Penetration Rate Of Probe Vehicles Research Articles

Bayesian inference for estimating the penetration rate of probe vehicles from interdetection times only

Data provided by floating vehicles have the same limitation as that provided by an imperfect stationary detector that undercounts vehicles: they provide data from an unknown proportion of the total flow. Since the knowledge of this proportion is critical for some applications, its value is usually estimated by complementing with data provided by other monitoring infrastructure. However, this type of infrastructure is not the norm in many cities, particularly in developing countries. This paper extends a previously proposed method to estimate this penetration solely from a series of inter-detection times. The improved method is based on Bayesian inference and supports a series of passage times coming from multilane infrastructure, albeit still requiring an uninterrupted traffic regime. The method was applied to actual RFID interdetection times from a four-lane weaving urban freeway segment in Santiago, Chile. The resulting estimated rates are consistent with those reported by the freeway operator, showing the method’s capabilities. Thus, the method is instrumental in successfully taking full advantage of technology already in place in many cities without needing new investments in monitoring infrastructure.

Sequence-to-Sequence Recurrent Graph Convolutional Networks for Traffic Estimation and Prediction Using Connected Probe Vehicle Data

Traffic estimation is imperative for conducting fundamental transportation engineering tasks such as transportation planning and traffic safety studies. Additionally, traffic prediction is vital for many data-driven intelligent transportation system applications. Most traffic estimation and prediction methods rely on infrastructure-based sensors to collect traffic parameters. However, infrastructure-based data collection can be costly and time consuming to set up and maintain. Additionally, the spatial distribution of the collected traffic data is limited by the location of the deployed hardware sensors. Probe vehicle data can be used to overcome these limitations. Traffic modeling for estimation and prediction is a complex task due to the stochastic nonlinear spatiotemporal dependencies exhibited by traffic parameters. In this paper, a deep learning-based sequence-to-sequence architecture called Seq2seq GCN-LSTM was proposed to estimate and predict network-wide traffic volume and speed. The proposed method utilizes short-term historical traffic data collected from a low-penetration rate probe vehicle fleet to estimate and predict traffic parameters up to 60-minutes ahead. The method utilizes Graph Convolutional Networks for spatial dependency extraction and Long Short-Term Memory networks to model temporal dependencies. The proposed method generated superior traffic results compared to the baseline models. Additionally, the model demonstrated robustness against perturbations caused by the low rate. Furthermore, the probe vehicle penetration rate was varied to test its effect on the proposed method’s modeling capability. The model was able to maintain traffic volume and speed estimation and prediction performance within a reasonable margin of error using penetration rates as low as 1.5% and 0.5%, respectively.

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.

Maximum Likelihood Estimation of Probe Vehicle Penetration Rates and Queue Length Distributions From Probe Vehicle Data

Queue length estimation plays an important role in traffic signal control and performance measures of signalized intersections. Traditionally, queue lengths are estimated by applying the shockwave theory to loop detector data. In recent years, the tremendous amount of vehicle trajectory data collected from probe vehicles such as ride-hailing vehicles and connected vehicles provides an alternative approach to queue length estimation. To estimate queue lengths cycle by cycle, many existing methods require the knowledge of the probe vehicle penetration rate and queue length distribution. However, the estimation of the two parameters has not been well studied. This paper proposes a maximum likelihood estimation method that can estimate the parameters from historical probe vehicle data. The maximum likelihood estimation problem is solved by the expectation-maximization (EM) algorithm iteratively. Validation results show that the proposed method could estimate the parameters accurately and thus enable the existing methods to estimate queue lengths cycle by cycle.

Improving Coverage Rate for Urban Link Travel Time Prediction Using Probe Data in the Low Penetration Rate Environment.

Short-term travel time prediction is an important consideration in modern traffic control and management systems. As probe data technology has developed, research interest has moved from highways to urban roads. Most research has only focused on improving the prediction accuracy on urban roads because it is the key index of evaluating a model. However, the low penetration rate of probe vehicles at urban networks may result in the low coverage rate which restricts prediction models from practical applications. This research proposed a non-parametric model based on Bayes’ theorem and a resampling process to predict short-term urban link travel time, which can enhance the coverage rate while maintaining the prediction accuracy. The proposed model used data from vehicles in both the target link and its crossing direction, so its coverage rate can be expanded, especially when the data penetration rate is low. In addition, the utilization of relationships between vehicles in both directions can reflect the influence of signal timing. The proposed model was evaluated in a computer simulation to test its robustness and reliability under different data penetration rates. The results implied that the proposed model has a high coverage rate, demonstrating stable and acceptable performance at different penetration rates.

A Bayesian approach for estimating vehicle queue lengths at signalized intersections using probe vehicle data

A novel Bayesian approach is proposed for estimating the maximum queue lengths of vehicles at signalized intersections using high-frequency trajectory data of probe vehicles. The queue length estimates are obtained from a distribution estimated over several neighboring cycles via a maximum a posteriori method. An expectation maximum algorithm is proposed for efficiently solving the estimation problem. Through a battery of simulation experiments and a real-world case study, the proposed approach is shown to produce more accurate and robust estimates than two benchmark estimation methods. Fairly good accuracy is achieved even when the probe vehicle penetration rate is 2%.

Determining the Required Probe Vehicle Size for Real-Time Travel Time Estimation on Signalized Arterial

Determining the required probe vehicle size for real-time travel time estimation is an important issue in probe-data-based applications, such as traffic monitoring on a roadway network. This paper provides an innovative approach for the determination of proper sample sizes with the aid of a simulation model. The model, which was built for El Camino Real, a major arterial in the California San Francisco Bay Area, helps to provide the necessary detailed data to verify the proposed methodology. Our proposed approach is based on the findings that the distribution of travel time estimate error can be constructed with the generalized Pareto distribution function. Considering that travel times vary within a signal cycle and among different movements (through, left-turning and right-turning) at intersections, our study uses data in 15-s intervals to examine the travel time variations associated with different intersection movements. Our findings show that when the penetration rate of probe vehicles is 40%, the probability that the relative error will be less than 0.10 within the time period is 90%, whereas a penetration rate greater than 60% is needed to attain a 0.95 confidence level at the same error rate. For left-turning vehicles, a 10% penetration of probe vehicles is sufficient for estimating their travel times with relative errors less than 0.10 at a 90% confidence level, whereas through vehicles and right-turning vehicles require substantially higher penetration rates of approximately 50% and 30%, respectively, to attain the same confidence level.

A resource allocation problem to estimate network fundamental diagram in heterogeneous networks: Optimal locating of fixed measurement points and sampling of probe trajectories

Network Fundamental Diagram (NFD) or Macroscopic Fundamental Diagram (MFD) represents dynamics of traffic flow at the network level. It is used to design various network-wide traffic control and pricing strategies to improve mobility and mitigate congestion. NFD is well defined when congestion distribution in the network is homogenous. However, in real world networks traffic is often heterogeneously distributed and initiated from an asymmetric and time-varying origin-destination (OD) demand matrix. In this paper, we formulate a resource allocation problem to find the optimal location of fixed measurement points and optimal sampling of probe trajectories to estimate NFD accounting for limited resources for data collection, network traffic heterogeneity and asymmetry in OD demand in a real-world network. Data from probe trajectories are used to estimate space-mean speed while data from fixed detectors are used to estimate traffic flow. Thus, the proposed model does not require an aggregate penetration rate of probe vehicles to be known a priori, which is one of the main contributions of this study. The proposed model is a mixed integer problem with non-linear constraints known to be NP-hard. A heuristic solution algorithm (Simulated Annealing) is implemented to solve the problem. Using a calibrated simulation-based dynamic traffic assignment model of Chicago downtown network, we present successful application of the proposed model and solution algorithm to estimate NFD. The results demonstrate sensitivity of the NFD estimation accuracy to the available budget, namely number of fixed measurement points and probe trajectories. We show that for a fixed proportion of OD trajectories, the increase in the proportion of fixed detection points increases the accuracy of NFD estimation as expected. However, when the proportion of fixed detection points is set to be constant, the increase in the proportion of OD trajectories does not necessarily improve the estimated NFD. Results hold true when varying demand is used to emulate variation in day-to-day traffic patterns. The robustness of the proposed methodology to the initial solution and trajectory availability for each OD pair is demonstrated in the numerical results section. We also found that a uniform distribution of selected links and ODs for NFD estimation across the network may not necessarily result in an optimal solution. Instead, distribution of links and OD pairs should follow the same distribution of links and OD pairs in the network.

Reconstructing maximum likelihood trajectory of probe vehicles between sparse updates

Data from connected probe vehicles can be critical in estimating road traffic conditions. Unfortunately, current available data is usually sparse due to the low reporting frequency and the low penetration rate of probe vehicles. To help fill the gaps in data, this paper presents an approach for estimating the maximum likelihood trajectory (MLT) of a probe vehicle in between two data updates on arterial roads. A public data feed from transit buses in the city of San Francisco is used as an example data source. Low frequency updates (at every 200m or 90s) leaves much to be inferred. We first estimate travel time statistics along the road and queue patterns at intersections from historical probe data. The path is divided into short segments, and an Expectation Maximization (EM) algorithm is proposed for allocating travel time statistics to each segment. Then the trajectory with the maximum likelihood is generated based on segment travel time statistics. The results are compared with high frequency ground truth data in multiple scenarios, which demonstrate the effectiveness of the proposed approach, in estimating both the trajectory while moving and the stop positions and durations at intersections.

Estimation of flow and density using probe vehicles with spacing measurement equipment

Probe vehicles provide some of the most useful data for road traffic monitoring because they can acquire wide-ranging and spatiotemporally detailed information at a relatively low cost compared with traditional fixed-point observation. However, current GPS-equipped probe vehicles cannot directly provide us volume-related variables such as flow and density. In this paper, we propose a new probe vehicle-based estimation method for obtaining volume-related variables by assuming that a probe vehicle can measure the spacing to its leading one. This assumption can be realized by utilizing key technologies in advanced driver assistance systems that are expected to spread in the near future. We developed a method of estimating the flow, density, and speed from the probe vehicle data without exogenous assumptions on traffic flow characteristics, such as a fundamental diagram. In order to quantify the characteristics of the method, we performed a field experiment at a real-world urban expressway by employing prototypes of the probe vehicles with spacing measurement equipment. The result showed that the proposed method could accurately estimate the 5min and hourly traffic volumes with probe vehicle penetration rate of 3.5% and 0.2%, respectively.

Second-order models and traffic data from mobile sensors

Mobile sensing enabled by GPS or smart phones has become an increasingly important source of traffic data. For sufficient coverage of the traffic stream, it is important to maintain a reasonable penetration rate of probe vehicles. From the standpoint of capturing higher-order traffic quantities such as acceleration/deceleration, emission and fuel consumption rates, it is desirable to examine the impact on the estimation accuracy of sampling frequency on vehicle position. Of the two issues raised above, the latter is rarely studied in the literature. This paper addresses the impact of both sampling frequency and penetration rate on mobile sensing of highway traffic. To capture inhomogeneous driving conditions and deviation of traffic from the equilibrium state, we employ the second-order phase transition model (PTM). Several data fusion schemes that incorporate vehicle trajectory data into the PTM are proposed. And, a case study of the NGSIM dataset is presented which shows the estimation results of various Eulerian and Lagrangian traffic quantities. The findings show that while first-order traffic quantities can be accurately estimated even with a low sampling frequency, higher-order traffic quantities, such as acceleration, deviation, and emission rate, tend to be misinterpreted due to insufficiently sampled vehicle locations. We also show that a correction factor approach has the potential to reduce the sensing error arising from low sampling frequency and penetration rate, making the estimation of higher-order quantities more robust against insufficient data coverage of the highway traffic.

Probe Vehicle-based Traffic Flow Estimation Method without Fundamental Diagram

This paper proposes a method of estimating the traffic state based on new probe vehicle data that contain the spacing and position of probe vehicles. In this study, the probe vehicles were assumed to observe spacing by utilizing an advanced driver assistance system, which has been implemented in practice and is expected to spread in the near future. The proposed method relies on the conservation law of traffic flow but is independent of the fundamental diagram. The conservation law is utilized for reasonable aggregation of the spacing data to acquire the traffic state, namely flow, density and speed. Its independence from the fundamental diagram means that the method does not require any predetermined assumptions with regard to the traffic flow model parameters. The estimation performance was validated through a field experiment conducted under actual traffic conditions. The results confirmed that the proposed method can estimate the traffic state precisely, even if the probe vehicle penetration rate is quite low.

Development and evaluation of arterial incident detection models using fusion of simulated probe vehicle and loop detector data

This paper describes the development of neural network models for automatic incident detection on arterial roads, using simulated data derived from inductive loop detectors and probe vehicles. The work reported in this paper extends previous research by comparing the performance of various data fusion neural network architectures and assessing model performance for various probe vehicle penetration rates and loop detector configurations. Data from 108 incidents was collected from loop detectors and probe vehicles using a calibrated and validated traffic simulation model. The best performance was obtained for detector configurations found on most existing road networks, with a detection rate of 86%, false alarm rate of 0.36% and probe vehicle penetration rate of 20%. Fusion of speed data further improved performance, resulting in an incident detection rate of 90% and a false alarm rate of 0.5%. The results reported in this paper demonstrate the feasibility of developing advanced data fusion neural network architectures for detection of incidents on urban arterials using data from existing loop detector configurations and probe vehicles.

Freeway Sensor Spacing and Probe Vehicle Penetration

Accurate travel time prediction–estimation is important for advanced traveler information systems and advanced traffic management systems. Traffic managers and operators are interested in estimating optimal sensor density for new construction and retrofits. In addition, with the development of vehicle-tracking technologies, they may be interested in estimating optimal probe vehicle percentage. Unlike most studies focusing on data-driven models, this paper extends some limited previous work and describes a concept developed from first principles of traffic flow. The goal is to establish analytical relationships between travel time prediction–estimation accuracy and sensor spacing by means of two basic travel time prediction–estimation algorithms, as well as to probe vehicle penetration rate. The methods are based on computing the magnitude of under- and overprediction–estimation of total travel time (TTT) during shock passages in a time–space plane by using the midpoint method for online travel time prediction and the Coifman method for offline travel time estimation. Three shock wave configurations are assessed with each method so as to consider representative traffic dynamics situations. TTT prediction–estimation errors are calculated and expressed as a function of sensor spacing and probe vehicle percentage. Optimal sensor spacing is calculated with consideration of the tradeoff between TTT estimation error and sensor deployment cost. The results from this study can provide simple and effective support for detector placement and probe vehicle deployment, especially along a freeway corridor with existing detectors. Optimal sensor spacing results are analyzed and compared for various methods of travel time estimation during different types of shock waves.