A shockwave profile model for traffic flow on congested urban arterials

In this paper a new traffic flow model for congested arterial networks, named shockwave profile model (SPM), is presented. Taking advantage of the fact that traffic states within a congested link can be simplified as free-flow, saturated, and jammed conditions, SPM simulates traffic dynamics by analytically deriving the trajectories of four major shockwaves: queuing, discharge, departure, and compression waves. Unlike conventional macroscopic models, in which space is often discretized into small cells for numerical solutions, SPM treats each homogeneous road segment with constant capacity as a section; and the queuing dynamics within each section are described by tracing the shockwave fronts. SPM is particularly suitable for simulating traffic flow on congested signalized arterials especially with queue spillover problems, where the steady-state periodic pattern of queue build-up and dissipation process may break down. Depending on when and where spillover occurs along a signalized arterial, a large number of queuing patterns may be possible. Therefore it becomes difficult to apply the conventional approach directly to track shockwave fronts. To overcome this difficulty, a novel approach is proposed as part of the SPM, in which queue spillover is treated as either extending a red phase or creating new smaller cycles, so that the analytical solutions for tracing the shockwave fronts can be easily applied. Since only the essential features of arterial traffic flow, i.e., queue build-up and dissipation, are considered, SPM significantly reduces the computational load and improves the numerical efficiency. We further validated SPM using real-world traffic signal data collected from a major arterial in the Twin Cities. The results clearly demonstrate the effectiveness and accuracy of the model. We expect that in the future this model can be applied in a number of real-time applications such as arterial performance prediction and signal optimization.     

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.     

On development of arterial fundamental diagrams based on surrogate density measures from adaptive traffic control systems utilizing stop-line detection

A promising framework for understanding flow-density relationship in traffic flow theory is the Fundamental Diagram, originally developed for uninterrupted traffic flow facilities. The concept has been extended to the Arterial Fundamental Diagram (AFD), which has shown that the same relationship holds on arterial streets. However, constructing an AFD is subject to considerable variability in the measured quantities, due to the highly cyclical nature of signalized intersections. In most cases, these diagrams are based on the data from upstream detectors, located away from traffic signals. Recent scientific literature has shown a value of using stop-line detection data to develop AFDs, opening a plethora of opportunities to further investigate traffic dynamics utilizing the data from adaptive traffic control systems (ATCSs). This can, however, be problematic for two major reasons. First, the data may come from detectors unfit to provide good-quality inputs to develop an AFD. Second, such ATCSs may use their own surrogate measures of density and traffic flow, primarily developed for the purpose of controlling traffic, which may be inappropriate for developing fundamental relationships. This study aims to address these issues by investigating appropriateness of using Degree of Saturation (DS), a density-like measure from Sydney Coordinated Adaptive Traffic System (SCATS), to develop an AFD. Empirical SCATS data shows an interesting pattern of the AFD, which cannot be explained by the data itself. Hence, we derive a new analytical model of DS based on the high-resolution signal and detection data, which reveals parameters that drive its behavior. Additionally, we develop the Cyclical Vehicle Arrival and Discharge Model to simulate SCATS-like operations and derive causal relationships between traffic flow variables and density-like performance measures in a controlled environment. The findings show that DS does not have to be a poor estimator of traffic conditions, but when it is combined with SCATS-measured traffic flows it gives a false representation of near-capacity and over-saturated conditions.     

Real-time estimation of turning movement counts at signalized intersections using signal phase information

A variety of sensor technologies, such as loop detectors, traffic cameras, and radar have been developed for real-time traffic monitoring at intersections most of which are limited to providing link traffic information with few being capable of detecting turning movements. Accurate real-time information on turning movement counts at signalized intersections is a critical requirement for applications such as adaptive traffic signal control. Several attempts have been made in the past to develop algorithms for inferring turning movements at intersections from entry and exit counts; however, the estimation quality of these algorithms varies considerably. This paper introduces a method to improve accuracy and robustness of turning movement estimation at signalized intersections. The new algorithm makes use of signal phase status to minimize the underlying estimation ambiguity. A case study was conducted based on turning movement data obtained from a four-leg signalized intersection to evaluate the performance of the proposed method and compare it with two other existing well-known estimation methods. The results show that the algorithm is accurate, robust and fairly straightforward for real world implementation.     

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.     

Continuum signalized junction model for dynamic traffic networks: Offset,spillback, and multiple signal phases

This paper extends the continuum signalized intersection model exhaustively studied in Han et al. (2014) to more accurately account for three realistic complications: signal offsets, queue spillbacks, and complex signal phasing schemes. The model extensions are derived theoretically based on signal cycle, green split, and offset, and are shown to approximate well traffic operations at signalized intersections treated using the traditional (and more realistic) on-and-off model. We propose a generalized continuum signal model, which explicitly handles complex vehicle spillback patterns on signalized networks with provable error estimates. Under mild conditions, the errors are small and bounded by fixed values that do not grow with time. Overall, this represents a significant improvement over the original continuum model, which had errors that grew quickly with time in the presence of any queue spillbacks and for which errors were not explicitly derived for different offset cases. Thus, the new model is able to more accurately approximate traffic dynamics in large networks with multiple signals under more realistic conditions. We also qualitatively describe how this new model can be applied to several realistic intersection configurations that might be encountered in typical urban networks. These include intersections with multiple entry and exit links, complex signal phasing, all-red times, and the presence of dedicated turning lanes. Numerical tests of the models show remarkable consistency with the on-and-off model, as expected from the theory, with the added benefit of significant computational savings and higher signal control resolution when using the continuum model.     

Automated cars: Queue discharge at signalized intersections with ‘Assured-Clear-Distance-Ahead’ driving strategies

This study addresses the impacts of automated cars on traffic flow at signalized intersections. We develop and subsequently employ a deterministic simulation model of the kinematics of automated cars at a signalized intersection approach, when proceeding forward from a stationary queue at the beginning of a signal phase. In the discrete-time simulation, each vehicle pursues an operational strategy that is consistent with the ‘Assured Clear Distance Ahead’ criterion: each vehicle limits its speed and spacing from the vehicle ahead of it by its objective of not striking it, regardless of whether or not the future behavior of the vehicle ahead is cooperative. The simulation incorporates a set of assumptions regarding the values of operational parameters that will govern automated cars’ kinematics in the immediate future, which are sourced from the relevant literature.We report several findings of note. First, under a set of assumed ‘central’ (i.e. most plausible) parameter values, the time requirement to process a standing queue of ten vehicles is decreased by 25% relative to human driven vehicles. Second, it was found that the standard queue discharge model for human–driven cars does not directly transfer to queue discharge of automated vehicles. Third, a wet roadway surface may result in an increase in capacity at signalized intersections. Fourth, a specific form of vehicle-to-vehicle (V2V) communications that allows all automated vehicles in the stationary queue to begin moving simultaneously at the beginning of a signal phase provides relatively minor increases in capacity in this analysis. Fifth, in recognition of uncertainty regarding the value of each operational parameter, we identify (via scenario analysis, calculation of arc elasticities, and Monte-Carlo methods) the relative sensitivity of overall traffic flow efficiency to the value of each operational parameter.This study comprises an incremental step towards the broader objective of adapting standard techniques for analyzing traffic operations to account for the capabilities of automated vehicles.     

Identification of oversaturated intersections using high-resolution traffic signal data

Conceptually, an oversaturated traffic intersection is defined as one where traffic demand exceeds the capacity. Such a definition, however, cannot be applied directly to identify oversaturated intersections because measuring traffic demand under congested conditions is not an easy task, particularly with fixed-location sensors. In this paper, we circumvent this issue by quantifying the detrimental effects of oversaturation on signal operations, both temporally and spatially. The detrimental effect is characterized temporally by a residual queue at the end of a cycle, which will require a portion of green time in the next cycle; or spatially by a spill-over from downstream traffic whereby usable green time is reduced because of the downstream blockage. The oversaturation severity index (OSI), in either the temporal dimension (T-OSI) or the spatial dimension (S-OSI) can then be measured using high-resolution traffic signal data by calculating the ratio between the unusable green time due to detrimental effects and the total available green time in a cycle. To quantify the T-OSI, in this paper, we adopt a shockwave-based queue estimation algorithm to estimate the residual queue length. S-OSI can be identified by a phenomenon denoted as “Queue-Over-Detector (QOD)”, which is the condition when high occupancy on a detector is caused by downstream congestion. We believe that the persistence duration and the spatial extent with OSI greater than zero provide an important indicator for measuring traffic network performance so that corresponding congestion mitigation strategies can be prepared. The proposed algorithms for identifying oversaturated intersections and quantifying the oversaturation severity index have been field-tested using traffic signal data from a major arterial in the Twin Cities of Minnesota.     

Effects of countdown timers on queue discharge characteristics of through movement at a signalized intersection

This study investigates how countdown timers installed at a signalized intersection affect the queue discharge characteristics of through movement during the green phase. Since the countdown timers display the time remaining (in seconds) until the onset of the green phase, drivers waiting in the queue at the intersection are aware of the upcoming phase change, and are likely to respond quicker. Thus, the countdown timers could reduce the start-up lost time, decrease the saturation headway, and increase the saturation flow rate. This study observed vehicle flow at an intersection in Bangkok for 24 h when the countdown timers were operating, and for another 24 h when the countdown timers were switched off. The signal plans and timings remained unchanged in both cases. Standard statistical t-tests were used to compare the difference in traffic characteristics between the “with timer” and “without timer” cases. It was found that the countdown timers had a significant impact on the start-up lost time, reducing it by 1.00–1.92 s per cycle, or a 17–32% time saving. However, the effects on saturation headway were found to be trivial, which implies that the countdown timers do not have much impact on the saturation flow rate of signalized intersections, especially during the off-peak day period and the late night period. The savings in the start-up lost time from the countdown timers was estimated to be equivalent to an 8–24 vehicles/h increase for each through movement lane at the intersection being studied.     

Noise level in the vicinity of signalized roundabouts

The analysis, assessment and estimation of noise levels in the vicinity of intersections is a more complex problem than a similar analysis for roads and streets. This is due to the varied geometry of the intersections, differences in the loads of individual movements, participation of heavy vehicles and mass transport vehicles, as well as the various types of traffic management and traffic control. This article analyses the influence of intersection type and traffic characteristics on the noise levels in the vicinity of classic channelized intersections with signalization, roundabouts and signalized roundabouts. Based on the conducted measurements, it has been established that, with comparable traffic parameters and the same distance from the geometric centre of the intersection, the L_Aeq value for signalized roundabouts is 2.5–10.8 dB higher in comparison to classic channelized intersections with signalization and 3.3–6.7 dB higher in relations to the analysed roundabout. Additionally the differences between L_Aeq levels at individual entries at the same signalized roundabouts may reach the value of approximately 4.5 dB. Such situation is influenced by differences in the intersection geometry, diameter of the intersection’s central island, traffic flow type, traffic management at the entries and traffic volume, especially the amount and traffic movements of multiple axle heavy vehicles. These factors have been analysed in detail in relation to signalized roundabouts in this paper.     

Modeling traffic operation at signalized intersections without explicit left‐turn yielding rules with an enhanced cell transmission model

This paper presents an enhanced cell transmission model (CTM) to capture traffic operation at signalized intersections without explicit permissive left‐turn yielding rules (i.e. aggressive permissive left‐turn maneuvers may not necessarily yield to opposing through traffic), which can be widely observed in many developing countries. Different from previous studies that focus on traffic dynamics on approaching links, this study contributes to modeling traffic operations within the intersection. A novel cell transmission framework with various types of virtual cells is proposed to model the dynamics of traffic movements from approach to exit. The unique phenomenon of competitive occupying of the conflict point between the left turn and opposing through movements is modeled. The cell state indicating its blockage is proposed to capture the dynamic queue formulation and dissipation and to evaluate the operational traffic performance at the intersection. Field validation results show that the proposed model can capture the operation of traffic at signalized intersections without explicit permissive left‐turn yielding rules with significantly higher level of accuracy than traditional traffic flow models. Copyright © 2016 John Wiley & Sons, Ltd.     

An intersection turning movement estimation procedure based on path flow estimator

Estimation of intersection turning movements is one of the key inputs required for a variety of transportation analysis, including intersection geometric design, signal timing design, traffic impact assessment, and transportation planning. Conventional approaches that use manual techniques for estimation of turning movements are insensitive to congestion. The drawbacks of the manual techniques can be amended by integrating a network traffic model with a computation procedure capable of estimating turning movements from a set of link traffic counts and intersection turning movement counts. This study proposes using the path flow estimator, originally used to estimate path flows (hence origin–destination flows), to derive not only complete link flows, but also turning movements for the whole road network given some counts at selected roads and intersections. Two case studies using actual traffic counts are used to demonstrate the proposed intersection turning movement estimation procedure. Copyright © 2010 John Wiley & Sons, Ltd.     

Using stop bar detector information to determine turning movement proportions in shared lanes

Turning vehicle volumes at signalized intersections are critical inputs for various transportation studies such as level of service, signal timing, and traffic safety analysis. There are various types of detectors installed at signalized intersections for control and operation. These detectors have the potential of producing volume estimates. However, it is quite a challenge to use such detectors for conducting turning movement counts in shared lanes. The purpose of this paper was to provide three methods to estimate turning movement proportions in shared lanes. These methods are characterized as flow characteristics (FC), volume and queue (VQ) length, and network equilibrium (NE). FC and VQ methods are based on the geometry of an intersection and behavior of drivers. The NE method does not depend on these factors and is purely based on detector counts from the study intersection and the downstream intersection. These methods were tested using regression and genetic programming (GP). It was found that the hourly average error ranged between 4 and 27% using linear regression and 1 to 15% using GP. A general conclusion was that the proposed methods have the potential of being applied to locations where appropriate detectors are installed for obtaining the required data. Copyright © 2016 John Wiley & Sons, Ltd.     

Disaggregate safety evaluation for signalized intersections and evaluation tool

This study was to evaluate traffic safety of four‐legged signalized intersections and to develop a spreadsheet tool for identifying high‐risk intersections taking into consideration vehicle movements, left‐turn signal phase types, and times of day. The study used data from Virginia and employed count data models and the empirical Bayes (EB) method for safety evaluation of such intersections. It was found that crash pattern defined by vehicle movements involved in a crash and time of day are important factors for intersection crash analysis. Especially for a safety performance function (SPF), a model specification (Poisson or NB), inclusion of left‐turn signal types, type of traffic flow variables, variable functional forms, and/or magnitudes of coefficients turned out to be different across times of day and crash patterns. The spreadsheet application tool was developed incorporating the developed SPFs and the EB method. As long as Synchro files for signal plans and crash database are maintained, no additional field data collection efforts are required. Adjusting the developed SPFs and the spreadsheet for recent traffic and safety conditions can be done by applying the calibration methods employed in the SafetyAnalyst software and the Highway Safety Manual. Implementing the developed tool equipped with streamlining data entry would greatly improve accuracy and efficiency of safety evaluation of four‐legged signalized intersections in localities and highway agencies that cannot operate the SafetyAnalyst. Copyright © 2010 John Wiley & Sons, Ltd.     

Real-time estimation of lane-based queue lengths at isolated signalized junctions

In this study, we develop a real-time estimation approach for lane-based queue lengths. Our aim is to determine the numbers of queued vehicles in each lane, based on detector information at isolated signalized junctions. The challenges involved in this task are to identify whether there is a residual queue at the start time of each cycle and to determine the proportions of lane-to-lane traffic volumes in each lane. Discriminant models are developed based on time occupancy rates and impulse memories, as calculated by the detector and signal information from a set of upstream and downstream detectors. To determine the proportions of total traffic volume in each lane, the downstream arrivals for each cycle are estimated by using the Kalman filter, which is based on upstream arrivals and downstream discharges collected during the previous cycle. Both the computer simulations and the case study of real-world traffic show that the proposed method is robust and accurate for the estimation of lane-based queue lengths in real time under a wide range of traffic conditions. Calibrated discriminant models play a significant role in determining whether there are residual queued vehicles in each lane at the start time of each cycle. In addition, downstream arrivals estimated by the Kalman filter enhance the accuracy of the estimates by minimizing any error terms caused by lane-changing behavior.     

Queue discharge patterns at signalized intersections with green signal countdown device and long cycle length

Two apparent features that prevail at signalized intersections in China are green signal countdown device and long cycle lengths. The objective of this study is to investigate the impacts of green signal countdown device and long cycle length on queue discharge patterns and to discuss its implications on capacity estimation in the context of China's traffic. At five typical large intersections in Shanghai and Tianjin, 11 through lanes were observed, and 9251 saturation headways were obtained as valid samples. Statistical analyses indicate that the discharge process of queuing vehicles can be divided into three distinct stages according to the discharge flow rate: a start‐up stage, a steady stage, and a rush stage. The average time for queuing vehicles to reach a stationary saturation flow rate, that is, the start‐up stage, was found to be approximately 20–30 seconds; the rush stage usually occurs during the phase transition period. The finding is contrary to the conventional assumption that the discharge rate reaches a maximum value after the fourth vehicle is discharged and then remains constant during the green time until the queue is completely dissolved. The capacity estimation errors that might arise from the conventional methods are discussed through a comparative study and a sensitivity analysis that are based on the identified queue discharge patterns. In addition, a piecewise linear regression method was proposed in order to reduce such errors. The proposed method can be used for capacity estimation at signalized intersections with the identified queue discharge patterns. Copyright © 2017 John Wiley & Sons, Ltd.     

Traffic conflict models to evaluate the safety of signalized intersections at the cycle level

The safety of signalized intersections has often been evaluated at an aggregate level relating collisions to annual traffic volume and the geometric characteristics of the intersection. However, for many safety issues, it is essential to understand how changes in traffic parameters and signal control affect safety at the signal cycle level. This paper develops conflict-based safety performance functions (SPFs) for signalized intersections at the signal cycle level. Traffic video-data was recorded for six signalized intersections located in two cities in Canada. A video analysis procedure is proposed to collect rear-end conflicts and various traffic variables at each signal cycle from the recorded videos. The traffic variables include: traffic volume, maximum queue length, shock wave characteristics (e.g. shock wave speed and shock wave area), and the platoon ratio. The SPFs are developed using the generalized linear models (GLM) approach. The results show that all models have good fit and almost all the explanatory variables are statistically significant leading to better prediction of conflict occurrence beyond what can be expected from the traffic volume only. Furthermore, space-time conflict heat maps are developed to investigate the distribution of the traffic conflicts. The heat maps illustrate graphically the association between rear-end conflicts and various traffic parameters. The developed models can give insight about how changes in the signal cycle design affect the safety of signalized intersections. The overall goal is to use the developed models for the real-time optimization of signalized intersection safety by changing the signal design.     

Statistical characteristics of transitional queue conditions in signalized arterials

The performance of signalized arterials is related to queuing phenomena. The paper investigates the effect of transitional traffic flow conditions imposed by the formation and dissipation of queues. A cross-recurrence quantification analysis combined with Bayesian augmented networks are implemented to reveal the prevailing statistical characteristics of the short-term traffic flow patterns under the effect of transitional queue conditions. Results indicate that transitions between free-flow conditions, critical queue conditions that exceed the detector’s length, as well as the occurrence of spillovers impose a set of prevailing traffic flow patterns with different statistical characteristics with respect to determinism, nonlinearity, non-stationarity and laminarity. The complexity in critical queue conditions is further investigated by introducing two supplementary regions in the critical area before spillover occurrence. Results indicate that the supplementary information on the transitional conditions in the critical area increases the accuracy of the predictive relations between the statistical characteristics of traffic flow evolution and the occurrence of transitions.     

A robust optimization approach for dynamic traffic signal control with emission considerations

We consider an analytical signal control problem on a signalized network whose traffic flow dynamic is described by the Lighthill–Whitham–Richards (LWR) model (Lighthill and Whitham, 1955; Richards, 1956). This problem explicitly addresses traffic-derived emissions as constraints or objectives. We seek to tackle this problem using a mixed integer mathematical programming approach. Such class of problems, which we call LWR-Emission (LWR-E), has been analyzed before to certain extent. Since mixed integer programs are practically efficient to solve in many cases (Bertsimas et al., 2011b), the mere fact of having integer variables is not the most significant challenge to solving LWR-E problems; rather, it is the presence of the potentially nonlinear and nonconvex emission-related constraints/objectives that render the program computationally expensive.To address this computational challenge, we proposed a novel reformulation of the LWR-E problem as a mixed integer linear program (MILP). This approach relies on the existence of a statistically valid macroscopic relationship between the aggregate emission rate and the vehicle occupancy on the same link. This relationship is approximated with certain functional forms and the associated uncertainties are handled explicitly using robust optimization (RO) techniques. The RO allows emissions-related constraints and/or objectives to be reformulated as linear forms under mild conditions. To further reduce the computational cost, we employ a link-based LWR model to describe traffic dynamics with the benefit of fewer (integer) variables and less potential traffic holding. The proposed MILP explicitly captures vehicle spillback, avoids traffic holding, and simultaneously minimizes travel delay and addresses emission-related concerns.