Probe Vehicles Research Articles

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.

Identification of Spatiotemporal Relationships in Travel Speeds along Individual Roadways using Probe Vehicle Data

The existence of spatiotemporal correlations in traffic behavior on links in a transportation network is potentially very useful. However, traffic metrics are often strongly correlated simply because of natural variations in travel demand patterns and these temporal trends might obstruct more meaningful relationships caused by the physics of traffic. To overcome this challenge, the present paper proposes a non-parametric, moving average detrending method that can be used to remove these background trends, even during non-stationary periods in which traffic states are changing with time. Cross-correlations performed on the detrended data are then used to identify more meaningful trends. The proposed method can also incorporate temporal lags in correlations between individual links, which accounts for the time it takes for information to travel between them. Links that exhibit strong correlations after detrending can then be grouped into communities which behave together using graph theory methods, and this community structure can be leveraged to improve prediction of link performance when information is missing. The proposed methodology is applied to a case study network using real-time link travel speeds obtained from probe vehicles. The results reveal that the 40 links in the network can be grouped into between eight and 12 communities, depending on the day of the week. This suggests that only a handful of links may need to be monitored to estimate travel speeds across the entire network. Furthermore, the significant overlap in the community structure across these days reveals that the network structure plays a large role in spatiotemporal correlations in link travel speeds in a network.

Constructing a Network Fundamental Diagram: Synthetic Origin–Destination Approach

The network fundamental diagram (NFD) is increasingly used in traffic monitoring and control. One obstacle to a wider application of NFDs in network control is the difficulty of obtaining data from all vehicles traveling in the network to construct an accurate NFD. One solution is to estimate the NFD using data from only a fraction of vehicles (i.e., probe vehicles), where the probe vehicle market penetration rate (MPR) needs to be estimated. A previous study conducted by the authors demonstrated that a distance or time-weighted harmonic mean was needed to estimate the flow- and density-based MPRs, respectively, using a pairing k-mean clustering approach. This paper proposes another approach that utilizes probe vehicle and observed link volume data to estimate the MPR. A heuristic model is proposed to identify the optimum locations from which to collect link traffic volume data for use in the MPR estimation. The estimated MPR can then be used to construct the NFD. Results show that these models can accurately estimate the NFD with limited probe vehicle and link traffic volume data. Accordingly, the models can be used in the field to estimate the NFD using readily available loop detector and probe vehicle data. The ideal locations for traffic volume data collection can also be proactively chosen to generate optimum estimation results. As the models proposed here show no significant gains with an increased magnitude of collected data after a certain threshold, they will be helpful, particularly when large-scale data collection is not affordable or realistic.

Traffic State Estimation in Heterogeneous Networks with Stochastic Demand and Supply: Mixed Lagrangian–Eulerian Approach

A network fundamental diagram (NFD) represents the relationship between network-wide average flow and average density. Network traffic state estimation to observe NFD when congestion is heterogeneously distributed, as a result of a time-varying and asymmetric demand matrix, is a challenging problem. Recent studies have formulated the NFD estimation problem using both fixed measurements and probe trajectories. They are often based on a given ground-truth NFD for a single day demand. Stochastic variations in network demand and supply may significantly affect the approximation of an NFD. This study proposes a modified framework to estimate network traffic states to observe NFD while capturing the stochasticity in transportation networks. A mixed integer problem with non-linear constraints is formulated to address stochasticity in the NFD estimation problem. To solve this Nondeterministic Polynomial-hard (NP-hard) problem, a solution algorithm based on the simulated annealing method is applied. The problem is formulated and the solution algorithm is implemented to find an optimal configuration of loop detectors and probe vehicles to estimate the NFD of the Chicago downtown network and capture its day-to-day variations, considering a given available budget. Ground-truth NFDs and estimated NFDs based on a subset of loop detectors and probe vehicles are calculated using a simulation-based dynamic traffic assignment model, which is the best surrogate available to replicate real-world conditions. The main contribution of this study is to capture stochasticity in the demand and supply sides to find a more robust subset of links and trajectories to be acquired for the NFD estimation.

Empirical random phase transitions between free flow and synchronized flow at highway bottlenecks

Based on a study of probe vehicle data measured on different highways during different days we have revealed some common empirical microscopic characteristic features of sequences of phase transitions from free flow to synchronized flow and back from synchronized flow to free flow occurring before traffic breakdown at a highway bottleneck predicted theoretically by Kerner. Following common empirical features of sequences of these phase transitions have been found: (i) Sequences of empirical phase transitions from free flow to synchronized flow and back from synchronized flow to free flow are observed on different highways at different bottlenecks. (ii) Empirical sequences of the phase transitions exhibit a random character, in particular, at different days very different sequences of phase transitions from free flow to synchronized flow and back from synchronized flow to free flow have been observed at the same bottleneck. (iii) Time durations between the transition from free flow to synchronized flow and the subsequent transition from synchronized flow to free flow within a sequence of the phase transitions are random values. Time intervals between subsequent sequences of the phase transitions are also random values. (iv) Regions of dissolving synchronized flow that result from sequences of phase transitions from free flow to synchronized flow and back from synchronized flow to free flow exhibit random characteristics. (v) Several following each other sequences of phase transitions from free flow to synchronized flow and back from synchronized flow to free flow can lead to waves of synchronized flow between free flow.

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.

Modeling double time-scale travel time processes with application to assessing the resilience of transportation systems

This paper proposes a double time-scale model to capture the day-to-day evolution along with the within-day variability of travel time. The proposed model can be used to evaluate short-term to long-term effects of new transport policies and construction of critical infrastructures, and to analyze the resilience of road networks under disruptions. The within-day travel time variability is modeled using the functional data analysis, in which the effects of road traffic congestion and noise of traffic data are considered explicitly. The within-day process is then regarded as the local volatility (or the noise process) to drive the day-to-day process while the latter is described by a modified geometric Brownian motion (GBM). Then, the day-to-day travel time process is obtained by the statistics of the modified GBM. The model probabilistically captures the evolution of day-to-day and within-day travel time processes analytically. Moreover, an efficient method based on the cross-entropy method is developed for calibrating the model parameters. A lasso-like regularization is employed to guarantee a small bias between the model estimations and the measurement counterparts. Finally, two empirical studies are carried out to validate the proposed model at different scales with different traffic scenarios, i.e., a case study on the Guangzhou Airport Expressway (link to path scale) under traffic accident conditions and a case study in New York City (city-scale) to analyze the network resilience under Hurricane Sandy. Both case studies adopted probe vehicle data but with different configurations (fine versus coarse, small versus big data). The empirical studies confirm that the proposed model can accommodate the inherent variability in traffic conditions and data meanwhile being computationally tractable. The numerical results illustrate the applicability of the proposed model as a powerful tool in practice for analyzing the short-term and long-term impacts of disruptions and systematic changes in the performance of road networks.

Traffic Dynamics Exploration and Incident Detection Using Spatiotemporal Graphical Modeling

To discover the spatial and temporal traffic patterns, this paper proposes a spatiotemporal graphical modeling approach, spatiotemporal pattern network (STPN), to explore traffic dynamics in large traffic networks. A measurement based on Granger causality is used to identify the characteristics of spatial and temporal traffic patterns. An anomaly score is estimated to detect and locate traffic incidents in diverse types and severities, and also to quantify the influence of incidents on traffic flow fluctuations. Built upon symbolic dynamics filtering, the proposed approach implements spatial and temporal feature extraction via discovering causal dependencies among road segments using STPN, system-wide pattern learning through an energy-based model, restricted Boltzmann machine, and inference using a newly developed root-cause analysis algorithm. Case studies are carried out using the probe vehicle data collected on Interstate Highway 80 in Iowa and the results show that the proposed approach is capable of (1) discovering and representing causal interactions among sub-systems (e.g., road segment) of a traffic network that provide valuable information for developing and applying customized traffic management strategies, (2) adaptively handling multiple nominal patterns mixed with anomalous data for effectively differentiating abnormal traffic system status and locating traffic incidents, and (3) quantifying the fluctuation of traffic flow and the severity of the detected incident via anomaly scores estimated from traffic speed behaviors. The findings from the case studies reiterate the importance of incorporating both temporal and spatial features for pattern analysis and incident detection. The proposed approach is built for real-time application and can be utilized for on-line incident detection.

Traffic state estimation and its sensitivity utilizing measurements from the opposite lane

This study proposes a method that estimates traffic states using measurements from a vehicle running on the opposite lane in addition to probe vehicle data and examine the sensitivity of the estimates in relation to variabilities of the input data and measurements. A number of studies on traffic state estimation fusing several sensing data have been reported. Most of the studies use data from traffic detectors installed at fixed locations and data from moving objects such as probe vehicles. Traffic detectors provide valuable volume information of all running vehicles which cannot be observed from sample moving objects. However, in local areas in Japan as well as in Asian cities, detector installations are very much limited like one in every 10 to 15 km on a motorway in our country. This study therefore attempts to utilize measurements from a vehicle running on the opposite lane instead of detector measurements, since a vehicle on the opposite lane running backward can in principle measure counts of passing vehicles running forward. In this study, we employ the variational theory to estimate the traffic states utilizing the count measurement from the opposite lane in addition to probe vehicle data on the forward direction and examine the sensitivity of the estimates in relation to variabilities of the input data and measurements. The validation finds that the proposed method can estimate traffic states more accurately than one using only probe vehicle data. Especially, this method has the advantage in quickly responding unexpected incidences such as accidents and vehicle malfunctions.

Application of High-Resolution Trip Trace Stitching to Evaluate Traffic Signal System Changes

Second-by-second GPS trajectories, called trip traces, of vehicles moving along an arterial provide the highest fidelity measure of corridor operations. However, large samples of such contiguous trajectories are not always possible because of varying techniques to reset probe vehicle IDs for data privacy, varying probe data penetration rates, and varying vehicle routing. This paper analyzes changes in segment travel time using the Mann–Whitney U test and proposes a method for creating a composite travel time metric using trip trace data. These techniques were applied to a four-corridor signal improvement and upgrade project in southeastern Salt Lake County. The study found that on average three out of the four corridors decreased in composite median travel time, by 32 s, 16 s, and 14 s. Interquartile range (IQR) was used to assess travel time reliability and the IQR travel time reduced (improved) on average by 33 s, 23 s, 18 s, and 1 s. In addition, a rank-sums method for statistically comparing the two composite travel time distributions is applied to the results. The four corridors had a total of 48 links and were evaluated during five time-of-day periods. Out of the 240 link-periods, the rank-sums analysis method found that overall, 68 link-periods improved and 13 link-periods slowed, at a 95% significance level. The annualized user benefit from the improvements was estimated at $2.2 million for the four corridors.

Data-Driven Methodology for Prioritizing Traffic Signal Retiming Operations

Signal retiming is one of the chief responsibilities of municipal transportation agencies, and is an important means of reducing congestion and improving transportation quality and reliability. Many agencies conduct signal retiming and adjustment in a schedule-based manner. However, leveraging a data-driven, need-based approach to signal retiming to prioritize operations could better optimize use of agency resources. Additionally, the growing availability of probe vehicle data has made it an increasingly popular tool for use in roadway performance measurement. This paper presents a methodology for using segment-level probe-based speed data to rank the performance of traffic signal corridors for retiming purposes. This methodology is then demonstrated in an analysis of 79 traffic signal corridors maintained by the City of Austin, Texas. The analysis considers 15-minute speed records for all weekdays in September 2016 and September 2017 to compute metrics and rank corridors based on their relative performance across time periods. The results show that the ranking methodology compares corridors equitably despite differences in road length, functional class, and traffic signal density. Additionally, the results indicate that the corridors prioritized by the ranking methodology represent a much greater potential for improving travel time than the corridors selected under the schedule-based approach.

Identification of Time-of-Day Breakpoints Based on Trajectory Data of Probe Vehicles

The time-of-day (TOD) mode is the most widely used strategy for traffic signal control with fluctuating flows. Most studies determine TOD breakpoints based on traffic volumes collected by infrastructure-based detectors (e.g., loop detectors). However, these infrastructure-based detectors have low coverage and high maintenance cost. With the deployment of probe vehicles, vehicle trajectory data has become available, providing a new data source for signal control. This paper proposes an approach to identify TOD breakpoints at an isolated intersection based on the trajectory data of probe vehicles, instead of conventional traffic volumes, with under-saturated traffic conditions. It is shown that the speeds of queueing shockwaves capture the characteristics of the traffic volumes according to the queueing shockwave theory. Data from multiple sampling days are aggregated to compensate for the limitations of low market penetration rates and long sampling intervals. Queue joining vehicles are then identified to obtain the speeds of queueing shockwaves. The bisecting K-means algorithm is applied to cluster periods, which are characterized by queueing shockwave speeds, to identify TOD breakpoints. The numerical studies validate that the speeds of queueing shockwaves capture the trend of traffic volumes. The clustering algorithm identifies the same TOD breakpoints for queueing shockwave speeds and traffic volumes. As long as the number of sampling days is large enough, the proposed method can handle low penetration rates (e.g., 2%) and long sampling intervals (e.g., 20 s), and thus achieve a comparable performance to the ideal conditions with high penetration rates (e.g., 100%) and short sampling intervals (e.g., 1 s).

Visualizing and Evaluating Interdependent Regional Traffic Congestion and System Resiliency, a Case Study Using Big Data from Probe Vehicles

Big data from probe vehicles is increasingly becoming an important contributor for determining the regional performance of a transportation roadway network. Recent research has applied aggregated speed data from probe vehicles to quantify travel time variations as a result of recurring congestion, incidents, weather events and other non-recurring congestion. Through the establishment of a base travel time for all roadway segments in a region, any increase in travel time characteristics in the regional networks can be quantified temporally and spatially. This characterization is especially important when determining a region’s congestion resiliency, which is being defined as the ability of a roadway network accommodate failures and return to a baseline congestion after a major capacity reduction to the roadway network. This paper demonstrates how aggregated big data on vehicle speeds obtained from regionally deployed probe vehicles could be used to characterize and visualize the interdependent congestion impacts between regions and across roadway types (interstate, arterial, and local). To demonstrate the models and methodologies, an in-depth analysis of the I-276 Bridge closure incident in Burlington County, NJ near Philadelphia, PA was conducted. The bridge was clzosed after a routine inspected identified a crack in one of the structural members. In total, 90 days of data, which included 90-million speed records, were commercially collected for 1765 roadway segments, was analyzed. A novel performance metric was developed to allow an impact analysis by comparing Burlington County to two adjacent counties, Mercer and Camden. The results showed that the bridge closure did have a definitive, quantifiable impact on the primary road network of the adjacent counties. Subsequent analysis identified specific roadways that were most impacted by the closure. Although this research explores historic speed data, the methodologies presented can be applied to real-time speed data to assist in developing efficient traffic operation plans during major incidents, lane closures and weather events.

Personalized Travel Time Prediction Using a Small Number of Probe Vehicles

Predicting the travel time of a path is an important task in route planning and navigation applications. As more GPS probe data has been collected to monitor urban traffic, GPS trajectories of the probe vehicles have been frequently used to predict path travel time. However, most trajectory-based methods rely on deploying GPS devices and collect real-time data on a large taxi fleet, which can be expensive and unreliable in smaller cities. This work deals with the problem of predicting path travel time when only a small number of cars are available. We propose an algorithm that learns local congestion patterns of a compact set of frequently shared paths from historical data. Given a travel time prediction query, we identify the current congestion patterns around the query path from recent trajectories, then infer its travel time in the near future. Driver identities are also used in predicting personalized travel time. Experimental results using 10--25 taxis in urban areas of Shenzhen, China, show that personal prediction has on average 3.4mins of error on trips of duration 10--75mins. This result improves the baseline approach of using purely historical trajectories by 16.8% on average, over four regions with various degrees of path regularity. It also outperforms a state-of-the-art travel time prediction method that uses both historical trajectories and real-time trajectories.

Traffic state estimation on a two-dimensional network by a state-space model

This study proposes a state-space model that estimates traffic states over a two-dimensional network with alternative routes available by a data assimilation technique that fuses probe vehicle data with a traffic flow model. Although a number of studies propose traffic monitoring methods based on physical flow dynamics using sensing data such as probe vehicle and traffic detector data, they are basically limited to traffic monitoring along a simple road section. This study extends the analysis to a two-dimensional network, in which several alternative routes exist for each OD, with consideration of the route choice behaviours of users. Our proposed method employs sequential Bayesian filtering with a cell transmission model (CTM) for the flow model and probe vehicle data. From the probe vehicle data, not only cell densities but also diverging ratios are assumed to be measured and these measurements are assimilated into the flow model. The model validation in a hypothetical network reveals the potential of the model and discloses future issues.

Smart Parking: Using a Crowd of Taxis to Sense On-Street Parking Space Availability

Monitoring the occupancy of on-street parking spaces on a city-wide scale is still an open issue. Past research demonstrated the viability of parking crowd-sensing by means of the standard on-board sensors of probe vehicles, foreseeing the use of high-mileage vehicles, like taxis. Nevertheless, the achievable spatio-temporal sensing coverage has never been deeply investigated. In this paper, we investigate the suitability of taxi fleets of different sizes to crowd-sense on-street parking availability. We considered 579 road segments in San Francisco (USA), covered both by sensors of the SFpark project and by the GPS traces of 536 taxis. For each of these segments, we computed the taxi transit frequencies, representing the achievable coverage by vehicles equipped with sensors detecting empty parking spots. By combining these frequencies with parking occupancy data coming from SFpark, we estimated the potential quality of crowd-sensed on-street parking information for different fleet sizes. Moreover, we investigated the impact of different misdetection amounts, and Kalman filters to handle them. The results show that a total of 300 taxis can crowd-sense on-street parking availability with an error of up to ±1 stall in 86% of the cases. Moreover, the quality of the sensors is as important as the fleet size (300 taxis with 10% probability of misreadings provide availability information comparable to 486 taxis with 16% probability), while the use of Kalman filters did not lead to statistically significant improvements. In conclusion, the traffic management authorities should consider parking crowd-sensing via probe vehicles as a promising alternative to the expensive deployment of the static parking sensors.

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.

Vehicle–space traffic-state estimation of a motorway corridor with slip roads

Traffic-state estimation is a key component of an advanced traffic management system. The Eulerian traffic-state estimation based on an X-T traffic-flow model has proved successful in processing traditional X-T data sources such as inductive loop data. However, over the past decade, the emergence of probe vehicle data from paired sensors has created challenges for X-T traffic-state estimation. The vehicle–space (N-X) model has shown potential benefits in modelling paired-probe data. In this paper, an original N-X traffic-state estimation framework is proposed and validated by numerical experiments. In addition, an original first-order conservation formulation is derived to address the entry and exit slip road issue for motorway corridors. An evaluation is conducted by comparing the proposed N-X estimation with the X-T estimation. The results show that the proposed model is superior to the X-T estimation in terms of accuracy and efficiency. It performs well, particularly during congestion, and can track traffic breakdowns and recoveries effectively.

Evaluation of Interstate Work Zone Mobility using Probe Vehicle Data and Machine Learning Techniques

According to the Federal Highway Administration (FHWA), US work zones on freeways account for nearly 24% of nonrecurring freeway delays and 10% of overall congestion. Historically, there have been limited scalable datasets to investigate the specific causes of congestion due to work zones or to improve work zone planning processes to characterize the impact of work zone congestion. In recent years, third-party data vendors have provided scalable speed data from Global Positioning System (GPS) devices and cell phones which can be used to characterize mobility on all roadways. Each work zone has unique characteristics and varying mobility impacts which are predicted during the planning and design phases, but can realistically be quite different from what is ultimately experienced by the traveling public. This paper uses these datasets to introduce a scalable Work Zone Mobility Audit (WZMA) template. Additionally, the paper uses metrics developed for individual work zones to characterize the impact of more than 250 work zones varying in length and duration from Southeast Michigan. The authors make recommendations to work zone engineers on useful data to collect for improving the WZMA. As more systematic work zone data are collected, improved analytical assessment techniques, such as machine learning processes, can be used to identify the factors that will predict future work zone impacts. The paper concludes by demonstrating two machine learning algorithms, Random Forest and XGBoost, which show historical speed variation is a critical component when predicting the mobility impact of work zones.

A Real-Time Queue Length Estimation Method Based on Probe Vehicles in CV Environment

The real-time traffic status estimation in urban signalized intersections is highly valuable for modern traffic control and management. This paper presents a real-time queue length estimation method based on probe vehicles' data in the connected vehicle (CV) environment. The probe data are used to identify the stopping states of CVs. Based on this, a queue length time series referring to the stopping time and the positions of CVs is built for describing the queuing process at an intersection. Considering the statistical average traffic rate, queue length time series in historical cycles, and the stopping states for real-time CV arrival features in the current cycle, the critical queuing time is forecasted based on the linear fitting method and the real-time queue length is estimated based on the Markov model. The overall scheme is thoroughly tested and demonstrated in a realistic scenario at different penetration rates. Under different conditions, the stationarity of the queue length series is tested by the augmented Dickey-Fuller. Two Markov models based on the transition matrices of the current cycle and both the current and historical cycles are verified, respectively. The results demonstrate the high accuracy in the real-time queue length estimation, and the proposed method shows good performance in handling the randomness, especially when the CV penetration rate is low.