A generic data assimilation framework for vehicle trajectory reconstruction on signalized urban arterials using particle filters

With trajectory data, a complete microscopic and macroscopic picture of traffic flow operations can be obtained. However, trajectory data are difficult to observe over large spatiotemporal regions—particularly in urban contexts—due to practical, technical and financial constraints. The next best thing is to estimate plausible trajectories from whatever data are available. This paper presents a generic data assimilation framework to reconstruct such plausible trajectories on signalized urban arterials using microscopic traffic flow models and data from loops (individual vehicle passages and thus vehicle counts); traffic control data; and (sparse) travel time measurements from whatever source available. The key problem we address is that loops suffer from miss- and over-counts, which result in unbounded errors in vehicle accumulations, rendering trajectory reconstruction highly problematic. Our framework solves this problem in two ways. First, we correct the systematic error in vehicle accumulation by fusing the counts with sparsely available travel times. Second, the proposed framework uses particle filtering and an innovative hierarchical resampling scheme, which effectively integrates over the remaining error distribution, resulting in plausible trajectories. The proposed data assimilation framework is tested and validated using simulated data. Experiments and an extensive sensitivity analysis show that the proposed method is robust to errors both in the model and in the measurements, and provides good estimations for vehicle accumulation and vehicle trajectories with moderate sensor quality. The framework does not impose restrictions on the type of microscopic models used and can be naturally extended to include and estimate additional trajectory attributes such as destination and path, given data are available for assimilation.     

Theory of safety surrogates using vehicle trajectories in macroscopic and microscopic settings: Application to dynamic message signs controlled traffic at work zones

This paper presents a new mathematical framework for obtaining quantitative safety measure using macroscopic as well as microscopic traffic data. The safety surrogate obtained from the macroscopic data is in terms of analysis performed on vehicle trajectories obtained from the macroscopic data. This method of obtaining safety measure can be used for many different types of applications. The safety surrogate for the traffic dynamics are developed in terms of a new concept of Negative Speed Differentials (NSD) that involve a convolution of vehicle speed function obtained from vehicle trajectories and then performing the integration of the square of the output for its negative values. The framework is applicable to microscopic traffic dynamics as well where we can use car following models for microscopic dynamics or the LWR model for macroscopic dynamics. This paper then presents the use of this new safety surrogate on the development of a feedback control law for controlling traffic in work zones using Dynamic Message Signs. A hybrid dynamics model is used to represent the switching dynamics due to changing DMS messages. A feedback control design for choosing those messages is presented as well as a simple simulation example to show its application.     

A kinematic wave approach to traffic statics and dynamics in a double-ring network

Recently there has been much interest in understanding macroscopic fundamental diagrams of stationary road networks. However, there lacks a systematic method to define and solve stationary states in a road network with complex junctions. In this study we propose a kinematic wave approach to defining, analyzing, and simulating static and dynamic traffic characteristics in a network of two ring roads connected by a 2 × 2 junction, which can be either an uninterrupted interchange or a signalized intersection. This study is enabled by recently developed macroscopic junction models of general junctions. With a junction model based on fair merging and first-in-first-out diverging rules, we first define and solve stationary states and then derive the macroscopic fundamental diagram (MFD) of a stationary uninterrupted network. We conclude that the flow-density relationship of the uninterrupted double-ring network is not unique for high average network densities (i.e., when one ring becomes congested) and unveil the existence of infinitely many stationary states that can arise with a zero-speed shockwave. From simulation results with a corresponding Cell Transmission Model, we verify that all stationary states in the MFD are stable and can be reached, but show that randomness in the retaining ratio of each ring drives the network to more symmetric traffic patterns and higher flow-rates. Furthermore we model a signalized intersection as two alternate diverge junctions and demonstrate that the signalized double-ring network can reach asymptotically periodic traffic patterns, which are therefore defined as “stationary” states in signalized networks. With simulations we show that the flow-density relation is well defined in such “stationary” states, and asymptotic traffic patterns can be impacted by signal cycle lengths and retaining ratios. But compared with uninterrupted interchanges, signalized intersections lead to more asymmetric traffic patterns, lower flow-rates, and even gridlocks when the average density is higher than half of the jam density. The results are consistent between this study and existing studies, but the network kinematic wave model, with appropriate junction models, is mathematically tractable and physically meaningful. It has offered a more complete picture regarding the number and type of stationary states, their stability, and MFD in freeway and signalized networks.     

Origin-destination pattern estimation based on trajectory reconstruction using automatic license plate recognition data

Origin-destination (OD) pattern estimation is a vital step for traffic simulation applications and active urban traffic management. Many methods have been proposed to estimate OD patterns based on different data sources, such as GPS data and automatic license plate recognition (ALPR) data. These data can be used to identify vehicle IDs and estimate their trajectories by matching vehicles identified by different sensors across the network. OD pattern estimation using ALPR data remains a challenge in real-life applications due to the difficulty in reconstructing vehicle trajectories. This paper proposes an offline method for historical OD pattern estimation based on ALPR data. A particle filter is used to estimate the probability of a vehicle’s trajectory from all possible candidate trajectories. The initial particles are generated by searching potential paths in a pre-determined area based on the time geography theory. Then, the path flow estimation process is conducted through dividing the reconstructed complete trajectories of all detected vehicles into multiple trips. Finally, the OD patterns are estimated by adding up the path flows with the same ODs. The proposed method was implemented on a real-world traffic network in Kunshan, China and verified through a calibrated microscopic traffic simulation model. The results show that the MAPEs of the OD estimation are lower than 19%. Further investigation shows that there exists a minimum required ALPR sampling rate (60% in the test network) for accurately estimating the OD patterns. The findings of this study demonstrate the effectiveness of the proposed method in OD pattern estimation.     

The identification and empirical characterization of vehicular (Lagrangian) fundamental diagrams in multilane traffic flow

Traditional macroscopic traffic flow modeling framework adopts the spatial–temporal coordinate system to analyze traffic flow dynamics. With such modeling and analysis paradigm, complications arise for traffic flow data collected from mobile sensors such as probe vehicles equipped with mobile phones, Bluetooth, and Global Positioning System devices. The vehicle‐based measurement technologies call for new modeling thoughts that address the unique features of moving measurements and explore their full potential. In this paper, we look into the concept of vehicular fundamental diagram (VFD) and discuss its engineering implications. VFD corresponds to a conventional fundamental diagram (FD) in the kinematic wave (KW) theory that adopts space–time coordinates. Similar to the regular FD in the KW theory, VFD encapsulates all traffic flow dynamics. In this paper, to demonstrate the full potential of VFD in interpreting multilane traffic flow dynamics, we generalize the classical Edie's formula and propose a direct approach of reconstructing VFD from traffic measurements in the vehicular coordinates. A smoothing algorithm is proposed to effectively reduce the nonphysical fluctuation of traffic states calculated from multilane vehicle trajectories. As an example, we apply the proposed methodology to explore the next‐generation simulation datasets and identify the existence and forms of shock waves in different coordinate systems. Our findings provide empirical justifications and further insight for the Lagrangian traffic flow theory and models when applied in practice. Copyright © 2015 John Wiley & Sons, Ltd.     

A two-dimensional simulation model for modelling turning vehicles at mixed-flow intersections

The turning behavior is one of the most challenging driving maneuvers under non-protected phase at mixed-flow intersections. Currently, one-dimensional simulation models focus on car-following and gap-acceptance behaviors in pre-defined lanes with few lane-changing behaviors, and they cannot model the lateral and longitudinal behaviors simultaneously, which has limitation in representing the realistic turning behavior. This paper proposes a three-layered “plan-decision-action” (PDA) framework to obtain acceleration and angular velocity in the turning process. The plan layer firstly calculates the two-dimensional optimal path and dynamically adjusts the trajectories according to interacting objects. The decision layer then uses the decision tree method to select a suitable behavior in three alternatives: car-following, turning and yielding. Finally, in the action layer, a set of corresponding operational models specify the decided behavior into control parameters. The proposed model is tested by reproducing 210 trajectories of left-turn vehicles at a two-phase mixed-flow intersection in Shanghai. As a result, the simulation reproduces the variation of trajectories, while the coverage rate of the trajectories is 88.8%. Meanwhile, both the travel time and post-encroachment time of simulation and empirical turning vehicles are similar and do not show statistically significant difference.     

A mesoscopic integrated urban traffic flow-emission model

Due to the noticeable environmental and economical problems caused by traffic congestion and by the emissions produced by traffic, analysis and control of traffic is essential. One of the various traffic analysis approaches is the model-based approach, where a mathematical model of the traffic system is developed/used based on the governing physical rules of the system. In this paper, we propose a framework to interface and integrate macroscopic flow models and microscopic emission models. As a result, a new mesoscopic integrated flow-emission model is obtained that provides a balanced trade-off between high accuracy and low computation time. The proposed approach considers an aggregated behavior for different groups of vehicles (mesoscopic) instead of considering the behavior of individual vehicles (microscopic) or the entire group of vehicles (macroscopic). A case study is done to evaluate the proposed framework, considering the performance of the resulting mesoscopic integrated flow-emission model. The traffic simulation software SUMO combined with the microscopic emission model VT-micro is used as the comparison platform. The results of the case study prove that the proposed approach provides excellent results with high accuracy levels. In addition, the mesoscopic nature of the integrated flow-emission model guarantees a low CPU time, which makes the proposed framework suitable for real-time model-based applications.     

Spatial and temporal characterization of travel patterns in a traffic network using vehicle trajectories

This paper presents a trajectory clustering method to discover spatial and temporal travel patterns in a traffic network. The study focuses on identifying spatially distinct traffic flow groups using trajectory clustering and investigating temporal traffic patterns of each spatial group. The main contribution of this paper is the development of a systematic framework for clustering and classifying vehicle trajectory data, which does not require a pre-processing step known as map-matching and directly applies to trajectory data without requiring the information on the underlying road network. The framework consists of four steps: similarity measurement, trajectory clustering, generation of cluster representative subsequences, and trajectory classification. First, we propose the use of the Longest Common Subsequence (LCS) between two vehicle trajectories as their similarity measure, assuming that the extent to which vehicles’ routes overlap indicates the level of closeness and relatedness as well as potential interactions between these vehicles. We then extend a density-based clustering algorithm, DBSCAN, to incorporate the LCS-based distance in our trajectory clustering problem. The output of the proposed clustering approach is a few spatially distinct traffic stream clusters, which together provide an informative and succinct representation of major network traffic streams. Next, we introduce the notion of Cluster Representative Subsequence (CRS), which reflects dense road segments shared by trajectories belonging to a given traffic stream cluster, and present the procedure of generating a set of CRSs by merging the pairwise LCSs via hierarchical agglomerative clustering. The CRSs are then used in the trajectory classification step to measure the similarity between a new trajectory and a cluster. The proposed framework is demonstrated using actual vehicle trajectory data collected from New York City, USA. A simple experiment was performed to illustrate the use of the proposed spatial traffic stream clustering in application areas such as network-level traffic flow pattern analysis and travel time reliability analysis.     

Commuter ride-sharing using topology-based vehicle trajectory clustering: Methodology,application and impact evaluation

This paper illustrates a ride matching method for commuting trips based on clustering trajectories, and a modeling and simulation framework with ride-sharing behaviors to illustrate its potential impact. It proposes data mining solutions to reduce traffic demand and encourage more environment-friendly behaviors. The main contribution is a new data-driven ride-matching method, which tracks personal preferences of road choices and travel patterns to identify potential ride-sharing routes for carpool commuters. Compared with prevalent carpooling algorithms, which allow users to enter departure and destination information for on-demand trips, the proposed method focuses more on regular commuting trips. The potential effectiveness of the approach is evaluated using a traffic simulation-assignment framework with ride-sharing participation using the routes suggested by our algorithm. Two types of ride-sharing participation scenarios, with and without carpooling information, are considered. A case study with the Chicago tested is conducted to demonstrate the proposed framework’s ability to support better decision-making for carpool commuters. The results indicate that with ride-matching recommendations using shared vehicle trajectory data, carpool programs for commuters contribute to a less congested traffic state and environment-friendly travel patterns.     

Three-phase traffic theory and two-phase models with a fundamental diagram in the light of empirical stylized facts

Despite the availability of large empirical data sets and the long history of traffic modeling, the theory of traffic congestion on freeways is still highly controversial. In this contribution, we compare Kerner’s three-phase traffic theory with the phase diagram approach for traffic models with a fundamental diagram. We discuss the inconsistent use of the term “traffic phase” and show that patterns demanded by three-phase traffic theory can be reproduced with simple two-phase models, if the model parameters are suitably specified and factors characteristic for real traffic flows are considered, such as effects of noise or heterogeneity or the actual freeway design (e.g. combinations of off- and on-ramps). Conversely, we demonstrate that models created to reproduce three-phase traffic theory create similar spatiotemporal traffic states and associated phase diagrams, no matter whether the parameters imply a fundamental diagram in equilibrium or non-unique flow-density relationships. In conclusion, there are different ways of reproducing the empirical stylized facts of spatiotemporal congestion patterns summarized in this contribution, and it appears possible to overcome the controversy by a more precise definition of the scientific terms and a more careful comparison of models and data, considering effects of the measurement process and the right level of detail in the traffic model used.     

Online calibration for microscopic traffic simulation and dynamic multi-step prediction of traffic speed

Simulating driving behavior in high accuracy allows short-term prediction of traffic parameters, such as speeds and travel times, which are basic components of Advanced Traveler Information Systems (ATIS). Models with static parameters are often unable to respond to varying traffic conditions and simulate effectively the corresponding driving behavior. It has therefore been widely accepted that the model parameters vary in multiple dimensions, including across individual drivers, but also spatially across the network and temporally. While typically on-line, predictive models are macroscopic or mesoscopic, due to computational and data considerations, nowadays microscopic models are becoming increasingly practical for dynamic applications. In this research, we develop a methodology for online calibration of microscopic traffic simulation models for dynamic multi-step prediction of traffic measures, and apply it to car-following models, one of the key models in microscopic traffic simulation models. The methodology is illustrated using real trajectory data available from an experiment conducted in Naples, using a well-established car-following model. The performance of the application with the dynamic model parameters consistently outperforms the corresponding static calibrated model in all cases, and leads to less than 10% error in speed prediction even for ten steps into the future, in all considered data-sets.     

Real-time bus route state forecasting using particle filter and mesoscopic modeling

In the absence of system control strategies, it is common to observe bus bunching in transit operations. A transit operator would benefit from an accurate forecast of bus operations in order to control the system before it becomes too disrupted to be restored to a stable condition. To accomplish this, we present a general bus prediction framework. This framework relies on a stochastic and event-based bus operation model that provides sets of possible bus trajectories based on the observation of current bus positions, available via global positioning system (GPS) data. The median of the set of possible trajectories, called a particle, is used as the prediction. In particular, this enables the anticipation of irregularities between buses. Several bus models are proposed depending on the dwell and inter-stop running time representations. These models are calibrated and applied to a real case study thanks to the high quality data provided by TriMet (the Portland, Oregon, USA transit district). Predictions are finally evaluated by an a posteriori comparison with the real trajectories. The results highlight that only bus models accounting for the bus load can provide valid forecasts of a bus route over a large prediction horizon, especially for headway variations. Accounting for traffic signal timings and actual traffic flows does not significantly improves the prediction. Such a framework paves the way for further development of refined dynamic control strategies for bus operations.     

Closed-form multiclass cell transmission model enhanced with overtaking,lane-changing,and first-in first-out properties

A novel multiclass macroscopic model is proposed in this article. In order to enhance first-in, first-out property (FIFO) and transmission function in the multiclass traffic modeling, a new multiclass cell transmission model with FIFO property (herein called FM-CTM) is extended from its prior multiclass cell transmission model (M-CTM). Also, to enhance its analytical compactness and resultant computational convenience, FM-CTM is formulated in this paper as a set of closed-form matrix equations. The objective is to improve the accuracy of traffic state estimation by enforcing FIFO property when a fast vehicle cannot overtake a slow vehicle due to a limitation of a single-lane road. Moreover, the proposed model takes into account a different priority for vehicles of each class to move forward through congested road conditions, and that makes the flow calculation independent from their free-flow speeds. Some hypothetical and real-world freeway networks with a constant or varying number of lanes are selected to verify FM-CTM by comparing with M-CTM and the conventional CTM. Observed densities of VISSIM and real-world dataset of I-80 are selected to compare with the simulated densities from the three CTMs. The numerical results show that FM-CTM outperforms the other two models by 15% of accuracy measures in most cases. Therefore, the proposed model is expected to be well applicable to the road network with a mixed traffic and varying number of lanes.     

Time-dependent congestion pricing system for large networks: Integrating departure time choice,dynamic traffic assignment and regional travel surveys in the Greater Toronto Area

Congestion pricing is one of the widely contemplated methods to manage traffic congestion. The purpose of congestion pricing is to manage traffic demand generation and supply allocation by charging fees (i.e., tolling) for the use of certain roads in order to distribute traffic demand more evenly over time and space. This study presents a framework for large-scale variable congestion pricing policy determination and evaluation. The proposed framework integrates departure time choice and route choice models within a regional dynamic traffic assignment (DTA) simulation environment. The framework addresses the impact of tolling on: (1) road traffic congestion (supply side), and (2) travelers’ choice dimensions including departure time and route choices (demand side). The framework is applied to a simulation-based case study of tolling a major freeway in Toronto while capturing the regional effects across the Greater Toronto Area (GTA). The models are developed and calibrated using regional household travel survey data that reflect the heterogeneity of travelers’ attributes. The DTA model is calibrated using actual traffic counts from the Ontario Ministry of Transportation and the City of Toronto. The case study examined two tolling scenarios: flat and variable tolling. The results indicate that: (1) more benefits are attained from variable pricing, that mirrors temporal congestion patterns, due to departure time rescheduling as opposed to predominantly re-routing only in the case of flat tolling, (2) widespread spatial and temporal re-distributions of traffic demand are observed across the regional network in response to tolling a significant, yet relatively short, expressway serving Downtown Toronto, and (3) flat tolling causes major and counterproductive rerouting patterns during peak hours, which was observed to block access to the tolled facility itself.     

Dynamic models of commuter behavior: Experimental investigation and application to the analysis of planned traffic disruptions

This paper reviews the results of a series of experiments aimed at investigating the day-to-day dynamics of commuter behavior in congested traffic systems. The interactive experiments involve actual work commuters in a simulated traffic system, whereby commuters noncooperatively supply their decisions to a traffic simulation model that determines the resulting arrival times and associated trip times; these in turn form the basis of the commuters' decisions on the next day. Models are developed to predict the daily switching of departure time and/or route by individual commuters in response to experienced congestion in the system or to exogenously supplied information. These models are incorporated in a dynamic modelling framework for the analysis of the impacts of planned traffic disruptions, such as those associated with major highway repair and reconstruction activities.     

Real-time queue length estimation for congested signalized intersections

How to estimate queue length in real-time at signalized intersection is a long-standing problem. The problem gets even more difficult when signal links are congested. The traditional input–output approach for queue length estimation can only handle queues that are shorter than the distance between vehicle detector and intersection stop line, because cumulative vehicle count for arrival traffic is not available once the detector is occupied by the queue. In this paper, instead of counting arrival traffic flow in the current signal cycle, we solve the problem of measuring intersection queue length by exploiting the queue discharge process in the immediate past cycle. Using high-resolution “event-based” traffic signal data, and applying Lighthill–Whitham–Richards (LWR) shockwave theory, we are able to identify traffic state changes that distinguish queue discharge flow from upstream arrival traffic. Therefore, our approach can estimate time-dependent queue length even when the signal links are congested with long queues. Variations of the queue length estimation model are also presented when “event-based” data is not available. Our models are evaluated by comparing the estimated maximum queue length with the ground truth data observed from the field. Evaluation results demonstrate that the proposed models can estimate long queues with satisfactory accuracy. Limitations of the proposed model are also discussed in the paper.     

Robust calibration of macroscopic traffic simulation models using stochastic collocation

The predictions of a well-calibrated traffic simulation model are much more valid if made for various conditions. Variation in traffic can arise due to many factors such as time of day, work zones and weather. Calibration of traffic simulation models for traffic conditions requires larger datasets to capture the stochasticity in traffic conditions. In this study we use datasets spanning large time periods to incorporate variability in traffic flow, speed for various time periods. However, large data poses a challenge in terms of computational effort. With the increase in number of stochastic factors, the numerical methods suffer from the curse of dimensionality. In this study, we propose a novel methodology to address the computational complexity due to the need for the calibration of simulation models under highly stochastic traffic conditions. This methodology is based on sparse grid stochastic collocation, which, treats each stochastic factor as a different dimension and uses a limited number of points where simulation and calibration are performed. A computationally efficient interpolant is constructed to generate the full distribution of the simulated flow output. We use real-world examples to calibrate for different times of day and conditions and show that this methodology is much more efficient that the traditional Monte Carlo-type sampling. We validate the model using a hold out dataset and also show the drawback of using limited data for the calibration of a macroscopic simulation model. We also discuss the drawbacks of the predictive ability of a single calibrated model for all the conditions.     

Recognition and tracking of spatial–temporal congested traffic patterns on freeways

The two models FOTO (Forecasting of Traffic Objects) and ASDA (Automatische Staudynamikanalyse: Automatic Tracking of Moving Traffic Jams) for the automatic recognition and tracking of congested spatial–temporal traffic flow patterns on freeways are presented. The models are based on a spatial–temporal traffic phase classification made in the three-phase traffic theory by Kerner. In this traffic theory, in congested traffic two different phases are distinguished: “wide moving jam” and “synchronized flow”. The model FOTO is devoted to the identification of traffic phases and to the tracking of synchronized flow. The model ASDA is devoted to the tracking of the propagation of moving jams. The general approach and the different extensions of the models FOTO and ASDA are explained in detail. It is stressed that the models FOTO and ASDA perform without any validation of model parameters in different environmental and traffic conditions. Results of the online application of the models FOTO and ASDA at the TCC (Traffic Control Center) of Hessen near Frankfurt (Germany) are presented and evaluated.     

Within day rescheduling microsimulation combined with macrosimulated traffic

The concept of rescheduling is essential to activity-based modeling in order to calculate effects of both unexpected incidents and adaptation of individuals to traffic demand management measures. When collaboration between individuals is involved or timetable based public transportation modes are chosen, rescheduling becomes complex. This paper describes a new framework to investigate algorithms for rescheduling at a large scale. The framework allows to explicitly model the information flow between traffic information services and travelers. It combines macroscopic traffic assignment with microscopic simulation of agents adapting their schedules. Perception filtering is introduced to allow for traveler specific interpretation of perceived macroscopic data and for information going unnoticed; perception filters feed person specific short term predictions about the environment required for schedule adaptation. Individuals are assumed to maximize schedule utility. Initial agendas are created by the FEATHERS activity-based schedule generator for mutually independent individuals using an undisturbed loaded transportation network. The new framework allows both actor behavior and external phenomena to influence the transportation network state; individuals interpret the state changes via perception filtering and start adapting their schedules, again affecting the network via updated traffic demand. The first rescheduling mechanism that has been investigated uses marginal utility that monotonically decreases with activity duration and a monotonically converging relaxation algorithm to efficiently determine the new activity timing. The current framework implementation is aimed to support re-timing, re-location and activity re-sequencing; re-routing at the level of the individual however, requires microscopic travel simulation.     

A methodology for classification by priority for action: Selecting road stretches for network noise action plans

Road traffic noise is an element of outstanding importance within the overall context of environmental impact. This problem must be technically addressed from an efficient viewpoint, and solutions or alternatives should be considered by means of appropriate and consolidated procedures.Up to now, there is no regulated guideline for establishing well-founded priorities when dealing with the diverse road stretches included in the corresponding Action Plans against noise under the Environmental Noise Directive (2002/49/EC). To this end, the present study proposes a methodology to sort, by priority, road stretches identified by their noise problems and therefore requiring appropriate action. The methodology is based on the so-called “road stretch priority index” (henceforth referred to as RSPI). This index involves a number of variables (called “road stretch priority variables”) that are weighted according to their influence on the road traffic noise problem. Thus, the RSPI makes it possible to prioritize different stretches of the Action Plan. To illustrate the application of the proposed methodology, this paper also describes a real case entailing a difficult choice, applying the proposed methodology to a review of the Action Plan against Noise 2008–2012 in the province of Almería, for the road network of the regional government of Andalusia, Spain.