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.     

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.

A data fusion approach for real-time traffic state estimation in urban signalized links

Real-time estimation of the traffic state in urban signalized links is valuable information for modern traffic control and management. In recent years, with the development of in-vehicle and communication technologies, connected vehicle data has been increasingly used in literature and practice. In this work, a novel data fusion approach is proposed for the high-resolution (second-by-second) estimation of queue length, vehicle accumulation, and outflow in urban signalized links. Required data includes input flow from a fixed detector at the upstream end of the link as well as location and speed of the connected vehicles. A probability-based approach is derived to compensate the error associated with low penetration rates while estimating the queue tail location, which renders the proposed methodology more robust to varying penetration rates of connected vehicles. A well-defined nonlinear function based on traffic flow theory is developed to attain the number of vehicles inside the queue based on queue tail location and average speed of connected vehicles. The overall scheme is thoroughly tested and demonstrated in a realistic microscopic simulation environment for three types of links with different penetration rates of connected vehicles. In order to test the efficiency of the proposed methodology in case that data are available at higher sampling times, the estimation procedure is also demonstrated for different time resolutions. The results demonstrate the efficiency and accuracy of the approach for high-resolution estimation, even in the presence of measurement noise.     

Forecasting Travel Demand with Alternatively Structured Models of Trip Frequency

Abstract

This paper develops alternatively structured trip frequency/generation models, and investigates their forecast performance. The first model presented is the simple linear model with a discussion of its theoretical shortcomings. Models that address, in a progressive fashion, the underlying shortcomings of the linear model are then presented. These models are namely the truncated normal model, the Poisson model, the negative binomial model, and an ordered logit model. The modeling unit employed in the study is the individual. The models are assessed by how closely they are able to replicate trips produced by each individual in the dataset, and by each traffic zone. This assessment of performance in prediction is conducted on an estimation dataset collected in the Toronto Region in 1986, and on an independent dataset collected in the same geographic region, 10 years later, in 1996. The results show that, notwithstanding the simplicity of the simple linear model and its lack of an explicit underlying travel behavioral theory, it predicts travel in the base and forecast years with less error compared to any of the more complex models.     

Efficient multiple model particle filtering for joint traffic state estimation and incident detection

This article proposes an efficient multiple model particle filter (EMMPF) to solve the problems of traffic state estimation and incident detection, which requires significantly less computation time compared to existing multiple model nonlinear filters. To incorporate the on ramps and off ramps on the highway, junction solvers for a traffic flow model with incident dynamics are developed. The effectiveness of the proposed EMMPF is assessed using a benchmark hybrid state estimation problem, and using synthetic traffic data generated by a micro-simulation software. Then, the traffic estimation framework is implemented using field data collected on Interstate 880 in California. The results show the EMMPF is capable of estimating the traffic state and detecting incidents and requires an order of magnitude less computation time compared to existing algorithms, especially when the hybrid system has a large number of rare models.     

Highway traffic state estimation with mixed connected and conventional vehicles: Microscopic simulation-based testing

This paper presents a thorough microscopic simulation investigation of a recently proposed methodology for highway traffic estimation with mixed traffic, i.e., traffic comprising both connected and conventional vehicles, which employs only speed measurements stemming from connected vehicles and a limited number (sufficient to guarantee observability) of flow measurements from spot sensors. The estimation scheme is tested using the commercial traffic simulator Aimsun under various penetration rates of connected vehicles, employing a traffic scenario that features congested as well as free-flow conditions. The case of mixed traffic comprising conventional and connected vehicles equipped with adaptive cruise control, which feature a systematically different car-following behavior than regular vehicles, is also considered. In both cases, it is demonstrated that the estimation results are satisfactory, even for low penetration rates.     

Short-term traffic flow prediction using time-varying Vasicek model

This paper provides a two-step approach based on the stochastic differential equations (SDEs) to improve short-term prediction. In the first step of this framework, a Hull-White (HW) model is applied to obtain a baseline prediction model from previous days. Then, the extended Vasicek model (EV) is employed for modeling the difference between observations and baseline predictions (residuals) during an individual day. The parameters of this time-varying model are estimated at each sample using the residuals in a short duration of time before the time point of prediction; so it provides a real time prediction. The extracted model recovers the valuable local variation information during each day. The performance of our method in comparison with other methods improves significantly in terms of root mean squared error (RMSE), mean absolute error (MAE) and mean relative error (MRE) for real data from Tehran’s highways and the open-access PeMS database. We also demonstrate that the proposed model is appropriate for imputing the missing data in traffic dataset and it is more efficient than the probabilistic principal component analysis (PPCA) and k-Nearest neighbors (k-NN) methods.     

Estimating traffic volumes for signalized intersections using connected vehicle data

Recently connected vehicle (CV) technology has received significant attention thanks to active pilot deployments supported by the US Department of Transportation (USDOT). At signalized intersections, CVs may serve as mobile sensors, providing opportunities of reducing dependencies on conventional vehicle detectors for signal operation. However, most of the existing studies mainly focus on scenarios that penetration rates of CVs reach certain level, e.g., 25%, which may not be feasible in the near future. How to utilize data from a small number of CVs to improve traffic signal operation remains an open question. In this work, we develop an approach to estimate traffic volume, a key input to many signal optimization algorithms, using GPS trajectory data from CV or navigation devices under low market penetration rates. To estimate traffic volumes, we model vehicle arrivals at signalized intersections as a time-dependent Poisson process, which can account for signal coordination. The estimation problem is formulated as a maximum likelihood problem given multiple observed trajectories from CVs approaching to the intersection. An expectation maximization (EM) procedure is derived to solve the estimation problem. Two case studies were conducted to validate our estimation algorithm. One uses the CV data from the Safety Pilot Model Deployment (SPMD) project, in which around 2800 CVs were deployed in the City of Ann Arbor, MI. The other uses vehicle trajectory data from users of a commercial navigation service in China. Mean absolute percentage error (MAPE) of the estimation is found to be 9–12%, based on benchmark data manually collected and data from loop detectors. Considering the existing scale of CV deployments, the proposed approach could be of significant help to traffic management agencies for evaluating and operating traffic signals, paving the way of using CVs for detector-free signal operation in the future.     

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.     

Traffic state estimation through compressed sensing and Markov random field

This study focuses on information recovery from noisy traffic data and traffic state estimation. The main contributions of this paper are: i) a novel algorithm based on the compressed sensing theory is developed to recover traffic data with Gaussian measurement noise, partial data missing, and corrupted noise; ii) the accuracy of traffic state estimation (TSE) is improved by using Markov random field and total variation (TV) regularization, with introduction of smoothness prior; and iii) a recent TSE method is extended to handle traffic state variables with high dimension. Numerical experiments and field data are used to test performances of these proposed methods; consistent and satisfactory results are obtained.     

Norm approximation method for handling traffic count inconsistencies in path flow estimator

Path flow estimator (PFE) is a one-stage network observer proposed to estimate path flows and hence origin–destination (O–D) flows from traffic counts in a transportation network. Although PFE does not require traffic counts to be collected on all network links when inferring unmeasured traffic conditions, it does require all available counts to be reasonably consistent. This requirement is difficult to fulfill in practice due to errors inherited in data collection and processing. The original PFE model handles this issue by relaxing the requirement of perfect replication of traffic counts through the specification of error bounds. This method enhances the flexibility of PFE by allowing the incorporation of local knowledge, regarding the traffic conditions and the nature of traffic data, into the estimation process. However, specifying appropriate error bounds for all observed links in real networks turns out to be a difficult and time-consuming task. In addition, improper specification of the error bounds could lead to a biased estimation of total travel demand in the network. This paper therefore proposes the norm approximation method capable of internally handling inconsistent traffic counts in PFE. Specifically, three norm approximation criteria are adopted to formulate three L_p-PFE models for estimating consistent path flows and O–D flows that simultaneously minimize the deviation between the estimated and observed link volumes. A partial linearization algorithm embedded with an iterative balancing scheme and a column generation procedure is developed to solve the three L_p-PFE models. In addition, the proposed L_p-PFE models are illustrated with numerical examples and the characteristics of solutions obtained by these models are discussed.     

Distribution models for start-up lost time and effective departure flow rate

Due to its importance, lots of investigations had been carried out in the last four decades to study the relationship between phase duration and vehicle departure amount. In this paper, we aim to build appropriate distribution models for start-up lost time and effective departure flow rate, by considering their relations with the frequently mentioned departure headway distributions. The motivation behind is that distribution models could provide richer information than the conventional mean value models and thus better serve the need of traffic simulation and signal timing planning. To reach this goal, we first check empirical data collected in Beijing, China. Tests show that the departure headways at each position in a discharging queue are very weakly dependent or almost independent. Based on this new finding, two distribution models are proposed for start-up lost time and effective flow rate, respectively. We also examine the dependences of departure headways that are generated by three popular traffic simulation software: VISSIM, PARAMICS and TransModeler. Results suggest that in VISSIM, the departure headways at different positions are almost deterministically dependent and may not be in accordance with empirical observations. Finally, we discuss how the dependence of departure headways may influence traffic simulation and signal timing planning.     

Strategic sampling for large choice sets in estimation and application

Many discrete choice contexts in transportation deal with large choice sets, including destination, route, and vehicle choices. Model estimation with large numbers of alternatives remains computationally expensive. In the context of the multinomial logit (MNL) model, limiting the number of alternatives in estimation by simple random sampling (SRS) yields consistent parameter estimates, but estimator efficiency suffers. In the context of more general models, such as the mixed MNL, limiting the number of alternatives via SRS yields biased parameter estimates. In this paper, a new, strategic sampling scheme is introduced, which draws alternatives in proportion to updated choice-probability estimates. Since such probabilities are not known a priori, the first iteration uses SRS among all available alternatives. The sampling scheme is implemented here for a variety of simulated MNL and mixed-MNL data sets, with results suggesting that the new sampling scheme provides substantial efficiency benefits. Thanks to reductions in estimation error, parameter estimates are more accurate, on average. Moreover, in the mixed MNL case, where SRS produces biased estimates (due to violation of the independence of irrelevant alternatives property), the new sampling scheme appears to effectively eliminate such biases. Finally, it appears that only a single iteration of the new strategy (following the initialization step using SRS) is needed to deliver the strategy’s maximum efficiency gains.     

Reducing bias in probe-based arterial link travel time estimates

The use of probe vehicles to provide estimates of link travel times has been suggested as a means of obtaining travel times within signalized networks for use in advanced traveler information systems. Previous research has shown that bias in arrival time distributions of probe vehicles will lead to a systematic bias in the sample estimate of the mean. This paper proposes a methodology for reducing the effect of this bias. The method, based on stratified sampling techniques, requires that vehicle count data be obtained from an in-road loop detector or other traffic surveillance method. The effectiveness of the methodology is illustrated using simulation results for a single intersection approach and for an arterial corridor. The results for the single intersection approach indicate a correlation (R²) between the biased estimate and the population mean of 0.61, and an improved correlation between the proposed estimation method and the population mean of 0.81. Application of the proposed method to the arterial corridor resulted in a reduction in the mean travel time error of approximately 50%, further indicating that the proposed estimation method provides improved accuracy over the typical method of computing the arithmetic mean of the probe reports.     

A hybrid approach to integrate fuzzy C-means based imputation method with genetic algorithm for missing traffic volume data estimation

Although various innovative traffic sensing technologies have been widely employed, incomplete sensor data is one of the most major problems to significantly degrade traffic data quality and integrity. In this study, a hybrid approach integrating the Fuzzy C-Means (FCM)-based imputation method with the Genetic Algorithm (GA) is develop for missing traffic volume data estimation based on inductance loop detector outputs. By utilizing the weekly similarity among data, the conventional vector-based data structure is firstly transformed into the matrix-based data pattern. Then, the GA is applied to optimize the membership functions and centroids in the FCM model. The experimental tests are conducted to verify the effectiveness of the proposed approach. The traffic volume data collected at different temporal scales were used as the testing dataset, and three different indicators, including root mean square error, correlation coefficient, and relative accuracy, are utilized to quantify the imputation performance compared with some conventional methods (Historical method, Double Exponential Smoothing, and Autoregressive Integrated Moving Average model). The results show the proposed approach outperforms the conventional methods under prevailing traffic conditions.     

Evaluation of traffic data obtained via GPS-enabled mobile phones: The Mobile Century field experiment

The growing need of the driving public for accurate traffic information has spurred the deployment of large scale dedicated monitoring infrastructure systems, which mainly consist in the use of inductive loop detectors and video cameras. On-board electronic devices have been proposed as an alternative traffic sensing infrastructure, as they usually provide a cost-effective way to collect traffic data, leveraging existing communication infrastructure such as the cellular phone network. A traffic monitoring system based on GPS-enabled smartphones exploits the extensive coverage provided by the cellular network, the high accuracy in position and velocity measurements provided by GPS devices, and the existing infrastructure of the communication network. This article presents a field experiment nicknamed Mobile Century, which was conceived as a proof of concept of such a system. Mobile Century included 100 vehicles carrying a GPS-enabled Nokia N95 phone driving loops on a 10-mile stretch of I-880 near Union City, California, for 8 h. Data were collected using virtual trip lines, which are geographical markers stored in the handset that probabilistically trigger position and speed updates when the handset crosses them. The proposed prototype system provided sufficient data for traffic monitoring purposes while managing the privacy of participants. The data obtained in the experiment were processed in real-time and successfully broadcast on the internet, demonstrating the feasibility of the proposed system for real-time traffic monitoring. Results suggest that a 2–3% penetration of cell phones in the driver population is enough to provide accurate measurements of the velocity of the traffic flow. Data presented in this article can be downloaded from http://traffic.berkeley.edu.     

Simultaneous estimation of an origin–destination matrix and link choice proportions using traffic counts

A procedure for the simultaneous estimation of an origin–destination (OD) matrix and link choice proportions from OD survey data and traffic counts for congested network is proposed in this paper. Recognizing that link choice proportions in a network change with traffic conditions, and that the dispersion parameter of the route choice model should be updated for a current data set, this procedure performs statistical estimation and traffic assignment alternately until convergence in order to obtain the best estimators for both the OD matrix and link choice proportions, which are consistent with the survey data and traffic counts.Results from a numerical study using a hypothetical network have shown that a model allowing θ to be estimated simultaneously with an OD matrix from the observed data performs better than the model with a fixed predetermined θ. The application of the proposed model to the Tuen Mun Corridor network in Hong Kong is also presented in this paper. A reasonable estimate of the dispersion parameter θ for this network is obtained.     

Data fusion algorithm for macroscopic fundamental diagram estimation

A promising framework that describes traffic conditions in urban networks is the macroscopic fundamental diagram (MFD), relating average flow and average density in a relatively homogeneous urban network. It has been shown that the MFD can be used, for example, for traffic access control. However, an implementation requires an accurate estimation of the MFD with the available data sources.Most scientific literature has considered the estimation of MFDs based on either loop detector data (LDD) or floating car data (FCD). In this paper, however, we propose a methodology for estimating the MFD based on both data sources simultaneously. To that end, we have defined a fusion algorithm that separates the urban network into two sub-networks, one with loop detectors and one without. The LDD and the FCD are then fused taking into account the accuracy and network coverage of each data type. Simulations of an abstract grid network and the network of the city of Zurich show that the fusion algorithm always reduces the estimation error significantly with respect to an estimation where only one data source is used. This holds true, even when we account for the fact that the probe penetration rate of FCD needs to be estimated with loop detectors, hence it might also include some errors depending on the number of loop detectors, especially when probe vehicles are not homogeneously distributed within the network.     

An empirical analysis on the arterial fundamental diagram

For uninterrupted traffic flow, it is well-known that the fundamental diagram (FD) describes the relationship between traffic flow and density under steady state. For interrupted traffic flow on a signalized road, it has been recognized that the arterial fundamental diagram (AFD) is significantly affected by signal operations. But little research up to date has discussed in detail how signal operations impact the AFD. In this paper, based upon empirical observations from high-resolution event-based traffic signal data collected from a major arterial in the Twin Cities area, we study the impacts of g/C ratio, signal coordination, and turning movements on the cycle-based AFD, which describes the relationship between traffic flow and occupancy in a signal cycle. By microscopically investigating individual vehicle trajectories from event-based data, we demonstrate that not only g/C ratio constrains the capacity of a signalized approach, poor signal coordination and turning movements from upstream intersections also have significant impact on the capacity. We show that an arterial link may not be congested even with high occupancy values. Such high values could result from queue build-up during red light that occupies the detector, i.e. the Queue-Over-Detector (QOD) phenomenon discussed in this paper. More importantly, by removing the impact of QOD, a stable form of AFD is revealed, and one can use that to identify three different regimes including under-saturation, saturation, and over-saturation with queue spillovers. We believe the stable form of AFD is of great importance for traffic signal control because of its ability to identify traffic states on a signal link.