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.     

An observed traffic pattern in long freeway queues

A simple exercise in data analysis showed that, in queued traffic, a well-defined relation exists between the flow on a homogeneous freeway segment and the segment’s vehicle accumulation. The exercise consisted of constructing cumulative vehicle arrival curves to measure the flows and densities on multiple segments of a queued freeway. At this particular site, each interchange enveloped by the queue exhibited a higher on-ramp flow than off-ramp flow and as a consequence, motorists encountered a steady improvement in traffic conditions (e.g., reduced densities and increased speeds) as they traveled from the tail of the queue to the bottleneck. This finding has practical implications for freeway traffic planning and management. Perhaps most notably, it suggests that the first-order hydrodynamic theory of traffic is adequate for describing some of the more relevant features of queue evolution. This and other practical issues are discussed in some detail.     

RENAISSANCE – A unified macroscopic model-based approach to real-time freeway network traffic surveillance

The paper presents a unified macroscopic model-based approach to real-time freeway network traffic surveillance as well as a software tool RENAISSANCE that has been recently developed to implement this approach for field applications. RENAISSANCE is designed on the basis of stochastic macroscopic freeway network traffic flow modeling, extended Kalman filtering, and a number of traffic surveillance algorithms. Fed with a limited amount of real-time traffic measurements, RENAISSANCE enables a number of freeway network traffic surveillance tasks, including traffic state estimation and short-term traffic state prediction, travel time estimation and prediction, queue tail/head/length estimation and prediction, and incident alarm. The traffic state estimation and prediction lay the operating foundation of RENAISSANCE since RENAISSANCE bases the other traffic surveillance tasks on its traffic state estimation or prediction results. The paper first introduces the utilized stochastic macroscopic freeway network traffic flow model and a real-time traffic measurement model, upon which the complete dynamic system model of RENAISSANCE is established with special attention to the handling of some important model parameters. The algorithms for the various traffic surveillance tasks addressed are described along with the functional architecture of the tool. A simulation test was conducted via application of RENAISSANCE to a hypothetical freeway network example with a sparse detector configuration, and the testing results are presented in some detail. Final conclusions and future work are outlined.     

Traffic state estimation and uncertainty quantification based on heterogeneous data sources: A three detector approach

This study focuses on how to use multiple data sources, including loop detector counts, AVI Bluetooth travel time readings and GPS location samples, to estimate macroscopic traffic states on a homogeneous freeway segment. With a generalized least square estimation framework, this research constructs a number of linear equations that map the traffic measurements as functions of cumulative vehicle counts on both ends of a traffic segment. We extend Newell’s method to solve a stochastic three-detector problem, where the mean and variance estimates of cell-based density and flow can be analytically derived through a multinomial probit model and an innovative use of Clark’s approximation method. An information measure is further introduced to quantify the value of heterogeneous traffic measurements for improving traffic state estimation on a freeway segment.     

A stochastic model of traffic flow: Theoretical foundations

In a variety of applications of traffic flow, including traffic simulation, real-time estimation and prediction, one requires a probabilistic model of traffic flow. The usual approach to constructing such models involves the addition of random noise terms to deterministic equations, which could lead to negative traffic densities and mean dynamics that are inconsistent with the original deterministic dynamics. This paper offers a new stochastic model of traffic flow that addresses these issues. The source of randomness in the proposed model is the uncertainty inherent in driver gap choice, which is represented by random state dependent vehicle time headways. A wide range of time headway distributions is allowed. From the random time headways, counting processes are defined, which represent cumulative flows across cell boundaries in a discrete space and continuous time conservation framework. We show that our construction implicitly ensures non-negativity of traffic densities and that the fluid limit of the stochastic model is consistent with cell transmission model (CTM) based deterministic dynamics.     

Understanding the variability of speed distributions under mixed traffic conditions caused by holiday traffic

Understanding the variability of speed patterns and congestion characteristics of interstate freeway systems caused by holiday traffic is beneficial because appropriate countermeasures for safety improvement and congestion mitigation can be prepared and drivers can avoid traffic congestion and change their holiday travel schedules. This study evaluated the traffic congestion patterns during the Thanksgiving holiday period in 2006 using a Gaussian mixture speed distribution estimated by the Expectation–Maximization (EM) algorithm. This mathematical approach showed the potential of improving freeway operational performance evaluation schemes for holiday periods (even non-holiday periods). This study suggested that a Gaussian mixture model using the EM algorithm could be used to properly characterize the severity and the variability of congestion on certain interstate roadway systems. However, this study also pointed out that the fundamental limitations of the mixture model and the statistical significance test about the mixture components should be well understood and need to be further investigated. In addition, because this study investigated the changing patterns of speed distributions with only one interstate freeway system, I-95 northbound, other freeway systems with both directions need to be evaluated so that a more broad and confident analysis on holiday traffic can be achieved.     

Closed-form multiclass cell transmission model enhanced with overtaking,lane-changing,and first-in first-out properties

A novel multiclass macroscopic model is proposed in this article. In order to enhance first-in, first-out property (FIFO) and transmission function in the multiclass traffic modeling, a new multiclass cell transmission model with FIFO property (herein called FM-CTM) is extended from its prior multiclass cell transmission model (M-CTM). Also, to enhance its analytical compactness and resultant computational convenience, FM-CTM is formulated in this paper as a set of closed-form matrix equations. The objective is to improve the accuracy of traffic state estimation by enforcing FIFO property when a fast vehicle cannot overtake a slow vehicle due to a limitation of a single-lane road. Moreover, the proposed model takes into account a different priority for vehicles of each class to move forward through congested road conditions, and that makes the flow calculation independent from their free-flow speeds. Some hypothetical and real-world freeway networks with a constant or varying number of lanes are selected to verify FM-CTM by comparing with M-CTM and the conventional CTM. Observed densities of VISSIM and real-world dataset of I-80 are selected to compare with the simulated densities from the three CTMs. The numerical results show that FM-CTM outperforms the other two models by 15% of accuracy measures in most cases. Therefore, the proposed model is expected to be well applicable to the road network with a mixed traffic and varying number of lanes.     

A Pareto-optimization approach for a fair ramp metering

This paper deals with a fair ramp metering problem which takes into account average travel delay distribution among on-ramps for an expressway system comprising expressways, on-ramps and off-ramps. A novel spatial equity index is defined to measure the evenness of travel delay distribution among on-ramps within the predefined on-ramp groups. An ideal fair ramp metering problem therefore aims to find an optimal dynamic ramp metering rate solution that not only minimizes the total system delay, but also maximizes the equity indexes associated to the groups. Some of these objectives, however, contradict with each other, and their Pareto-optimality is explored. The fair ramp metering problem proposed in this paper is formulated as a multiobjective optimization model incorporating a modified cell-transmission model (MCTM) that captures dynamic traffic flow pattern with ramp metering operations. The MCTM then is embedded in the Non-dominated Sorting Genetic Algorithm II (NSGA-II) to solve the multiobjective optimization model. Finally, the Interstate I-210 W expressway-ramp network in the United States is adopted to assess the methodology proposed in this paper.     

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.     

Modelling a signal controlled traffic stream using cellular automata

Cellular automata models have formed the theory for the development of several transportation models to simulate various types of elements such as vehicles, pedestrians or even railway traffic. Furthermore, they have been applied to simulate several scenarios from very simple (freeway traffic) to rather complicated ones (lane reduction and signal optimisation). However, the properties of the model when used to simulate a signal controlled traffic stream have not been dealt with in great detail. This paper discusses several issues that arise while using the model for the simulation of traffic at signalised intersections. It also investigates the relationships between the randomisation parameter of the model, the model dynamics and the estimated saturation flow. For the deterministic version of the model, the formulas describing traffic quantities at the intersection are derived and are dependent on the desired speed – a parameter of the model. For the stochastic version, one can adopt several different approaches for the application of the randomisation rule, depending on the simulation needs.     

A macroscopic traffic model for highway work zones: Formulations and numerical results

This study presents a multilane model for analyzing the dynamic traffic properties of a highway segment under a lane‐closure operation that often incurs complex interactions between mandatory lane‐changing vehicles and traffic at unblocked lanes. The proposed traffic flow formulations employ the hyperbolic model used in the non‐Newtonian fluid dynamics, and assume the lane‐changing intensity between neighboring lanes as a function of their difference in density. The results of extensive simulation experiments indicate that the proposed model is capable of realistically replicating the impacts of lane‐changing maneuvers from the blocked lanes on the overall traffic conditions, including the interrelations between the approaching flow density, the resulting congestion level, and the exiting flow rate from the lane‐closure zone. Our extensive experimental analyses also confirm that traffic conditions will deteriorate dramatically and evolve to the state of traffic jam if the density has exceeded its critical level that varies with the type of lane‐closure operations. This study also provides a convenient way for computing such a critical density under various lane‐closure conditions, and offers a theoretical basis for understanding the formation as well as dissipation of traffic jam.     

Modeling the day-to-day traffic evolution process after an unexpected network disruption

Although various approaches have been proposed for modeling day-to-day traffic flow evolution, none of them, to the best of our knowledge, have been validated for disrupted networks due to the lack of empirical observations. By carefully studying the driving behavioral changes after the collapse of I-35W Mississippi River Bridge in Minneapolis, Minnesota, we found that most of the existing day-to-day traffic assignment models would not be suitable for modeling the traffic evolution under network disruption, because they assume that drivers’ travel cost perception depends solely on their experiences from previous days. When a significant network change occurs unexpectedly, travelers’ past experience on a traffic network may not be entirely useful because the unexpected network change could disturb the traffic greatly. To remedy this, in this paper, we propose a prediction-correction model to describe the traffic equilibration process. A “predicted” flow pattern is constructed inside the model to accommodate the imperfect perception of congestion that is gradually corrected by actual travel experiences. We also prove rigorously that, under mild assumptions, the proposed prediction-correction process has the user equilibrium flow as a globally attractive point. The proposed model is calibrated and validated with the field data collected after the collapse of I-35W Bridge. This study bridges the gap between theoretical modeling and practical applications of day-to-day traffic equilibration approaches and furthers the understanding of traffic equilibration process after network disruption.     

Optimization of mainline traffic via an adaptive co-ordinated ramp-metering control model with dynamic OD estimation

Frequently implemented at freeway accesses to streamline traffic, ramp-metering control strategy is often implemented during rush hours in heavily congested areas. This paper presents a novel ramp-metering control model capable of optimizing mainline traffic by providing metering rates for accesses within the control segments. Based on Payne's continuum traffic stream model, a linear dynamic model with a quadratic objective function is constructed for integrated-responsive ramp-metering control. Incorporating on-line origin–destination (OD) estimation of co-ordinated interchanges into the proposed model increases efficiency of the control. In addition, an iterative algorithm is proposed to obtain the optimal solution. Simulation results demonstrate the robustness of the proposed model and its ability to streamline freeway traffic while avoiding traffic congestion.     

A phenomenological model for dynamic traffic flow in networks

A macroscopic model for dynamic traffic flow is presented. The main goal of the model is the real time simulation of large freeway networks with multiple sources and sinks. First, we introduce the model in its discrete formulation and consider some of its properties. It turns out, that our non-hydrodynamical ansatz for the flows results in a very advantageous behavior of the model. Next the fitting conditions at junctions of a traffic network are discussed. In the following sections we carry out a continuous approximation of our discrete model in order to derive stationary solutions and to consider the stability of the homogeneous one. It turns out, that for certain conditions unstable traffic flow occurs. In a subsequent section, we compare the stability of the discrete model and the corresponding continuous approximation. This confirms in retrospection the close similarities of both model versions. Finally we compare the results of our model with the results of another macroscopic model, that was recently suggested by Kerner and Konhäuser [Phys. Rev. E 48, 2335–2338 (1993)].     

Brake light cellular automaton model with advanced randomization for traffic breakdown

Traffic breakdown is one of the most important empirical phenomena in traffic flow theory. Unfortunately, it cannot be simulated by many traffic flow models. In order to clarify its mechanism, the new brake light cellular automaton model has been proposed. Comparing with previous brake light models, three different aspects have been considered: (i) drivers tend to take large decelerations if the time gap is smaller than the safe time gap and the leading vehicle’s brake light is on; (ii) the brake light rule is set according to the reality; (iii) the randomization rule is put forward before the acceleration rule to weaken the impact of brake light on driving behaviors. Analyses show that the new model can explain the mechanism of traffic breakdown and the failures of other brake light models. Simulations confirm that all empirical features of traffic breakdown are successfully reproduced. At last, brake light models are calibrated and validated by the I-80 empirical data provided by NGSIM. Results show that the performance of the new model is the best and models in the three-phase theory are not necessarily better than models in the fundamental diagram approach and vice versa, at least for the brake light models.     

Exploring the impact of connected and autonomous vehicles on freeway capacity using a revised Intelligent Driver Model

ABSTRACT

Connected and autonomous vehicle (CAV) technologies are expected to change driving/vehicle behavior on freeways. This study investigates the impact of CAVs on freeway capacity using a microsimulation tool. A four-lane basic freeway segment is selected as the case study through the Caltrans Performance Measurement System (PeMS). To obtain valid results, various driving behavior parameters are calibrated to the real traffic conditions for human-driven vehicles. In particular, the calibration is conducted using genetic algorithm. A revised Intelligent Driver Model (IDM) is developed and used as the car-following model for CAVs. The simulation is conducted on the basic freeway segment under different penetration rates of CAVs and different freeway speed limits. The results show that with an increase in the market penetration rate, freeway capacity increases, and will increase significantly as the speed limit increases.     

A chance-constrained based stochastic dynamic traffic assignment model: Analysis, formulation and solution algorithms

This paper is concerned with the system optimum-dynamic traffic assignment (SO-DTA) problem when the time-dependent demands are random variables with known probability distributions. The model is a stochastic extension of a deterministic linear programming formulation for SO-DTA introduced by Ziliaskopoulos (Ziliaskopoulos, A.K., 2000. A linear programming model for the single destination system optimum dynamic traffic assignment problem, Transportation Science, 34, 1–12). The proposed formulation is chance-constrained based and we demonstrate that it provides a robust SO solution with a user specified level of reliability. The model provides numerous insights and can be a useful tool in producing robust control and management strategies that account for uncertainty in applications where SO-DTA is relevant (e.g. evacuation modeling, computing alternate routes around freeway incidents and establishing lower bounds on network performance).     

On the macroscopic stability of freeway traffic

A simple model of traffic flow is used to analyze the spatio-temporal distribution of flow and density on closed-loop homogeneous freeways with many ramps, which produce inflows and allow outflows. As we would expect, if the on-ramp demand is space-independent then this distribution tends toward uniformity in space if the freeway is either: (i) uncongested; or (ii) congested with queues on its on-ramps and enough inflow to cause the average freeway density to increase with time. In all other cases, however, including any recovery phase of a rush hour where the freeway’s average density declines, the distribution of flow and density quickly becomes uneven. This happens even under conditions of perfect symmetry, where the percentage of vehicles exiting at every off ramp is the same. The flow-density deviations from the average are shown to grow exponentially in time and propagate backwards in space with a fixed wave speed. A consequence of this type of instability is that, during recovery, gaps of uncongested traffic will quickly appear in the unevenly congested stream, reducing average flow. This extends the duration of recovery and invariably creates clockwise hysteresis loops on scatter-plots of average system flow vs. density during any rush hour that oversaturates the freeway. All these effects are quantified with formulas and verified with simulations. Some have been observed in real networks. In a more practical vein, it is also shown that the negative effects of instability diminish (i.e., freeway flows increase) if (a) some drivers choose to exit the freeway prematurely when it is too congested and/or (b) freeway access is regulated in a certain traffic-responsive way. These two findings could be used to improve the algorithms behind VMS displays for driver guidance (finding a), and on-ramp metering rates (finding b).     

A mesoscopic integrated urban traffic flow-emission model

Due to the noticeable environmental and economical problems caused by traffic congestion and by the emissions produced by traffic, analysis and control of traffic is essential. One of the various traffic analysis approaches is the model-based approach, where a mathematical model of the traffic system is developed/used based on the governing physical rules of the system. In this paper, we propose a framework to interface and integrate macroscopic flow models and microscopic emission models. As a result, a new mesoscopic integrated flow-emission model is obtained that provides a balanced trade-off between high accuracy and low computation time. The proposed approach considers an aggregated behavior for different groups of vehicles (mesoscopic) instead of considering the behavior of individual vehicles (microscopic) or the entire group of vehicles (macroscopic). A case study is done to evaluate the proposed framework, considering the performance of the resulting mesoscopic integrated flow-emission model. The traffic simulation software SUMO combined with the microscopic emission model VT-micro is used as the comparison platform. The results of the case study prove that the proposed approach provides excellent results with high accuracy levels. In addition, the mesoscopic nature of the integrated flow-emission model guarantees a low CPU time, which makes the proposed framework suitable for real-time model-based applications.     

A phase-based smoothing method for accurate traffic speed estimation with floating car data

In this paper, a novel freeway traffic speed estimation method based on probe data is presented. In contrast to other traffic speed estimators, it only requires velocity data from probes and does not depend on any additional data inputs such as density or flow information. In the first step the method determines the three traffic phases free flow, synchronized flow, and Wide Moving Jam (WMJ) described by Kerner et al. in space and time. Subsequently, reported data is processed with respect to the prevailing traffic phase in order to estimate traffic velocities. This two-step approach allows incorporating empirical features of phase fronts into the estimation procedure. For instance, downstream fronts of WMJs always propagate upstream with approximately constant velocity, and downstream fronts of synchronized flow phases usually stick to bottlenecks. The second step assures the validity of measured velocities is limited to the extent of its assigned phase. Effectively, velocity information in space-time can be estimated more distinctively and the result is therefore more accurate even if the input data density is low.The accuracy of the proposed Phase-Based Smoothing Method (PSM) is evaluated using real floating car data collected during two traffic congestions on the German freeway A99 and compared to the performance of the Generalized Adaptive Smoothing Method (GASM) as well as a naive algorithm. The quantitative and qualitative results show that the PSM reconstructs the congestion pattern more accurately than the other two. A subsequent analysis of the computational efficiency and sensitivity demonstrates its practical suitability.