for this study. All parameters after the calibration were within reasonable boundaries. The calibration methodology was developed independently of the characteristics of the traffic flow models. Hence, it is easily used for the calibration of any other model. The proposed methodology has the capability to calibrate all model parameters, considering multiple performance measures and time periods simultaneously. A comparison between the proposed MA and the Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm was provided; results were similar between the two. However, the effort required to fine-tune the MA was considerably smaller when compared to the SPSA. The running time of the MA-based calibration was larger when it was compared to the SPSA running time. The MA still required some knowledge of the model in order to set adequate optimization parameters. The perturbation of the parameters during the mutation process must have been large enough to create a measurable change in the objective function, but not too large to avoid noisy measurements.     

Automatic calibration of fundamental diagram for first‐order macroscopic freeway traffic models

Despite its importance in macroscopic traffic flow modeling, comprehensive method for the calibration of fundamental diagram is very limited. Conventional empirical methods adopt a steady state analysis of the aggregate traffic data collected from measurement devices installed on a particular site without considering the traffic dynamics, which renders the simulation may not be adaptive to the variability of data. Nonetheless, determining the fundamental diagram for each detection site is often infeasible. To remedy these, this study presents an automatic calibration method to estimate the parameters of a fundamental diagram through a dynamic approach. Simulated flow from the cell transmission model is compared against the measured flow wherein an optimization merit is conducted to minimize the discrepancy between model‐generated data and real data. The empirical results prove that the proposed automatic calibration algorithm can significantly improve the accuracy of traffic state estimation by adapting to the variability of traffic data when compared with several existing methods under both recurrent and abnormal traffic conditions. Results also highlight the robustness of the proposed algorithm. The automatic calibration algorithm provides a powerful tool for model calibration when freeways are equipped with sparse detectors, new traffic surveillance systems lack of comprehensive traffic data, or the case that lots of detectors lose their effectiveness for aging systems. Furthermore, the proposed method is useful for off‐line model calibration under abnormal traffic conditions, for example, incident scenarios. Copyright © 2015 John Wiley & Sons, Ltd.     

Enhancing the performance of existing urban traffic light control through extremum-seeking

Urban traffic light controllers are responsible for maintaining good performance within the transport network. Most existing and proposed controllers have design parameters that require some degree of tuning, with the sensitivity of the performance measure to the parameter often high. To date, tuning has been largely treated as a manual calibration exercise but ignores the effects of changes in traffic condition, such as demand profile evolution due to urban population growth. To address this potential shortcoming, we seek to use a newly developed extremum-seeker to calibrate the parameters of existing urban traffic light controllers in real-time such that a certain performance measure is optimised. The results are demonstrated for three categories of traffic controllers on a microscopic urban traffic simulation. It is demonstrated that the extremum-seeking scheme is able to seek the optimal parameters, with respect to a certain performance measure, for each of these traffic light controllers in an urban, uni-modal traffic environment.     

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.     

Robust calibration of macroscopic traffic simulation models using stochastic collocation

The predictions of a well-calibrated traffic simulation model are much more valid if made for various conditions. Variation in traffic can arise due to many factors such as time of day, work zones and weather. Calibration of traffic simulation models for traffic conditions requires larger datasets to capture the stochasticity in traffic conditions. In this study we use datasets spanning large time periods to incorporate variability in traffic flow, speed for various time periods. However, large data poses a challenge in terms of computational effort. With the increase in number of stochastic factors, the numerical methods suffer from the curse of dimensionality. In this study, we propose a novel methodology to address the computational complexity due to the need for the calibration of simulation models under highly stochastic traffic conditions. This methodology is based on sparse grid stochastic collocation, which, treats each stochastic factor as a different dimension and uses a limited number of points where simulation and calibration are performed. A computationally efficient interpolant is constructed to generate the full distribution of the simulated flow output. We use real-world examples to calibrate for different times of day and conditions and show that this methodology is much more efficient that the traditional Monte Carlo-type sampling. We validate the model using a hold out dataset and also show the drawback of using limited data for the calibration of a macroscopic simulation model. We also discuss the drawbacks of the predictive ability of a single calibrated model for all the conditions.     

Online calibration for microscopic traffic simulation and dynamic multi-step prediction of traffic speed

Simulating driving behavior in high accuracy allows short-term prediction of traffic parameters, such as speeds and travel times, which are basic components of Advanced Traveler Information Systems (ATIS). Models with static parameters are often unable to respond to varying traffic conditions and simulate effectively the corresponding driving behavior. It has therefore been widely accepted that the model parameters vary in multiple dimensions, including across individual drivers, but also spatially across the network and temporally. While typically on-line, predictive models are macroscopic or mesoscopic, due to computational and data considerations, nowadays microscopic models are becoming increasingly practical for dynamic applications. In this research, we develop a methodology for online calibration of microscopic traffic simulation models for dynamic multi-step prediction of traffic measures, and apply it to car-following models, one of the key models in microscopic traffic simulation models. The methodology is illustrated using real trajectory data available from an experiment conducted in Naples, using a well-established car-following model. The performance of the application with the dynamic model parameters consistently outperforms the corresponding static calibrated model in all cases, and leads to less than 10% error in speed prediction even for ten steps into the future, in all considered data-sets.     

Robust real-time pedestrians detection in urban environments with low-resolution cameras

Detecting that pedestrians are present in front of a vehicle is highly desirable to avoid dangerous traffic situations. A novel vision-based system is presented to automatically detect far-away pedestrians with low-resolution cameras mounted in vehicles given the contributions of fixed cameras present in the scene.Fixed cameras detect pedestrians by solving an inverse problem built upon a multi-class dictionary of atoms approximating the foreground silhouettes. A sparse-sensing strategy is proposed to extract the foreground silhouettes and classify them in real-time. Mobile cameras detect pedestrians given only their appearance in the fixed cameras. A cascade of compact binary strings is presented to model the appearance of pedestrians and match them across cameras.The proposed system addresses the practical requirements of transportation systems: it runs in real-time with low memory loads and bandwidth consumption. We evaluate the performance of our system when extracted features are severely degraded and the sensing devices are of low quality. Experimental results demonstrate the feasibility of our collaborative vision-based system.     

Multilane first-order traffic flow model with endogenous representation of lane-flow equilibrium

In this study, we develop a multilane first-order traffic flow model for freeway networks. In the model, lane changing is considered as a stochastic behavior that can decrease an individual driver’s disutility or cost, and is represented as dynamics toward the equilibrium of lane-flow distribution along with longitudinal traffic dynamics. The proposed method can be differentiated from those in previous studies because in this study, the motivation of lane changing is explicitly considered and it is treated as a utility defined by the current macroscopic traffic state. In addition, the entire process of lane changing is computed macroscopically by an extension of the kinematic wave theory employing IT principle; moreover, in the model framework, the lane-flow equilibrium curve is endogenously generated because of self-motivated lane changes. Furthermore, the parsimonious representation enables parameter calibration using the data collected from conventional loop detectors. The calibration of the data collected at four different sites, including a sag bottleneck, on the Chugoku expressway in Japan reveals that the proposed method can represent the lane-flow distribution of any observation site with high accuracy, and that the estimated parameters can reasonably explain the multilane traffic dynamics and the bottleneck phenomena uphill of sag sections.     

Modeling car-following behavior on urban expressways in Shanghai: A naturalistic driving study

Although car-following behavior is the core component of microscopic traffic simulation, intelligent transportation systems, and advanced driver assistance systems, the adequacy of the existing car-following models for Chinese drivers has not been investigated with real-world data yet. To address this gap, five representative car-following models were calibrated and evaluated for Shanghai drivers, using 2100 urban-expressway car-following periods extracted from the 161,055 km of driving data collected in the Shanghai Naturalistic Driving Study (SH-NDS). The models were calibrated for each of the 42 subject drivers, and their capabilities of predicting the drivers’ car-following behavior were evaluated.The results show that the intelligent driver model (IDM) has good transferability to model traffic situations not presented in calibration, and it performs best among the evaluated models. Compared to the Wiedemann 99 model used by VISSIM®, the IDM is easier to calibrate and demonstrates a better and more stable performance. These advantages justify its suitability for microscopic traffic simulation tools in Shanghai and likely in other regions of China. Additionally, considerable behavioral differences among different drivers were found, which demonstrates a need for archetypes of a variety of drivers to build a traffic mix in simulation. By comparing calibrated and observed values of the IDM parameters, this study found that (1) interpretable calibrated model parameters are linked with corresponding observable parameters in real world, but they are not necessarily numerically equivalent; and (2) parameters that can be measured in reality also need to be calibrated if better trajectory reproducing capability are to be achieved.     

Trajectory data reconstruction and simulation-based validation against macroscopic traffic patterns

This paper shows that the behavior of driver models, either individually or entangled in stochastic traffic simulation, is affected by the accuracy of empirical vehicle trajectories. To this aim, a “traffic-informed” methodology is proposed to restore physical and platoon integrity of trajectories in a finite time–space domain, and it is applied to one NGSIM I80 dataset. However, as the actual trajectories are unknown, it is not possible to verify directly whether the reconstructed trajectories are really “nearer” to the actual unknowns than the original measurements. Therefore, a simulation-based validation framework is proposed, that is also able to verify indirectly the efficacy of the reconstruction methodology. The framework exploits the main feature of NGSIM-like data that is the concurrent view of individual driving behaviors and emerging macroscopic traffic patterns. It allows showing that, at the scale of individual models, the accuracy of trajectories affects the distribution and the correlation structure of lane-changing model parameters (i.e. drivers heterogeneity), while it has very little impact on car-following calibration. At the scale of traffic simulation, when models interact in trace-driven simulation of the I80 scenario (multi-lane heterogeneous traffic), their ability to reproduce the observed macroscopic congested patterns is sensibly higher when model parameters from reconstructed trajectories are applied. These results are mainly due to lane changing, and are also the sought indirect validation of the proposed data reconstruction methodology.     

W-SPSA in practice: Approximation of weight matrices and calibration of traffic simulation models

The development and calibration of complex traffic models demands parsimonious techniques, because such models often involve hundreds of thousands of unknown parameters. The Weighted Simultaneous Perturbation Stochastic Approximation (W-SPSA) algorithm has been proven more efficient than its predecessor SPSA (Spall, 1998), particularly in situations where the correlation structure of the variables is not homogeneous. This is crucial in traffic simulation models where effectively some variables (e.g. readings from certain sensors) are strongly correlated, both in time and space, with some other variables (e.g. certain OD flows). In situations with reasonably sized traffic networks, the difference is relevant considering computational constraints. However, W-SPSA relies on determining a proper weight matrix (W) that represents those correlations, and such a process has been so far an open problem, and only heuristic approaches to obtain it have been considered.This paper presents W-SPSA in a formally comprehensive way, where effectively SPSA becomes an instance of W-SPSA, and explores alternative approaches for determining the matrix W. We demonstrate that, relying on a few simplifications that marginally affect the final solution, we can obtain W matrices that considerably outperform SPSA. We analyse the performance of our proposed algorithm in two applications in motorway networks in Singapore and Portugal, using a dynamic traffic assignment model and a microscopic traffic simulator, respectively.     

Online calibration of an integrated framework for information‐based evacuation operations

This study seeks to online calibrate the parameters of aggregate evacuee behavior models used in a behavior‐consistent information‐based control module for determining information strategies for real‐time evacuation operations. It enables the deployment of an operational framework for mass evacuation that integrates three aspects underlying an evacuation operation: demand (evacuee behavior), supply (network management), and disaster characteristics. To attain behavior‐consistency, the control module factors evacuees' likely responses to the disseminated information in determining information‐based control strategies. Hence, the ability of the behavior models to predict evacuees' likely responses is critical to the effectiveness of traffic routing by information strategies. The mixed logit structure is used for the aggregate behavior models to accommodate the behavioral heterogeneity across the population. An online calibration problem is proposed to calibrate the random parameters in the behavior models by using the least square estimator to minimize the gap between the predicted network flows and unfolding traffic dynamics. Background traffic, an important but rarely studied issue for modeling evacuation traffic, is also accounted for in the proposed problem. Numerical experiments are conducted to illustrate the importance of the calibration problem for addressing the system consistency issues and integrating the demand, supply, and disaster characteristics for more efficient evacuation operations. Copyright © 2016 John Wiley & Sons, Ltd.     

Discrete dynamic models for freeway incident detection systems

This paper considers the problem of freeway incident detection within the general framework of computer‐based freeway surveillance and control. A new approach to the detection of freeway traffic incidents is presented based on a discrete‐time stochastic model of the form ARIMA (0, 1, 3) that describes the dynamics of traffic occupancy observations. This approach utilizes real‐time estimates of the variability in traffic occupancies as detection thresholds, thus eliminating the need for threshold calibration and lessening the problem of false‐alarms. Because the moving average parameters of the ARIMA (0, 1, 3) model change over time, these parameters can be updated occasionally. The performance of the developed detection algorithm has been evaluated in terms of detection rate, false‐alarm rate, and average time‐lag to detection, using a total of 1692 minutes of occupancy observations recorded during 50 representative traffic incidents.     

Speed or spacing? Cumulative variables,and convolution of model errors and time in traffic flow models validation and calibration

This paper proves that in traffic flow model calibration and validation the cumulative sum of a variable has to be preferred to the variable itself as a measure of performance. As shown through analytical relationships, model residuals dynamics are preserved if discrepancy measures of a model against reality are calculated on a cumulative variable, rather than on the variable itself. Keeping memory of model residuals occurrence times is essential in traffic flow modelling where the ability of reproducing the dynamics of a phenomenon – as a bottleneck evolution or a vehicle deceleration profile – may count as much as the ability of reproducing its order of magnitude. According to the aforesaid finding, in a car-following models context, calibration on travelled space is more robust than calibration on speed or acceleration. Similarly in case of macroscopic traffic flow models validation and calibration, cumulative flows are to be preferred to flows. Actually, the findings above hold for any dynamic model.     

Real-time traffic estimation using data expansion

This paper presents a method for estimating missing real-time traffic volumes on a road network using both historical and real-time traffic data. The method was developed to address urban transportation networks where a non-negligible subset of the network links do not have real-time link volumes, and where that data is needed to populate other real-time traffic analytics. Computation is split between an offline calibration and a real-time estimation phase. The offline phase determines link-to-link splitting probabilities for traffic flow propagation that are subsequently used in real-time estimation. The real-time procedure uses current traffic data and is efficient enough to scale to full city-wide deployments. Simulation results on a medium-sized test network demonstrate the accuracy of the method and its robustness to missing data and variability in the data that is available. For traffic demands with a coefficient of variation as high as 40%, and a real-time feed in which as much as 60% of links lack data, we find the percentage root mean square error of link volume estimates ranges from 3.9% to 18.6%. We observe that the use of real-time data can reduce this error by as much as 20%.     

Real-time freeway traffic state estimation based on extended Kalman filter: Adaptive capabilities and real data testing

This paper reports on real data testing of a real-time freeway traffic state estimator, with a particular focus on its adaptive capabilities. The pursued general approach to the real-time adaptive estimation of complete traffic state in freeway stretches or networks is based on stochastic macroscopic traffic flow modeling and extended Kalman filtering. One major innovative feature of the traffic state estimator is the online joint estimation of important model parameters (free speed, critical density, and capacity) and traffic flow variables (flows, mean speeds, and densities), which leads to three significant advantages of the estimator: (1) avoidance of prior model calibration; (2) automatic adaptation to changing external conditions (e.g. weather and lighting conditions, traffic composition, control measures); (3) enabling of incident alarms. These three advantages are demonstrated via suitable real data testing. The achieved testing results are satisfactory and promising for subsequent applications.     

Four-step travel demand model implementation for estimating traffic volumes on rural low-volume roads in Wyoming

This study develops a four-step travel demand model for estimating traffic volumes for low-volume roads in Wyoming. The study utilizes urban travel behavior parameters and processes modified to reflect the rural and low-volume nature of Wyoming local roads. The methodology disaggregates readily available census block data to create transportation analysis zones adequate for estimating traffic on low-volume rural roads. After building an initial model, the predicted and actual traffic volumes are compared to develop a calibration factor for adjusting trip rates. The adjusted model is verified by comparing estimated and actual traffic volumes for 100 roads. The R-square value from fitting predicted to actual traffic volumes is determined to be 74% whereas the Percent Root Mean Square Error is found to be 50.3%. The prediction accuracy for the four-step travel demand model is found to be better than a regression model developed in a previous study.     

A flexible traffic stream model and its three representations of traffic flow

To connect microscopic driving behaviors with the macro-correspondence (i.e., the fundamental diagram), this study proposes a flexible traffic stream model, which is derived from a novel car-following model under steady-state conditions. Its four driving behavior-related parameters, i.e., reaction time, calmness parameter, speed- and spacing-related sensitivities, have an apparent effect in shaping the fundamental diagram. Its boundary conditions and homogenous case are also analyzed in detail and compared with other two models (i.e., Longitudinal Control Model and Intelligent Driver Model). Especially, these model formulations and properties under Lagrangian coordinates provide a new perspective to revisit the traffic flow and complement with those under Eulerian coordinate. One calibration methodology that incorporates the monkey algorithm with dynamic adaptation is employed to calibrate this model, based on real-field data from a wide range of locations. Results show that this model exhibits the well flexibility to fit these traffic data and performs better than other nine models. Finally, a concrete example of transportation application is designed, in which the impact of three critical parameters on vehicle trajectories and shock waves with three representations (i.e., respectively defined in x-t, n-t and x-n coordinates) is tested, and macro- and micro-solutions on shock waves well agree with each other. In summary, this traffic stream model with the advantages of flexibility and efficiency has the good potential in level of service analysis and transportation planning.     

Validation of traffic flow models with respect to the spatiotemporal evolution of congested traffic patterns

We propose a quantitative approach for calibrating and validating key features of traffic instabilities based on speed time series obtained from aggregated data of a series of neighboring stationary detectors. The approach can be used to validate models that are calibrated by other criteria with respect to their collective dynamics. We apply the proposed criteria to historic traffic databases of several freeways in Germany containing about 400 occurrences of congestions thereby providing a reference for model calibration and quality assessment with respect to the spatiotemporal dynamics. First tests with microscopic and macroscopic models indicate that the criteria are both robust and discriminative, i.e., clearly distinguishes between models of higher and lower predictive power.