Identifying optimal data aggregation interval sizes for link and corridor travel time estimation and forecasting

With the recent increase in the deployment of ITS technologies in urban areas throughout the world, traffic management centers have the ability to obtain and archive large amounts of data on the traffic system. These data can be used to estimate current conditions and predict future conditions on the roadway network. A general solution methodology for identifying the optimal aggregation interval sizes for four scenarios is proposed in this article: (1) link travel time estimation, (2) corridor/route travel time estimation, (3) link travel time forecasting, and (4) corridor/route travel time forecasting. The methodology explicitly considers traffic dynamics and frequency of observations. A formulation based on mean square error (MSE) is developed for each of the scenarios and interpreted from a traffic flow perspective. The methodology for estimating the optimal aggregation size is based on (1) the tradeoff between the estimated mean square error of prediction and the variance of the predictor, (2) the differences between estimation and forecasting, and (3) the direct consideration of the correlation between link travel time for corridor/route estimation and forecasting. The proposed methods are demonstrated using travel time data from Houston, Texas, that were collected as part of the automatic vehicle identification (AVI) system of the Houston Transtar system. It was found that the optimal aggregation size is a function of the application and traffic condition.

Deriving macroscopic fundamental diagrams from probe data: Issues and proposed solutions

Well-defined relationships between flow and density averaged spatially across urban traffic networks, more commonly known as Macroscopic Fundamental Diagrams (MFDs), have been recently verified to exist in reality. Researchers have proposed using MFDs to monitor the status of urban traffic networks and to inform the design of network-wide traffic control strategies. However, it is also well known that empirical MFDs are not easy to estimate in practice due to difficulties in obtaining the requisite data needed to construct them. Recent works have devised ways to estimate a network’s MFD using limited trajectory data that can be obtained from GPS-equipped mobile probe vehicles. These methods assume that the market penetration level of mobile probe vehicles is uniform across the entire set of OD pairs in the network; however, in reality the probe vehicle market penetration rate varies regionally within a network. When this variation is combined with the imbalance of probe trip lengths and travel times, the compound effects will further complicate the estimation of the MFD.To overcome this deficit, we propose a method to estimate a network’s MFD using mobile probe data when the market penetration rates are not necessarily the same across an entire network. This method relies on the determination of appropriate average probe penetration rates, which are weighted harmonic means using individual probe vehicle travel times and distances as the weights. The accuracy of this method is tested using synthetic data generated in the INTEGRATION micro-simulation environment by comparing the estimated MFDs to the ground truth MFD obtained using a 100% market penetration of probe vehicles. The results show that the weighted harmonic mean probe penetration rates outperform simple (arithmetic) average probe penetration rates, as expected. This especially holds true as the imbalance of demand and penetration level increases. Furthermore, as the probe penetration rates are generally not known, an algorithm to estimate the probe penetration rates of regional OD pairs is proposed. This algorithm links count data from sporadic fixed detectors in the network to information from probe vehicles that pass the detectors. The simulation results indicate that the proposed algorithm is very effective. Since the data needed to apply this algorithm are readily available and easy to collect, the proposed algorithm is practically feasible and offers a better approach for the estimation of the MFD using mobile probe data, which are becoming increasingly available in urban environments.     

Travel time estimation for urban road networks using low frequency probe vehicle data

The paper presents a statistical model for urban road network travel time estimation using vehicle trajectories obtained from low frequency GPS probes as observations, where the vehicles typically cover multiple network links between reports. The network model separates trip travel times into link travel times and intersection delays and allows correlation between travel times on different network links based on a spatial moving average (SMA) structure. The observation model presents a way to estimate the parameters of the network model, including the correlation structure, through low frequency sampling of vehicle traces. Link-specific effects are combined with link attributes (speed limit, functional class, etc.) and trip conditions (day of week, season, weather, etc.) as explanatory variables. The approach captures the underlying factors behind spatial and temporal variations in speeds, which is useful for traffic management, planning and forecasting. The model is estimated using maximum likelihood. The model is applied in a case study for the network of Stockholm, Sweden. Link attributes and trip conditions (including recent snowfall) have significant effects on travel times and there is significant positive correlation between segments. The case study highlights the potential of using sparse probe vehicle data for monitoring the performance of the urban transport system.     

A virtual vehicle probe model for time-dependent travel time estimation on signalized arterials

Estimation of time-dependent arterial travel time is a challenging task because of the interrupted nature of urban traffic flows. Many research efforts have been devoted to this topic, but their successes are limited and most of them can only be used for offline purposes due to the limited availability of traffic data from signalized intersections. In this paper, we describe a real-time arterial data collection and archival system developed at the University of Minnesota, followed by an innovative algorithm for time-dependent arterial travel time estimation using the archived traffic data. The data collection system simultaneously collects high-resolution “event-based” traffic data including every vehicle actuations over loop detector and every signal phase changes from multiple intersections. Using the “event-based” data, we estimate time-dependent travel time along an arterial by tracing a virtual probe vehicle. At each time step, the virtual probe has three possible maneuvers: acceleration, deceleration and no-speed-change. The maneuver decision is determined by its own status and surrounding traffic conditions, which can be estimated based on the availability of traffic data at intersections. An interesting property of the proposed model is that travel time estimation errors can be self-corrected, because the trajectory differences between a virtual probe vehicle and a real one can be reduced when both vehicles meet a red signal phase and/or a vehicle queue. Field studies at a 11-intersection arterial corridor along France Avenue in Minneapolis, MN, demonstrate that the proposed model can generate accurate time-dependent travel times under various traffic conditions.     

Real time queue length estimation for signalized intersections using travel times from mobile sensors

We study how to estimate real time queue lengths at signalized intersections using intersection travel times collected from mobile traffic sensors. The estimation is based on the observation that critical pattern changes of intersection travel times or delays, such as the discontinuities (i.e., sudden and dramatic increases in travel times) and non-smoothness (i.e., changes of slopes of travel times), indicate signal timing or queue length changes. By detecting these critical points in intersection travel times or delays, the real time queue length can be re-constructed. We first introduce the concept of Queue Rear No-delay Arrival Time which is related to the non-smoothness of queuing delay patterns and queue length changes. We then show how measured intersection travel times from mobile sensors can be processed to generate sample vehicle queuing delays. Under the uniform arrival assumption, the queuing delays reduce linearly within a cycle. The delay pattern can be estimated by a linear fitting method using sample queuing delays. Queue Rear No-delay Arrival Time can then be obtained from the delay pattern, and be used to estimate the maximum and minimum queue lengths of a cycle, based on which the real-time queue length curve can also be constructed. The model and algorithm are tested in a field experiment and in simulation.     

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 200 m or 90 s) 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.     

A framework for neighbour links travel time estimation in an urban network

This paper proposes a solution to the problem of limited network sensor coverage caused by insufficient sample size of probe vehicles or inadequate numbers of fixed sensors. A framework is proposed to estimate link travel times using available data from neighbouring links. Two clues are used for real-time travel time estimation: link historical travel time data and online travel time data from neighbour links. In the absence of online travel time data from neighbour links, historical records only have to be relied upon. However, where the two types of data are available, a data fusion scheme can be applied to make use of the two clues. The proposed framework is validated using real-life data from the City of Vancouver, British Columbia. The estimation accuracy is found to be comparable to the existing literature. Overall, the results demonstrate the feasibility of using neighbour links data as an additional source of information that might not have been extensively explored before.     

Arterial travel time estimation based on vehicle re-identification using wireless magnetic sensors

A practical system is described for the real-time estimation of travel time across an arterial segment with multiple intersections. The system relies on matching vehicle signatures from wireless sensors. The sensors provide a noisy magnetic signature of a vehicle and the precise time when it crosses the sensors. A match (re-identification) of signatures at two locations gives the corresponding travel time of the vehicle. The travel times for all matched vehicles yield the travel time distribution. Matching results can be processed to provide other important arterial performance measures including capacity, volume/capacity ratio, queue lengths, and number of vehicles in the link. The matching algorithm is based on a statistical model of the signatures. The statistical model itself is estimated from the data, and does not require measurement of ‘ground truth’. The procedure does not require measurements of signal settings; in fact, signal settings can be inferred from the matched vehicle results. The procedure is tested on a 1.5 km (0.9 mile)-long segment of San Pablo Avenue in Albany, CA, under different traffic conditions. The segment is divided into three links: one link spans four intersections, and two links each span one intersection.     

Travel time estimation from sparse floating car data with consistent path inference: A fixed point approach

Estimation of urban network link travel times from sparse floating car data (FCD) usually needs pre-processing, mainly map-matching and path inference for finding the most likely vehicle paths that are consistent with reported locations. Path inference requires a priori assumptions about link travel times; using unrealistic initial link travel times can bias the travel time estimation and subsequent identification of shortest paths. Thus, the combination of path inference and travel time estimation is a joint problem. This paper investigates the sensitivity of estimated travel times, and proposes a fixed point formulation of the simultaneous path inference and travel time estimation problem. The methodology is applied in a case study to estimate travel times from taxi FCD in Stockholm, Sweden. The results show that standard fixed point iterations converge quickly to a solution where input and output travel times are consistent. The solution is robust under different initial travel times assumptions and data sizes. Validation against actual path travel time measurements from the Google API and an instrumented vehicle deployed for this purpose shows that the fixed point algorithm improves shortest path finding. The results highlight the importance of the joint solution of the path inference and travel time estimation problem, in particular for accurate path finding and route optimization.     

Estimating origin‐destination matrices from link volume counts: a simple intercity auto travel demand model for Sri Lanka

The cost of nation wide travel surveys is high. Hence in many developing countries, planners have found it difficult to develop intercity transportation plans due to the non availability of origin‐destination trip matrices. This paper will describe a method for the intercity auto travel estimation for Sri Lanka with link traffic volume data.

The paper outlines the rationale of selecting the district capitals of Sri Lanka as its “cities,” the methodology for selecting the intercity road network, determination of link travel times from express bus schedules and the location of link volume counting positions.

Initially, the total auto travel demand model is formulated with various trip purpose sub‐models. This model is finally modified to a simple demand model with district urban population and travel times between city pairs as the exogenous variables, to overcome statistical estimation difficulties. The final demand model has statistics within the acceptable regions.

The advantages of a simple model are discussed and possible extensions are proposed.     

Probe vehicle based real-time traffic monitoring on urban roadways

Travel time estimation and prediction on urban arterials is an important component of Active Traffic and Demand Management Systems (ATDMS). This paper aims in using the information of GPS probes to augment less dynamic but available information describing arterial travel times. The direction followed in this paper chooses a cooperative approach in travel time estimation using static information describing arterial geometry and signal timing, semi-dynamic information of historical travel time distributions per time of day, and utilizes GPS probe information to augment and improve the latter. First, arterial travel times are classified by identifying different travel time states, then link travel time distributions are approximated using mixtures of normal distributions. If prior travel time data is available, travel time distributions can be estimated empirically. Otherwise, travel time distribution can be estimated based on signal timing and arterial geometry. Real-time GPS travel time data is then used to identify the current traffic condition based on Bayes Theorem. Moreover, these GPS data can also be used to update the parameters of the travel time distributions using a Bayesian update. The iterative update process makes the posterior distributions more and more accurate. Finally, two comprehensive case studies using the NGSIM Peachtree Street dataset, and GPS data of Washington Avenue in Minneapolis, were conducted. The first case study estimated prior travel time distributions based on signal timing and arterial geometry under different traffic conditions. Travel time data were classified and corresponding distributions were updated. In addition, results from the Bayesian update and EM algorithm were compared. The second case study first tested the methodologies based on real GPS data and showed the importance of sample size. In addition, a methodology was proposed to distinguish new traffic conditions in the second case study.     

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 5 min and hourly traffic volumes with probe vehicle penetration rate of 3.5% and 0.2%, respectively.     

Connected vehicle penetration rate for estimation of arterial measures of effectiveness

The Connected Vehicle (CV) technology is a mobile platform that enables a new dimension of data exchange among vehicles and between vehicles and infrastructure. This data source could improve the estimation of Measures of Effectiveness (MOEs) for traffic operations in real-time, allowing to perfectly monitor traffic states after being fully adopted. However, as with any novel technology, the CV adoption will be a gradual process. This research focuses on determining minimum CV technology penetration rates that would guarantee accurate MOE estimates on signalized arterials. First, we present estimation methods for various MOEs such as average speed, number of stops, acceleration noise, and delay, followed by an initial assessment of the penetration rates required to accurately estimate them in undersaturated and oversaturated conditions. Next, we propose a methodology to determine the minimum CV market penetration rates to guarantee accurate MOE estimates as a function of traffic conditions, signal settings, sampling duration, and the MOE variability. A correction factor is also provided to account for small vehicle populations where sampling is done without replacement. The methodology is tested in a simulated segment of the San Pablo Avenue arterial in Berkeley, CA. The outcomes show that the minimum penetration rate required can be estimated within 1% for most MOEs under a wide range of traffic conditions. The proposed methodology can be used to determine if MOE estimates obtained with a portion of CV equipped vehicles can yield accurate enough results. The methodology could also be used to develop and assess control strategies towards improved arterial traffic operations.     

Estimating link travel time functions for heterogeneous traffic flows on freeways

Oversized vehicles, such as trucks, significantly contribute to traffic delays on freeways. Heterogeneous traffic populations, that is, those consisting of multiple vehicles types, can exhibit more complicated travel behaviors in the operating speed and performance, depending on the traffic volume as well as the proportions of vehicle types. In order to estimate the component travel time functions for heterogeneous traffic flows on a freeway, this study develops a microscopic traffic‐simulation based four‐step method. A piecewise continuous function is proposed for each vehicle type and its parameters are estimated using the traffic data generated by a microscopic traffic simulation model. The illustrated experiments based on VISSIM model indicate that (i) in addition to traffic volume, traffic composition has significant influence on the travel time of vehicles and (ii) the respective estimations for travel time of heterogeneous flows could greatly improve their estimation accuracy. Copyright © 2016 John Wiley & Sons, Ltd.     

The corridor problem: Preliminary results on the no-toll equilibrium

Consider a traffic corridor that connects a continuum of residential locations to a point central business district, and that is subject to flow congestion. The population density function along the corridor is exogenous, and except for location vehicles are identical. All vehicles travel along the corridor from home to work in the morning rush hour, and have the same work start-time but may arrive early. The two components of costs are travel time costs and schedule delay (time early) costs. Determining equilibrium and optimum traffic flow patterns for this continuous model, and possible extensions, is termed “The Corridor Problem”. Equilibria must satisfy the trip-timing condition, that at each location no vehicle can experience a lower trip price by departing at a different time. This paper investigates the no-toll equilibrium of the basic Corridor Problem.     

Length-based vehicle classification using event-based loop detector data

Length-based vehicle classification is an important topic in traffic engineering, because estimation of traffic speed from single loop detectors usually requires the knowledge of vehicle length. In this paper, we present an algorithm that can classify vehicles passing by a loop detector into two categories: long vehicles and regular cars. The proposed algorithm takes advantage of event-based loop detector data that contains every vehicle detector actuation and de-actuation “event”, therefore time gaps between consecutive vehicles and detector occupation time for each vehicle can be easily derived. The proposed algorithm is based on an intuitive observation that, for a vehicle platoon, longer vehicles in the platoon will have relatively longer detector occupation time. Therefore, we can identify longer vehicles by examining the changes of occupation time in a vehicle platoon. The method was tested using the event-based data collected from Trunk Highway 55 in Minnesota, which is a high speed arterial corridor controlled by semi-actuated coordinated traffic signals. The result shows that the proposed method can correctly classify most of the vehicles passing by a single loop detector.     

Estimating the most likely space–time paths,dwell times and path uncertainties from vehicle trajectory data: A time geographic method

Global Positioning System and other location-based services record vehicles’ spatial locations at discrete time stamps. Considering these recorded locations in space with given specific time stamps, this paper proposes a novel time-dependent graph model to estimate their likely space–time paths and their uncertainties within a transportation network. The proposed model adopts theories in time geography and produces the feasible network–time paths, the expected link travel times and dwell times at possible intermediate stops. A dynamic programming algorithm implements the model for both offline and real-time applications. To estimate the uncertainty, this paper also develops a method based on the potential path area for all feasible network–time paths. This paper uses a set of real-world trajectory data to illustrate the proposed model, prove the accuracy of estimated results and demonstrate the computational efficiency of the estimation algorithm.     

A copula-based approach for estimating the travel time reliability of urban arterial

Estimating the travel time reliability (TTR) of urban arterial is critical for real-time and reliable route guidance and provides theoretical bases and technical support for sophisticated traffic management and control. The state-of-art procedures for arterial TTR estimation usually assume that path travel time follows a certain distribution, with less consideration about segment correlations. However, the conventional approach is usually unrealistic because an important feature of urban arterial is the dependent structure of travel times on continuous segments. In this study, a copula-based approach that incorporates the stochastic characteristics of segments travel time is proposed to model arterial travel time distribution (TTD), which serves as a basis for TTR quantification. First, segments correlation is empirically analyzed and different types of copula models are examined. Then, fitting marginal distributions for segment TTD is conducted by parametric and non-parametric regression analysis, respectively. Based on the estimated parameters of the models, the best-fitting copula is determined in terms of the goodness-of-fit tests. Last, the model is examined at two study sites with AVI data and NGSIM trajectory data, respectively. The results of path TTD estimation demonstrate the advantage of the proposed copula-based approach, compared with the convolution model without capturing segments correlation and the empirical distribution fitting methods. Furthermore, when considering the segments correlation effect, it was found that the estimated path TTR is more accurate than that by the convolution model.     

Connected cruise control among human-driven vehicles: Experiment-based parameter estimation and optimal control design

In this paper, we consider connected cruise control design in mixed traffic flow where most vehicles are human-driven. We first propose a sweeping least square method to estimate in real time feedback gains and driver reaction time of human-driven vehicles around the connected automated vehicle. Then we propose an optimal connected cruise controller based on the mean dynamics of human driving behavior. We test the performance of both the estimation algorithm and the connected cruise control algorithm using experimental data. We demonstrate that by combining the proposed estimation algorithm and the optimal controller, the connected automated vehicle has significantly improved performance compared to a human-driven vehicle.     

A practical method to estimate the benefits of improved road network reliability: an application to departing air passengers

This paper develops and applies a practical method to estimate the benefits of improved reliability of road networks. We present a general methodology to estimate the scheduling costs due to travel time variability for car travel. In contrast to existing practical methods, we explicitly consider the effect of travel time variability on departure time choices. We focus on situations when only mean delays are known, which is typically the case when standard transport models are used. We first show how travel time variability can be predicted from mean delays. We then estimate the scheduling costs of travellers, taking into account their optimal departure time choice given the estimated travel time variability. We illustrate the methodology for air passengers traveling by car to Amsterdam Schiphol Airport. We find that on average planned improvements in network reliability only lead to a small reduction in access costs per trip in absolute terms, mainly because most air passengers drive to the airport outside peak hours, when travel time variability tends to be low. However, in relative terms the reduction in access costs due to the improvements in network reliability is substantial. In our case we find that for every 1 Euro reduction in travel time costs, there is an additional cost reduction of 0.7 Euro due to lower travel time variability, and hence lower scheduling costs. Ignoring the benefits from improved reliability may therefore lead to a severe underestimation of the total benefits of infrastructure improvements.