Probe Vehicle Trajectories Research Articles

Development of a Length-Based Cell-State Framework Toward the Re-Creation of Large-Scale Dense Congestion Patterns

This paper presents the results and novel findings of generating a simplified version of the prevailing traffic features that existed during a major evacuation. Leveraging the underlying framework provided by the widely used cell transmission model, the desire is to reconstruct the unique characteristics of large congestion patterns that propagate under dense traffic states, where limited attempts at scaling this base model have occurred. The length-based cell-state framework presented can reproduce large spatiotemporal congestion patterns that exist, specifically from large-scale evacuations. To further simplify, the framework considers traffic state heuristics which are calibrated through oblique cumulative count and occupancy curves. As a result of this preprocessing technique, an artifact was found from the use of the cumulative curves under the lens of Newell’s two-phase traffic flow theory where three unique, separate queued regimes were identified within the fundamental diagrams. The methodology re-created a unique large-scale congestion pattern that existed during a past regional evacuation event, Hurricane Irma, the subject of this paper. To test this methodology, a large-scale congested period was analyzed, both with probe vehicle trajectory data and stationary radar detector data. Results demonstrate that traffic re-creation into state-based contours was able to be verified near a 90% level of confidence even at large spatiotemporal extents.

Arterial Signal Timing Based on Probe Vehicle Trajectories Under Cyclic Stochastic Demand

Arterial Signal Timing Based on Probe Vehicle Trajectories Under Cyclic Stochastic Demand

Dynamic origin–destination flow estimation for urban road network solely using probe vehicle trajectory data

Dynamic origin–destination (OD) flow is a fundamental input for dynamic network models and simulators. Numerous studies have conducted dynamic OD estimations based on fixed detectors, where a high device coverage rate and data quality are often required to accomplish the desired results. Several existing methods have used probe vehicle trajectories as an additional data source, and generalized least squares (GLS) is commonly recognized as an effective framework. However, the prior matrices used in these models either came from historical data or data obtained by uniform scaling that neglected the variation in penetration rates and suffer from sparsity issues. Moreover, the microscopic information contained in the high-resolution probe vehicle trajectories has not been fully utilized. The possibility of estimating OD flows using only vehicle trajectories without external information is rarely discussed in current literature. Therefore, this paper introduces a dynamic OD flow estimation model solely using probe vehicle trajectories. In the proposed model, two methods based on probe OD pair distribution are proposed to infer prior OD flows. Then the GLS framework is extended by including link travel times as another objective term, and the solution algorithm is adapted to deal with uncertain priors. To validate the proposed model, extensive experiments were conducted on a simulation network. The results show that the proposed model could reliably estimate dynamic OD flows and showed superiority to two existing models. In sensitivity analysis concerning the penetration rate and degree of saturation, the proposed model presented satisfactory performance and could adapt to various conditions.

Route flow estimation based on the fusion of probe vehicle trajectory and automated vehicle identification data

Accurate estimation of route flow is crucial to traffic control optimization. Existing route flow estimation models are typically built upon strong assumptions on traveler route choice behavior or turn to data-driven approaches which heavily rely on prior OD estimation and high sensor coverage rate. This study proposes a route flow estimation framework by fusing the probe vehicle trajectory and automated vehicle identification (AVI) data. The notion of probe vehicle route penetration rate (RPR) is utilized for the construction of a novel data-driven objective function. Sensor-OD flow and observable route flow penetration are formulated as model constraints. The solution uniqueness is guaranteed though an iterative procedure under the principle of entropy maximization. Numerical studies are conducted based on pNEUMA, a large-scale full sample trajectory dataset. Results show that the proposed model performs better than the traditional path flow estimation model, especially when the prior flow information is not available. Sensitivity analysis on AVI sensor coverage rate, probe vehicle route coverage rate and RPR distribution demonstrates the proposed model’s applicability in practice.

Incorporating Kinematic Wave Theory Into a Deep Learning Method for High-Resolution Traffic Speed Estimation

We propose a kinematic wave-based Deep Convolutional Neural Network (Deep CNN) to estimate high-resolution traffic speed fields from sparse probe vehicle trajectories. We introduce two key approaches that allow us to incorporate kinematic wave theory principles to improve the robustness of existing learning-based estimation methods. First, we propose an anisotropic traffic kernel for the Deep CNN. The anisotropic kernel explicitly accounts for space-time correlations in macroscopic traffic and effectively reduces the number of trainable parameters in the Deep CNN model. Second, we propose to use simulated data for training the Deep CNN. Using a targeted simulated data for training provides an implicit way to impose desirable traffic physical features on the learning model. In the experiments, we highlight the benefits of using anisotropic kernels and evaluate the transferability of the trained model to real-world traffic using the Next Generation Simulation (NGSIM) and the German Highway Drone (HighD) datasets. The results demonstrate that anisotropic kernels significantly reduce model complexity and model over-fitting, and improve the physical correctness of the estimated speed fields. We find that model complexity scales linearly with problem size for anisotropic kernels compared to quadratic scaling for isotropic kernels. Furthermore, evaluation on real-world datasets shows acceptable performance, which establishes that simulation-based training is a viable surrogate to learning from real-world data. Finally, a comparison with standard estimation techniques shows the superior estimation accuracy of the proposed method.

A streaming-data-driven method for freeway traffic state estimation using probe vehicle trajectory data

This paper proposes a streaming-data-driven method for freeway traffic state estimation based on probe vehicle trajectory data, which are represented by a series of timestamps, spatial locations, and instantaneous speeds. The flow and density of a freeway section are reconstructed by estimating the numbers of normal vehicles between consecutive probe vehicles. Specifically, freeway traffic process is divided into different episodes based on the occurrence of shockwaves. The speed of a shockwave is assumed stochastic, and its posterior distribution is estimated via Bayesian regression. Based on the estimated shockwave speed, the number of vehicles between the most downstream and most upstream probe vehicles in an episode is estimated based on Newell’s simplified car-following theory. Then the penetration rate of probe vehicles can be obtained and the numbers of normal vehicles among the probe vehicles that are not captured by shockwaves can also be estimated. Finally, the trajectories of the normal vehicles are reconstructed using linear interpolation. The proposed approach is demonstrated by a simulation experiment and a real-world case study. A good estimation accuracy is achieved even when the penetration rates are as low as 5%–20%. The proposed method is also compared with a state-of-the-art method in the simulation study, which also estimates freeway traffic state solely based on probe vehicle trajectory data. It achieves a comparable performance without spacing information in the trajectory data.

Dynamic Path Flow Estimation Using Automatic Vehicle Identification and Probe Vehicle Trajectory Data: A 3D Convolutional Neural Network Model

Dynamic path flows, referring to the number of vehicles that choose each path in a network over time, are generally estimated with the partial observations as the input. The automatic vehicle identification (AVI) system and probe vehicle trajectories are now popular and can provide rich and complementary trip information, but the data fusion was rarely explored. Therefore, in this paper, the dynamic path flow estimation is based on these two data sources and transformed into a feature learning problem. To fuse the two data sources belonging to different detection ways at the data level, the virtual AVI points, analogous to the real AVI points (turning movements at nodes with AVI detectors), are defined and selected to statically observe the dynamic movement of the probe vehicles. The corresponding selection principles and a programming model considering the distribution of real AVI points are first established. The selected virtual AVI points are used to construct the input tensor, and the turning movement-based observations from both the data sources can be extracted and fused. Then, a three-dimensional (3D) convolutional neural network (CNN) model is designed to exploit the hidden patterns from the tensor and establish the high-dimensional correlations with path flows. As the path flow labels commonly with noises, the bootstrapping method is adopted for model training and the corresponding relabeling principle is defined to purify the noisy labels. The entire model is extensively tested based on a realistic road network, and the results show that the designed CNN model with the presented data fusion method can perform well in training time and estimation accuracy. The robustness of a model to noisy labels is also improved through the bootstrapping method. The dynamic path flows estimated by the trained model can be applied to travel information provision, proactive route guidance, and signal control with high real-time requirements.

Cycle-Based Queue Length Estimation for Signalized Intersections Using Sparse Vehicle Trajectory Data

Intersection queue length estimation using high-resolution probe vehicle trajectory data has received increasing attentions in recent years. Existing methods for cycle-based queue length estimation still face the challenge of low and/or unstable estimation accuracies under the condition of sparse vehicle trajectory data, i.e., there is no greater than one vehicle trajectory per cycle on average. To address this challenge, this study proposed a novel approach for cycle-based queue length estimation by fusing real-time and historical probe vehicle trajectory data, through a statistical parameter estimation method, i.e., maximum likelihood estimation (MLE). With known signal timing information, firstly, the historical probe trajectory data are used to acquire the arrival flow rate distribution over the entire study period. Then, a likelihood function of queue length is derived by fully exploiting real-time traffic flow information provided by the queued and non-queued probe vehicles. Finally, the MLE method is adopted to estimate the cycle-based queue lengths with the maximum probability. The proposed approach is verified using both simulation and empirical data. Results indicate that precise estimation for cycle-based queue lengths can be realized based on sparse vehicle trajectory data, while showing superiority to a representative existing method. The proposed method is basically an offline method, but it can also work in an online manner if provided a priori arrival distribution either acquired from historical probe vehicle trajectory data or a theoretical assumption.

Scalable and Actionable Performance Measures for Traffic Signal Systems using Probe Vehicle Trajectory Data

Scalable and actionable performance measures for traffic signal systems provide opportunities for practitioners to measure and improve the transportation network. Historically, traffic signal improvements have relied on scheduled signal retiming based on limited data collection, or on the public to call and alert engineers of an issue. This inefficient method of improving signal timing led to the creation of automated traffic signal performance measures (ATSPMs). These metrics rely on expensive infrastructure, including detection and communications, which has produced barriers for numerous agencies to fully adopt. Recently, third-party data providers have begun to release vehicle trajectory data, which allows for enhanced signal metrics with no investment in physical equipment. The purpose of this study is to demonstrate the use of these data and summarize the scalability of the created metrics. This work builds on previous efforts to quantify signal performance on nine intersections in Michigan, U.S. Ten signalized corridors in Columbus, Ohio, were chosen to scale a performance assessment using crowdsourced trajectory data. A total of 136 intersections were assessed in 2-h intervals using data from all weekdays in 2017. High-level corridor summary metrics including average percent of vehicles stopping (18%–32%), average delay (9.4–20.5 s), and level of travel time reliability (1.23–2.73) were calculated for each corridor direction. Intersection-level metrics were also introduced, which can be used by practitioners to identify problems, improve signal timings, and prioritize future infrastructure investments.

Replicating Advanced Detection using Low Ping Frequency Probe Vehicle Trajectory Data to Optimize Signal Progression

Probe vehicle trajectory data has the potential to transform the current practice of traffic signal optimization. Current scalable trajectory data is limited in both the penetration rate and the ping frequency, or the length of time between vehicle waypoints. This paper introduces a methodology to create binary vehicle trajectories which can be used in a neural network to predict when vehicles will arrive at a virtual detector. The methodology allows for vehicles with ping frequencies of up to 60 s to be utilized for the optimization of offsets at signalized intersections. A nine-signal corridor in west Michigan was used to test the proposed methodology. The neural network was compared to traditional linear interpolation strategies and found to improve the root mean squared error of the arrival times by up to 6.18 s. Using the virtual detector data stacked over time to optimize the offsets of the corridor resulted in 77% of the benefit of an offset optimization performed with continuously collected high resolution signal controller data. In the era of big data, this alternative approach can assist with the large-scale implementation of traffic signal performance measures for improved operations.

Characterizing Traffic-Signal Performance and Corridor Reliability Using Crowd-Sourced Probe Vehicle Trajectories

AbstractPerformance measures offer an essential management tool for transportation engineers to make decisions along signalized corridors. Current signal performance strategies assess coordination ...

Fuzing license plate recognition data and vehicle trajectory data for lane-based queue length estimation at signalized intersections

Queue length is one of the most important performance measures for signalized intersections. With recent advancements in connected vehicles and intelligent mobility technologies, utilizing vehicle trajectory data to estimate queue length has received considerable attentions. However, most of the existing methods are based on some assumptions, such as known arrival patterns and/or high penetration rates. Besides, existing models would probably be unstable or invalid under sparse trajectory environment. Hence, license plate recognition (LPR) data is introduced in this study to fuze with the vehicle trajectory data, and then, a lane-based queue length estimation method is proposed. First, by matching the LPR data with probe vehicle data, the two-dimensional probability density distribution of discharge headway and stop-line crossing time of various kinds of vehicles, i.e., queued and nonqueued vehicle for undersaturated condition and twice-queued and once-queued vehicle for oversaturated condition, can be calibrated. Then, the Bayesian theory is adopted to derive the lane-based queue length for undersaturated condition as well as the initial queue for oversaturated condition with the largest possibility, respectively. Where probe vehicle trajectories, if existed, will provide the boundaries for the estimated queue lengths. Finally, the performance of the proposed method is evaluated using both simulation and empirical data. Simulation results show that the proposed method could produce accurate estimates of queue lengths for both undersaturated and oversaturated conditions and can achieve reliable estimates even under low penetration rate (3%). Empirical results show that the proposed method outperforms an existing method using probe vehicle trajectories only.

Prediction of moving bottleneck through the use of probe vehicles: a simulation approach in the framework of three-phase traffic theory

Based on simulations in the framework of Kerner’s three-phase traffic theory, we present a methodology for the prediction of a moving bottleneck (MB) with the use of a small share of probe vehicles (floating car data – FCD) randomly distributed in traffic flow. In this methodology, a conclusion of the three-phase traffic theory has been used that in the vicinity of any bottleneck there can be observed phase transitions between free flow and synchronized flow. The presented methodology is based on the recognition of phase transition points from synchronized flow to free flow on probe vehicle trajectories. For the simulations, we have used the Kerner–Klenov microscopic stochastic traffic flow model. It has been found that the MB can be predicted even if about 1% of probe vehicles are in traffic flow. The time-function of the probability of MB prediction in dependence of the share of probe vehicles in traffic flow has been calculated. We have found that the time-dependence of the probability of MB prediction as well as the accuracy of the estimation of MB location depend considerably on the occurrence of sequences of phase transitions from free flow to synchronized flow and back from synchronized flow to free flow occurring before traffic breakdown at the MB as well as speed oscillations in synchronized flow at the MB. The methodology of MB prediction presented in the paper can be used by either automated driving vehicles or other ITS-applications for speed harmonization, collision avoidance that should increase traffic safety and comfort.

Various methods for queue length and traffic volume estimation using probe vehicle trajectories

The rapid development of connected vehicle technology and the emergence of ride-hailing services have enabled the collection of a tremendous amount of probe vehicle trajectory data. Due to the large scale, the trajectory data have become a potential substitute for the widely used fixed-location sensors in terms of the performance measures of transportation networks. Specifically, for traffic volume and queue length estimation, most of the trajectory data based methods in the existing literature either require high market penetration of the probe vehicles to identify the shockwave or require the prior information about the queue length distribution and the penetration rate, which may not be feasible in the real world. To overcome the limitations of the existing methods, this paper proposes a series of novel methods based on probability theory. By exploiting the stopping positions of the probe vehicles in the queues, the proposed methods try to establish and solve a single-variable equation for the penetration rate of the probe vehicles. Once the penetration rate is obtained, it can be used to project the total queue length and the total traffic volume. The validation results using both simulation data and real-world data show that the methods would be accurate enough for assistance in performance measures and traffic signal control at intersections, even when the penetration rate of the probe vehicles is very low.

Estimation of Queue Lengths, Probe Vehicle Penetration Rates, and Traffic Volumes at Signalized Intersections using Probe Vehicle Trajectories

With the development of connected vehicle technologies and the emergence of e-hailing services, a vast amount of vehicle trajectory data is being collected every day. This massive amount of trajectory data could provide a new perspective for sensing, diagnosing, and optimizing transportation networks. There has been some literature estimating traffic volumes and queue lengths at intersections using the data collected from these probe vehicles. Nevertheless, some of the existing methods only work when the penetration rate of the probe vehicles is high enough. Some other methods require two critical inputs, the distribution of the queue lengths and the penetration rate of the probe vehicles. However, these two inputs might vary a lot both spatially and temporally and are not usually known in the real world. To fill the gap, this paper proposes a novel method for the estimation of queue lengths, probe vehicle penetration rates, and traffic volumes at signalized intersections. The key step is to estimate the penetration rate of the probe vehicles from the distribution of their stopping positions at the intersections. Then, scaling up the number of probe vehicles in the queues and in the traffic according to the estimated penetration rate will give an estimate of the total queue length and the total traffic volume, respectively. The proposed method has been validated by both simulation data and real-field data. The testing results have shown that the method is ready for large-scale real-field applications.

Trajectory-Based Measurement of Signalized Intersection Capacity

Capacities of road intersections are a limiting factor and crucial for the performance of road networks. Therefore, for purposes of intersection design and of optimal signal timing, numerous methodologies have been proposed to either estimate or directly measure the capacity of single movements at road intersections. However, both model-based estimation and direct measurement suffer from the large effort that is needed to gather the relevant data. Even worse, once the data are collected they only represent a snapshot of the capacity over time. This paper proposes an alternative approach to estimate capacity of signalized road intersections over time using only automatically generated trajectories of probe vehicles. The obtained capacity can be used to evaluate the effective degree of saturation using real demand, or to assess hypothetic different conditions in demand or signaling. The cyclic operation of signalized intersections allows for the accumulation of trajectories, and thus in practical applications for the compensation of potentially low penetration rates. Within a sequential process the intersection’s cycle time and the approach green time and saturation flow rates are determined. The determination of the cycle time and the green times is based on an existing approach. The derivation of the saturation flow rates relies on its direct dependency to the saturation time headway and uses two parameters to be calibrated. Testing with a commercial dataset on an intersection in Munich produced a good signal timing estimation and saturation flow values that are comparable to a calculation based on the German guideline.

Fundamental diagram estimation by using trajectories of probe vehicles

The fundamental diagram (FD), also known as the flow–density relation, is one of the most fundamental concepts in the traffic flow theory. Conventionally, FDs are estimated by using data collected by detectors. However, detectors’ installation sites are generally limited due to their high cost, making practical implementation of traffic flow theoretical works difficult. On the other hand, probe vehicles can collect spatially continuous data from wide-ranging area, and thus they can be useful sensors for large-scale traffic management. In this study, a novel framework of FD estimation by using probe vehicle data is developed. It determines FD parameters based on trajectories of randomly sampled vehicles and a given jam density that is easily inferred by other data sources. A computational algorithm for estimating a triangular FD based on actual, potentially noisy traffic data obtained by multiple probe vehicles is developed. The algorithm was empirically validated by using real-world probe vehicle data on a highway. The results suggest that the algorithm accurately and robustly estimates the FD parameters.

Calibration of fundamental diagram using trajectories of probe vehicles: Basic formulation and heuristic algorithm

Abstract: A fundamental diagram (FD), also known as flow–density relation, is one of the most important principles in traffic flow theory. It would be valuable if an FD could be calibrated by using GPS-equipped probe vehicles; since they can continuously collect data from wide spatiotemporal area, compared to traditional fixed sensors. This paper proposes methods for calibrating an FD from trajectories of sampled vehicles. We formulate a method that identifies values of a free-flow speed and a critical density of a tri-angular FD, while it relies on exogenous assumptions on FD's functional form and a value of its jam density. Then, a heuristic algorithm for FD calibration in actual traffic environment is developed based on the proposed method. It was validated using traffic data generated by microscopic traffic simulator. The results suggested that the proposed methods can calibrate an FD precisely and robustly. It implies that FDs in road sections on which congestion happens frequently can be calibrated using probe vehicles, if probe vehicle data were collected for a long period. Therefore, the proposed methods would contribute to significant improvement of applicability of probe vehicle-based traffic management methods.

Real-Time Queue Length Estimation for Signalized Intersections Using Vehicle Trajectory Data

Queue length is one of the most important performance measures for signalized intersections. Many methods for queue length estimation based on various data sources have been proposed in the literature. With the latest developments and applications of probe vehicle systems, cycle-by-cycle queue length estimation based only on probe data has become a promising research topic. However, most existing methods assume that information such as signal timing, arrival pattern, and penetration rate is known, an assumption that constrains their applicability in practice. The objective of this study was to propose a cycle-by-cycle queue length estimation method using only probe data without the foregoing assumption. Based on the shock wave theory, the proposed method is capable of reproducing the dynamic queue forming and dissipating process cycles at signalized intersections by using probe vehicle trajectories. To reproduce the queuing processes, the inflection points of probe vehicle trajectories representing the changes of arrival patterns are identified and extracted from the trajectory points of vehicles joining and leaving the queue. A piecewise linear function is then used to fit all the inflection points to estimate the stopping and discharging shock waves. Finally, signal timing data and queue lengths can be calculated on the basis of the estimated shock waves. Under both saturated and oversaturated traffic conditions, the performance of the method is comprehensively evaluated through 60 simulation scenarios, which cover sampling intervals from 5 s to 60 s and penetration rates ranging from 5% to 100%. Results show that compared with the method proposed by Ramezani and Geroliminis in 2015, the proposed method has more robustness for all the sampling intervals and displays more estimation accuracy of queue length and a higher success rate under conditions of low penetration rate.

Estimating Freeway Traffic Volume Using Shockwaves and Probe Vehicle Trajectory Data

Abstract: Probe vehicle data are increasingly becoming the primary source of traffic data. In current practice, traffic volumes and speeds are collected from inductive loop or similar devices. As probe vehicle data become more widespread, it is imperative that methods are developed so that traffic state estimators like speed, density and flow can be derived from probe vehicle data as well. In this paper, a methodology to estimate traffic flow on a freeway based on probe vehicle trajectory data combined with traffic shockwave theory is proposed. In essence, probe vehicle trajectory can indicate the free-flowing and congested regimes. By using LWR kinematic wave model, a shockwave can be identified that separates both regimes. From the formation of the shockwave, flows for each regime are estimated. To identify the shockwave, k-means clustering is applied to the data. When applied to simulated data, the error of the estimated flow during free-flow ranges from -9% to 1% with an average of -5%. The estimated flow during congestion has an error of 0%. Based on the results, this paper shows that the proposed method can predict traffic flow with a reasonable accuracy under congested and free-flow conditions.