WP2: Traffic Flow Modelling in Presence of VACS

Task 2.1: Microscopic Modelling in Presence of VACS

2.1.1 Review and Tool Selection: Different open-source or commercial microscopic traffic simulators were extensively reviewed and tested, with respect to their ability to simulate traffic flow in the presence of VACS. The tools that such simulators provide to the user for the development of new models were identified. As a result, taking into account various criteria (such as suitability for TRAMAN21 needs, price, convenience, prior experience with the tool and more), it was decided that the microscopic simulation work will be based on Aimsun, as it provides all the necessary tools for the simulation of the VACS presence; it enables the insertion of new models of every aspect of the traffic flow simulation; and provides an appealing graphical user interface. The research team has a long experience on its use; as a result, the development and introduction of new models and tools is considered to be a comparably easier task.

2.1.2 Adaptive Cruise Control (ACC): Previous modelling efforts reported in the literature with respect to Adaptive Cruise Control (ACC) systems were reviewed, and some critical aspects, to be considered when designing or simulating such systems, were analyzed. Moreover, a simulator for ACC-equipped vehicles was developed and integrated in the commercial traffic simulator Aimsun. This simulation tool was subsequently used to run simulations for different penetration rates of ACC-equipped vehicles, different desired time-gap settings and different networks, to assess their impact on traffic flow characteristics. The results showed that the desired time-gap setting has direct impact on the capacity: The smaller the time-gap setting, the higher the capacity. Additionally, a large ACC penetration rate can improve the capacity as long as the desired time-gap setting is smaller than that of manual vehicles. If this is not the case, then one can observe deterioration in terms of capacity. This highlighted the need for the correct use of ACC systems, with regard to traffic management.

  • Ntousakis, I. A., Nikolos, I. K., Papageorgiou, M.: On Microscopic Modelling Of Adaptive Cruise Control Systems. Proceedings of the 4th International Symposium of Transport Simulation (ISTS), Ajaccio, France, June 1-4, 2014. -LINK-

2.1.3 Investigations on the Capacity Drop Phenomenon and its Mitigation: The capacity drop phenomenon is observed at bottleneck locations when the traffic breaks down (speed drop) due to overload. Capacity drop is the difference between the nominal bottleneck capacity (monitored before traffic breakdown) and the discharge flow after congestion sets in. Real traffic observations have shown that the bottleneck discharge flow may be 5 to 20 % lower than the nominal bottleneck capacity, which marks a significant infrastructure degradation leading to increased congestion extent and longer delays. Within the literature, there are a few works proposing possible explanations for the occurrence of capacity drop, while numerous studies propose various traffic control measures aiming to prevent or delay the traffic breakdown and the associated capacity drop. However, the exact reasons for the appearance of the capacity drop phenomenon have not been fully understood and explained yet. The subject of this research is to investigate the relation between the vehicles driving behavior and the capacity drop phenomenon. To this end, a simple car-following model is employed to simulate the driving behavior of vehicles as they enter and exit an active bottleneck location. In particular, the effect of the drivers’ reaction time, the vehicles’ acceleration capabilities, and the behavior of different vehicle classes are currently under investigation. The findings may lead to appropriate measures for mitigation of the capacity drop via VACS-equipped vehicles.

2.1.4 Microscopic model calibration: The calibration of a microscopic traffic flow model for a real motorway network is currently under development for use within various project Tasks and Activities. The modelled network is a 12km-long stretch of the motorway A20, from Rotterdam to Gouda, The Netherlands. Its topological characteristics (it includes lane-drops, on-ramps and partly saturated off-ramps) make it a very interesting test-bed for investigating various different scenarios. The microscopic simulator Aimsun is used, however with numerous adaptations made in order to improve the realism of the simulation and to reproduce more complex traffic phenomena (e.g., the capacity drop). Therefore, different new features are implemented, including a new car-following model (Intelligent Driver Model) and improved heuristic rules to capture more accurately the lane-changing behaviour in the proximity of on-ramps and lane-drops. This model can be then enriched with features related to VACS (e.g. partially and fully automated cars) and used for testing the accuracy of the proposed macroscopic models (Task 2.2), as well as numerous control strategies proposed within the project (WP3).

Task 2.2: Macroscopic Modelling in Presence of VACS

2.2.1 High-Order Modelling in Presence of VACS: A literature survey has been conducted on the available macroscopic traffic flow models, which include the presence of VACS. This survey concluded that the published work on the subject is not extended and only few researchers have been working on that. The more promising of the proposed models were further extensively studied and the methodologies that were used for their derivation were evaluated in detail. Two macroscopic approaches reflecting Adaptive Cruise Control (ACC) and Cooperative Adaptive Cruise Control (CACC) traffic dynamics have been incorporated in the already developed computational framework for macroscopic modelling (Task 2.3); both are based on the gas-kinetic (GKT) second- order traffic flow model. The first approach was recently analyzed by D. Ngoduy (Ngoduy D., Instability of cooperative adaptive cruise control traffic flow: A macroscopic approach, Communications in Nonlinear Science and Numerical Simulation, 18:2838-2851, 2013) aiming to describe the response of the ACC and CACC due to changes of the speed of the leader(s) by the introduction of an acceleration/deceleration term. The second approach is a novel one and is based on the introduction of a relaxation term that satisfies the time/space-gap principle of ACC or CACC systems. In both approaches, the relaxation time is distributed over multiple vehicles in the CACC case; whereas in the ACC case the relaxation time is only related to the direct leading vehicle. The resulting models have been discretized by an accurate and robust high-resolution finite volume relaxation scheme, where the nonlinear equations are first transformed to a semi-linear diagonilizable problem and are then discretized by a higher-order WENO scheme. Numerical simulations investigated the effect of the different ACC and CACC approaches to traffic flow macroscopic stability with respect to perturbations introduced in a ring road and to flow characteristics in open freeways with merging flows at an on-ramp. Following from the numerical results, it was found that CACC vehicles enhance the stabilization of traffic flow with respect to both small and large perturbations compared to ACC ones. Further, the proposed CACC approach can better improve the dynamic equilibrium capacity and traffic dynamics, especially at the on-ramp bottleneck.

The proposed macroscopic model for ACC/CACC traffic was further extended to simulate the characteristics of mixed manual and ACC or V2V CACC traffic. Numerical simulations were performed to investigate the effect of the penetration rates of ACC and CACC equipped vehicles to traffic flow macroscopic stability, with respect to perturbations introduced in a ring road, and to flow characteristics in an open freeway with merging flow at an on-ramp. It was shown numerically that CACC vehicles enhance the stabilization of traffic flow with respect to introduced perturbations compared to ACC ones. The observed enhanced dynamic equilibrium capacity for our CACC system resulted in the suppression of traffic congestion at an on-ramp bottleneck even at a penetration rate of around 30%.

In order to study the qualitative properties of the proposed ACC/CACC model and derive a proper stability condition with respect to small perturbations, the linear stability method was first applied, which refers to linear Taylor approximations, used throughout the analysis. Linear stability analysis is a widely established approach to estimate the stability performance of the systems controlling the traffic flow, as in general it provides a valuable insight into the general behavior and performance of the system. As a result of this analysis for the proposed macroscopic model, stability diagrams of ACC and CACC traffic flow dynamics were constructed for a certain model parameters set. Furthermore, a non-linear stability analysis of the proposed macroscopic model for ACC/CACC traffic was performed, as it allows to more accurately examine the global stability conditions under which a large perturbation travels against the traffic flow. A nonlinear stability criterion was derived, using a wavefront expansion method under large perturbations, which enables to investigate the shock wave propagation properties of the developed ACC/CACC macroscopic model. Moreover, numerical simulations were additionally conducted, to validate the derived non-linear stability conditions.

  • Delis, A. I., Nikolos, I. K., Papageorgiou, M.: Macroscopic traffic flow modelling with adaptive cruise control: Development and numerical solution. Computers & Mathematics with Applications, 2015, vol. 70, pp. 1921-1947.
  • Porfyri, K.N., Nikolos, I.K., Delis, A.I., Papageorgiou, M., “Stability analysis of a macroscopic traffic flow model for adaptive cruise control systems, Proceedings of the International Mechanical Engineering Congress and Exposition IMECE 2015, November 13-19, 2015, Houston, Texas, USA, IMECE2015-50977.
  • Nikolos, I.K., Delis, A.I., Papageorgiou, M.: Macroscopic Modelling and Simulation of ACC and CACC Traffic. 18th International IEEE Conference on Intelligent Transportation Systems (ITSC 2015), Las Palmas de Gran Canaria, Spain, 15-18 September 2015, pp. 2129-2134.
  • Delis, A.I., Nikolos, I.K., Papageorgiou, M.: Simulation of the penetration rate effects of ACC and CACC on macroscopic traffic dynamics. 2016 IEEE 19th International Conference on Intelligent Transportation Systems, Rio de Janeiro, Brazil, November 1-4, 2016, pp. 338-341.
  • Porfyri, K.N., Nikolos, I.K, Delis, A.I., Papageorgiou, M.: Nonlinear stability analysis of a macroscopic traffic flow model for Adaptive Cruise Control systems. Proceedings of the ASME 2016 International Mechanical Engineering Conference & Exposition, IMECE2016, Phoenix, A.Z., USA, November 11-17, 2016, Paper No. IMECE2016-66470.

2.2.2 Control-oriented Motorway Traffic Modelling: Traffic control strategies employing, beyond ramp metering, appropriate VACS-based actuators, such as vehicle speed control and lane-assignment or lane-changing recommendations, are developed in WP3, in the aim of mitigating motorway traffic congestion. To this end, an appropriate lower-complexity traffic flow model is needed, both for control strategy design and as a no-control base case for possible comparative evaluation studies. Such a model is built starting from the well-known cell-transmission model (CTM), which is modified and extended to consider additional aspects of the traffic dynamics, such as lane changing and the capacity drop. The model is derived with a view to combine realistic traffic flow description with a piecewise linear mathematical formulation, which can be exploited for efficient optimal control problem formulations (Task 3.3), as well as for the development of advanced nonlinear feedback control concepts (Activity 3.2.3). Although the model is primarily designed for use in future traffic conditions including VACS, it may also be used, with appropriate parameter values) for conventional traffic flow representation. The accuracy of the proposed modelling approach is demonstrated through calibration and validation procedures using conventional real data from an urban motorway located in Melbourne, Australia.

Since classic first-order traffic flow models are not able to reproduce the crucial phenomenon of capacity-drop, we thoroughly investigate different possibilities to include the capacity drop phenomenon in a first-order traffic flow model. Some modelling approaches presented in literature, together with some novel approaches, are investigated, with particular emphasis on the practical applicability of such models for traffic management and control. A subset of the most promising modelling approaches is thoroughly tested, calibrated and compared using real data from a motorway network in U.K., which include congestion caused by a merging on-ramp.

  • Roncoli, C., Papageorgiou, M., Papamichail, I. 2015: An optimisation-oriented first-order multi-lane model for motorway traffic, Proceedings of the 94th Annual Meeting of the Transportation Research Board (TRB), Washington, D.C., USA, 11-15 January 2015. -LINK-
  • Roncoli, C., Papageorgiou, M., Papamichail, I.: Traffic flow optimisation in presence of vehicle automation and communication systems - Part I: A first-order multi-lane model for motorway traffic. Transportation Research Part C, 2015, vol. 57, pp. 241-259.
  • Kontorinaki, M., Spiliopoulou, A., Roncoli, C., Papageorgiou, M.: Capacity drop in first-order traffic flow models: Overview and real-data validation. Proceedings of the 95th Annual Meeting of the Transportation Research Board (TRB), Washington, D.C., USA, 10-14 January 2016, paper no. 16-3541.
  • Kontorinaki, M., Spiliopoulou, A., Roncoli, C., Papageorgiou, M.: First-order traffic flow models incorporating capacity drop: Overview and real-data validation. submitted to Transportation Research Part B: Methodological.

Task 2.3: Simulation Tools

2.3.1 Numerical Scheme and Software: A novel numerical approach (and the corresponding software) was developed for the approximation of several, widely applied, second-order, non-equilibrium macroscopic traffic flow models. A relaxation-type approximation, written in conservation or balance law form, was considered. Using the relaxation approximation, the nonlinear equations were transformed to a semi-linear diagonalizable problem with linear characteristic variables and stiff source terms. The main feature of the proposed approach is its accuracy, simplicity and robustness. Finite volume shock capturing spatial discretizations, that are Riemann solver free, were used providing accurate resolution. To discretize the resulting relaxation system, low- and high-resolution reconstructions in space and implicit–explicit Runge–Kutta time integration schemes were utilized. The family of spatial discretizations includes a first-order scheme, a second-order MUSCL scheme and a fifth-order WENO scheme. To demonstrate the effectiveness of the proposed approach, extensive numerical tests were performed for the different models. Having simplicity as its main advantage and the attractive feature that neither Riemann solvers nor characteristic decomposition are in need, the relaxation approach can be considered as an alternative for practical applications in macroscopic traffic flow modeling. In particular, it is only necessary to provide the flux and source term functions and an estimate of the characteristic speeds. As relaxation is in a sense a flux approximation, we expect to produce reasonable results for any flux function as long as the system remains hyperbolic. Thus, considering different macroscopic models and real life simulations, the present approach is likely to be applicable then too and can be considered for further studies and development.

The outlined traffic flow model software was combined with an optimization procedure to enable the automatic estimation of the most crucial parameters of the flow model. The calibration and validation of second-order macroscopic traffic flow models constitutes a difficult task, as the assignment of appropriate values to the unknown model parameters is a challenging problem because of the highly non-linear nature of the model equations. As a matter of fact, relatively few calibration results for such macroscopic traffic flow models have been reported so far. The optimization problem consists in minimizing the deviation between the model calculations and the reference traffic data; whereby the reference traffic flow data can be either real-measured ones, or simulation data obtained from microscopic flow simulations. A relatively new optimization algorithm, namely a parallel, metamodel-assisted, Differential Evolution (DE) algorithm, was employed for the calibration of the model parameters in search for the global (or a good local) optimal solution. More precisely, the DE algorithm was combined with two Artificial Neural Networks (ANNs), a multi-layer perceptron (MLP) and a radial basis functions network (RBFN), which serve as surrogate models and accelerate the convergence of the optimization algorithm. DE was adopted as it has proven to be a very robust and computationally efficient optimization algorithm, compared to other types of Evolutionary Algorithms.

Firstly, a 9.45 km long 3-lane freeway stretch, part of the M56 motorway in the United Kingdom from Chester to Manchester, was considered for the assessment of both the macroscopic model and the optimization (calibration) procedure. Additionally, the calibration and validation procedure was applied to a particular freeway stretch in Greece (Attiki Odos motorway). The numerical simulations demonstrated that the proposed model is reasonably accurate in reproducing traffic dynamics, while the DE algorithm can be effectively used for its calibration.

  • Delis, A. I., Nikolos, I. K., Papageorgiou, M.: High-resolution relaxation approximations to second-order macroscopic traffic flow models. Transportation Research Part C: Emerging Technologies, 2014, vol. 44, pp. 318-349. -LINK-
  • Nikolos, I. K., Delis, A. I., Papageorgiou, M.: Relaxation approximations to second-order traffic flow models by high-resolution schemes. 12th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2014), Rhodes, Greece, 22-28 September 2014. -LINK-
  • Delis, A. I., Nikolos, I. K., Papageorgiou, M.: Numerical solution of second-order traffic flow models by high-resolution relaxation schemes. XV International Conference on Hyperbolic Problems (HYP2014), Rio de Janeiro, Brazil, 28 July - 1 August 2014.
  • Porfyri, K.N., Nikolos, I.K., Delis, A.I., Papageorgiou, M.: Calibration of a second-order traffic flow model using a metamodel-assisted Differential Evolution algorithm. 2016 IEEE 19th International Conference on Intelligent Transportation Systems, Rio de Janeiro, Brazil, November 1-4, 2016, pp. 366-371.
  • Strofylas, G.A., Porfyri, K.N., Nikolos, I.K., Delis, A.I., Papageorgiou, M.: Calibrating a traffic flow model with parallel differential evolution. submitted

2.3.2 Multi-Lane Highways and Junctions: The above mentioned methodology has been extended to handle multi-lane highways (including lane-drops). For this purpose, the methodology and the code were initially modified by introducing the required data structures, in order to simulate the flow in different road segments, consisting of different numbers of lanes and including on- and off-ramps. A tree-like structure of the road topology was adopted, which allows for the relatively simple generalization of the previously developed methodology, allowing for the use of different second-order traffic flow models in a multi-lane environment. Proper internal boundary conditions were developed, for the interfaces between successive road segments, which preserve the order of the spatial numerical schemes used. The lane-changing terms, simulating lane-changes due to vehicle interactions as well as spontaneous ones, are introduced as source and sink terms in the model equations. The model provides the ability to use different calibration parameters per lane. The methodology is currently being tested for different problems, including cases with lane-drop. Moreover, an extension of the methodology is under development for the simulation of the flow behavior at on- and off-ramps.

The multi-lane model was applied to a particular 9.45 km long freeway stretch composed of three lanes in the United Kingdom (part of the M56 motorway with direction from Chester to Manchester) to calibrate its parameters under recurrent traffic flow conditions. A parallel, metamodel-assisted Differential Evolution (DE) algorithm, was employed for the calibration of the model parameters by searching for the global optimal solution. The numerical simulations demonstrated that the proposed model is reasonably accurate in reproducing traffic dynamics in the multi-lane framework, while the Differential Evolution algorithm can be effectively used for its calibration, despite the large number of parameters to be estimated in the multi-lane model. Currently, the multi-lane model is applied to a freeway stretch in Greece (Attiki Odos motorway), along with the DE algorithm for parameter calibration.

  • Delis, A. I., Nikolos, I. K., Papageorgiou, M.: Macroscopic Modelling and Simulation of Multi-Lane Traffic. 18th International IEEE Conference on Intelligent Transportation Systems (ITSC 2015), Las Palmas de Gran Canaria, Spain, 15-18 September 2015, pp. 2213-2218.
  • Porfyri, K.N., Delis, A.I., Nikolos, I.K., Papageorgiou, M.: Calibration and validation of a macroscopic multi-lane traffic flow model using a differential evolution algorithm. Proceedings of the 96th Annual Meeting of the Transportation Research Board (TRB), Washington, D.C., USA, 8-12 January 2016, paper no. 17-01340.

Last updated on 13/02/2017.