A bi-level model of dynamic traffic signal control with continuum approximation

This paper proposes a bi-level model for traffic network signal control, which is formulated as a dynamic Stackelberg game and solved as a mathematical program with equilibrium constraints (MPEC). The lower-level problem is a dynamic user equilibrium (DUE) with embedded dynamic network loading (DNL) sub-problem based on the LWR model (Lighthill and Whitham, 1955; Richards, 1956). The upper-level decision variables are (time-varying) signal green splits with the objective of minimizing network-wide travel cost. Unlike most existing literature which mainly use an on-and-off (binary) representation of the signal controls, we employ a continuum signal model recently proposed and analyzed in Han et al. (2014), which aims at describing and predicting the aggregate behavior that exists at signalized intersections without relying on distinct signal phases. Advantages of this continuum signal model include fewer integer variables, less restrictive constraints on the time steps, and higher decision resolution. It simplifies the modeling representation of large-scale urban traffic networks with the benefit of improved computational efficiency in simulation or optimization. We present, for the LWR-based DNL model that explicitly captures vehicle spillback, an in-depth study on the implementation of the continuum signal model, as its approximation accuracy depends on a number of factors and may deteriorate greatly under certain conditions. The proposed MPEC is solved on two test networks with three metaheuristic methods. Parallel computing is employed to significantly accelerate the solution procedure.     

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.     

Signalized intersections with variable flow rates: II A model for delay estimation

This second part of our work develops a model for delay estimation at intersections whose traffic signal controls are continuously being updated. Generally, these traffic signals are centrally controlled. The foundation for the delay estimation model is based on a queuing theory model called “Preemptive resume discipline for M/G/1 with two priority levels.” This queuing model assumes that two customers arrive at acertain point by a Poisson arrival process, and that one customer has service priority over the second customer. The analogy for the case of intersection control is that the preferred customers are the red lights and the secondary customers are the vehicles. In order to adapt the model to the realistic behavior of vehicle traffic at continuously adjusted signals, components are derived to modify the model. The simulation results of the first part of this work are used to calculate adjustment factors that fairly accurately reproduce the simulated delays. This gives rise to the advantage of using in practice a closed mathematical model, in particular when trying to optimize the operation of signalized intersections at the network level.     

An application of shock wave theory to traffic signal control

A real time control policy minimizing total intersection delays subject to queue length constraints at an isolated signalized intersection is developed in this paper. The policy is derived from a new traffic model which describes the simultaneous evolution of queue lengths of two conflicting traffic streams, controlled by a traffic light, in both time and space. The model is based on the examination of shock waves generated upstream of the stop lines by the intermittent service of traffic at the signal. The proposed policy was tested against the existing pre-timed control policy at a high volume intersection and it was found superior, especially when demands increase well above the saturation level.     

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.     

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.     

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.     

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.     

Stochastic adaptive control model for traffic signal systems

An adaptive control model of a network of signalized intersections is proposed based on a discrete-time, stationary, Markov decision process. The model incorporates probabilistic forecasts of individual vehicle actuations at downstream inductance loop detectors that are derived from a macroscopic link transfer function. The model is tested both on a typical isolated traffic intersection and a simple network comprised of five four-legged signalized intersections, and compared to full-actuated control. Analyses of simulation results using this approach show significant improvement over traditional full-actuated control, especially for the case of high volume, but not saturated, traffic demand.     

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.     

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.     

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

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

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.     

Optimization of pedestrian phase patterns at signalized intersections: a multi‐objective approach

This paper presents a multi‐objective optimization model and its solution algorithm for optimization of pedestrian phase patterns, including the exclusive pedestrian phase (EPP) and the conventional two‐way crossing (TWC) at an intersection. The proposed model will determine the optimal pedestrian phase pattern and the corresponding signal timings at an intersection to best accommodate both vehicular traffic and pedestrian movements. The proposed model is unique with respect to the following three critical features: (1) proposing an unbiased performance index for comparison of EPP and TWC by explicitly modeling the pedestrian delay under the control of TWC and EPP; (2) developing a multi‐objective model to maximize the utilization of the available green time by vehicular traffic and pedestrian under both EPP or TWC; and (3) designing a genetic algorithm based heuristic algorithm to solve the model. Case study and sensitivity analysis results have shown the promising property of the proposed model to assist traffic practitioners, researchers, and authorities in properly selecting pedestrian phase patterns at signalized intersections. Copyright © 2013 John Wiley & Sons, Ltd.     

An exact modelling of the uniform control traffic delay in undersaturated signalized intersections

The average delay experienced by vehicles at a signalized intersection defines the level of service (LOS) at which the intersection operates. A major challenge in this regard is the ability to accurately estimate all the components underlying the overall control delay, including the uniform, incremental and initial queue delays. This paper tackles this challenging task by proposing a novel exact model of the uniform control delay component with a view to enhancing the accuracy of the existing approximate models, notably, the one reported in the Highway Capacity Manual 2010. Both graphical and analytical proofs are employed to derive exact closed‐form expressions for the uniform control delay at undersaturated signalized intersections. The high degree of accuracy of the proposed models is analysed through extensive simulations to demonstrate their abilities to exactly characterize the performance of real‐life intersections in terms of the resulting vehicle delay. Unlike the existing widely adopted uniform delay models, which tend to overestimate the LOS of real‐life intersections, the delay models introduced in this paper have the merit of exactly capturing such a LOS. Copyright © 2016 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.     

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.     

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.