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.     

Lane-based real-time queue length estimation using license plate recognition data

License plate recognition (LPR) data are emerging data sources that provide rich information in estimating the traffic conditions of urban arterials. While large-scale LPR system is not common in US, last few years have seen rapid developments and implementations in many other parts of world (e.g. China, Thailand and Middle East). Due to privacy issues, LPR data are seldom available to research communities. However, when available, this data source can be valuable in estimating real-time operational metrics in transportation systems. This paper proposes a lane-based real-time queue length estimation model using the license plate recognition (LPR) data. In the model, an interpolation method based on Gaussian process is developed to reconstruct the equivalent cumulative arrival–departure curve for each lane. The missing information for unrecognized or unmatched vehicles is obtained from the reconstructed arrival curve. With the complete arrival and departure information, a car-following based simulation scheme is applied to estimate the real-time queue length for each lane. The proposed model is validated using ground truth information of the maximum queue lengths from the city of Langfang in China. The results show that the model can capture the variations in queue lengths in the ground truth data, and the maximum queue length for each signal cycle can be estimated with a reasonable accuracy. The estimated queue length information using the proposed model can serve as a useful performance metric for various real-time traffic control applications.     

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.     

Distributions of queue lengths at fixed time traffic signals

This paper presents a new model which studies probability distributions of queue lengths at fixed time traffic signals. It extends Haight's model for Poisson arrivals that the arrival distribution during the effective red period is general and the headway between two successive departures is not less than the minimum departure headway. Moreover, the probability generating function of the queue length, at the end of the effective red period, is derived. The probabilities of the queue lengths, at the ends of the effective green, actual red and amber periods, are also obtained. Comparison is made with Haight's model. Finally a case study for the proposed model is reported.     

Designing heterogeneous sensor networks for estimating and predicting path travel time dynamics: An information-theoretic modeling approach

With a particular emphasis on the end-to-end travel time prediction problem, this paper proposes an information-theoretic sensor location model that aims to minimize total travel time uncertainties from a set of point, point-to-point and probe sensors in a traffic network. Based on a Kalman filtering structure, the proposed measurement and uncertainty quantification models explicitly take into account several important sources of errors in the travel time estimation/prediction process, such as the uncertainty associated with prior travel time estimates, measurement errors and sampling errors. By considering only critical paths and limited time intervals, this paper selects a path travel time uncertainty criterion to construct a joint sensor location and travel time estimation/prediction framework with a unified modeling of both recurring and non-recurring traffic conditions. An analytical determinant maximization model and heuristic beam-search algorithm are used to find an effective lower bound and solve the combinatorial sensor selection problem. A number of illustrative examples and one case study are used to demonstrate the effectiveness of the proposed methodology.     

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.     

Queue length estimation at metered freeway‐to‐freeway connectors

Freeway‐to‐freeway connector metering is a cost‐effective and proven freeway management strategy for relieving recurrent congestion. However, one of the critical challenges in design and operation of freeway‐to‐freeway connector metering is the lack of up‐to‐date queue storage length design guidance. In this study, it was found that ramp queue is dynamically related to the metering rate, on‐ramp demand, and traffic flow arrival pattern. Hence, simply using an average demand cannot provide accurate queue length estimation and is also not suitable for queue storage design where the maximum or a percentile queue length is generally used. A mesoscopic queue length simulation model was developed based on the input–output method for estimating queue lengths under various demand‐to‐capacity ratio scenarios. Simulation results indicate that for under‐saturated situations, the ramp queue may exist temporally due to the random short‐term surge of traffic arrivals, and the exponential function could best capture the relationship between queue length and demand‐to‐capacity ratio. For over‐saturated situations, the ramp queue tends to prolong linearly with the demand‐to‐capacity ratio. Based on the simulation, it was recommended that queue storage length be designed as 4.3% of on‐ramp demand when demand is lower than 1200 vph or 2.3% when demand is between 1200 and 2400 vph. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

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.     

Modeling and simulation of vehicle projection arrival–discharge process in adaptive traffic signal controls

Real‐time signal control operates as a function of the vehicular arrival and discharge process to satisfy a pre‐specified operational performance. This process is often predicted based on loop detectors placed upstream of the signal. In our newly developed signal control for diamond interchanges, a microscopic model is proposed to estimate traffic flows at the stop‐line. The model considers the traffic dynamics of vehicular detection, arrivals, and departures, by taking into account varying speeds, length of queues, and signal control. As the signal control is optimized over a rolling horizon that is divided into intervals, the vehicular detection for and projection into the corresponding horizon intervals are also modeled. The signal control algorithm is based on dynamic programming and the optimization of signal policy is performed using a certain performance measure involving delays, queue lengths, and queue storage ratios. The arrival–discharge model is embedded in the optimization algorithm and both are programmed into AIMSUN, a microscopic stochastic simulation program. AIMSUN is then used to simulate the traffic flow and implement the optimal signal control by accessing internal data including detected traffic demand and vehicle speeds. Sensitivity analysis is conducted to study the effect of selecting different optimization criteria on the signal control performance. It is concluded that the queue length and queue storage ratio are the most appropriate performance measures in real‐time signal control of interchanges. Copyright © 2010 John Wiley & Sons, Ltd.     

Preliminary analysis on dynamic route choice behavior: Using probe‐vehicle data

Dynamic traffic assignment models have been attracting increasing attention with the progress of traffic management policies based on information technology. These dynamic estimation tools, however, just apply static route choice models either at only origin node or at every arrival node. This paper aims at providing some knowledge on drivers' dynamic route choice behavior using probe‐vehicle data. The results of analyses show that route choice behavior relates to the distance from driver's position to the destination and that dynamic route choice behavior is modeled better by considering decision process during the trip.     

Modeling probability distribution of delay at signalized intersections

Accurate estimation of vehicle delay is difficult because of the randomness of traffic flow and large number of factors affecting intersection capacity. Existing delay models simplify the real traffic conditions and provide only approximate point estimates of average delay, whereas its variability should also be of interest. A stochastic model was used to study the changing probability distribution of delay. The model is based on sequential calculation of queue length probabilities with any type of arrival process. Delay probability distribution was investigated for different degrees of saturation, arrival types and control conditions. The variance of delay increases rapidly with degree of saturation and is inversely proportional to the approach capacity. Other parameters such as cycle time and saturation flow do not have a significant effect on delay distribution. Both the mean and variance of delay are sensitive to arrival process characteristics and increase with the variance of arrivals.     

Optimisation of parking guidance and information systems display configurations

Operators of parking guidance and information (PGI) systems often have difficulty in determining the best car park availability information to present to drivers in periods of high demand. This paper describes a behavioural model of parking choice incorporating drivers perceptions of waiting times at car parks based on PGI signs. This model was used to predict the influence of PGI signs on the overall performance of the traffic system.Relationships were developed for estimating the arrival rates at car parks based on trip patterns, driver characteristics, car park attributes as well as the car park availability information displayed on PGI signs. Drivers' perceptions of waiting times at car parks were assumed to be influenced by the PGI signs for observers of the signs and actual car park utilisation levels for non-observers. The model assumes that the choice of car park does not change after entering the city centre, even if conditions observed are different from those initially perceived.A mathematical programme was formulated to determine the optimal display PGI sign configuration to minimise queue lengths and vehicle kilometres of travel (VKT). The model was limited to off-street parking choices and illegal parking was not incorporated. A simple genetic algorithm was used to identify solutions that significantly reduced queue lengths and VKT compared with existing practices.These procedures were applied to an existing PGI system operating in Tama New Town near Tokyo. Significant reductions in queue lengths and VKT were predicted using the optimisation model. This would reduce traffic congestion and lead to various environmental benefits.     

A probabilistic model for traffic at actuated control signals

Vehicle actuated controls are designed to adapt green and red times automatically, according to the actual dynamics of the arrival, departure and queuing processes. In turn, drivers experience variable delays and waiting times at these signals. However, in practice, delays and waiting times are computed at these systems with models that assume stationariety in the arrival process, and that are capable of computing simply expectation values, while no information is given on the uncertainty around this expectation. The growing interest on measures like travel time reliability, or network robustness motivates the development of models able to quantify the variability of traffic at these systems.This paper presents a new modeling approach for estimating queues and signal phase times, based on probabilistic theory. This model overcomes the limitations of existing models in that it does not assume stationary arrival rates, but it assumes any temporal distribution as input, and allows one to compute the temporal evolution of queue length and signal sequence probabilities. By doing so, one can also quantify the uncertainty in the estimation of delays and waiting times as time-dependent processes. The results of the probabilistic approach have been compared to the results of repeated microscopic simulations, showing good agreement. The smaller number of parameters and shorter computing times required in the probabilistic approach makes the model suitable for, e.g., planning and design problems, as well as model-based travel time estimation.     

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

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

Network traffic flow optimization under performance constraints

In this paper, a model-based perimeter control policy for large-scale urban vehicular networks is proposed. Assuming a homogeneously loaded vehicle network and the existence of a well-posed Network Fundamental Diagram (NFD), we describe a protected network throughout its aggregated dynamics including nonlinear exit flow characteristics. Within this framework of constrained optimal boundary flow gating, two main performance metrics are considered: (a) first, connected to the NFD, the concept of average network travel time and delay as a performance metric is defined; (b) second, at boundaries, we take into account additional external network queue dynamics governed by uncontrolled inflow demands. External queue capacities in terms of finite-link lengths are used as the second performance metric. Hence, the corresponding performance requirement is an upper bound of external queues. While external queues represent vehicles waiting to enter the protected network, internal queue describes the protected network’s aggregated behavior.By controlling the number of vehicles joining the internal queue from the external ones, herewith a network traffic flow maximization solution subject to the internal and external dynamics and their performance constraints is developed. The originally non-convex optimization problem is transformed to a numerically efficiently convex one by relaxing the performance constraints into time-dependent state boundaries. The control solution can be interpreted as a mechanism which transforms the unknown arrival process governing the number of vehicles entering the network to a regulated process, such that prescribed performance requirements on travel time in the network and upper bound on the external queue are satisfied. Comparative numerical simulation studies on a microscopic traffic simulator are carried out to show the benefits of the proposed method.     

An observed traffic pattern in long freeway queues

A simple exercise in data analysis showed that, in queued traffic, a well-defined relation exists between the flow on a homogeneous freeway segment and the segment’s vehicle accumulation. The exercise consisted of constructing cumulative vehicle arrival curves to measure the flows and densities on multiple segments of a queued freeway. At this particular site, each interchange enveloped by the queue exhibited a higher on-ramp flow than off-ramp flow and as a consequence, motorists encountered a steady improvement in traffic conditions (e.g., reduced densities and increased speeds) as they traveled from the tail of the queue to the bottleneck. This finding has practical implications for freeway traffic planning and management. Perhaps most notably, it suggests that the first-order hydrodynamic theory of traffic is adequate for describing some of the more relevant features of queue evolution. This and other practical issues are discussed in some detail.     

Nonlinear gating control for urban road traffic network using the network fundamental diagram

This work proposes a nonlinear model predictive controller for the urban gating problem. The system model is formalized based on a research on existing models of the network fundamental diagram and the perimeter control systems. For the existing models, modifications are suggested: additional state variables are allocated to describe the queue dynamics at the network gates. Using the extended model, a nonlinear model predictive controller is designed offering a ‘non‐greedy’ policy compared with previous, ‘greedy’ gating control designs. The greedy and non‐greedy nonlinear model predictive control (NMPC) controllers are compared with a greedy linear feedback proportional‐integral‐derivative (PID) controller in different traffic situations. The proposed non‐greedy NMPC controller outperforms the other two approaches in terms of travel distance performance and queue lengths. The performance results justify the consideration of queue lengths in dynamic modeling, and the use of NMPC approach for controller design. Copyright © 2014 John Wiley & Sons, Ltd.     

Estimating median velocity instead of mean velocity at single loop detectors

Loop detectors are the preeminent vehicle detector for freeway traffic surveillance. Although single loops have been used for decades, debate continues on how to interpret the measurements. Many researchers have sought better estimates of velocity from single loops. The preceding work has emphasized techniques that use many samples of aggregate flow and occupancy to reduce the estimation error. Although rarely noted, these techniques effectively seek to reduce the bias due to long vehicles in measured occupancy. This paper presents a different approach, using a new aggregation methodology to estimate velocity and reduce the impact of long vehicles in the original traffic measurements. In contrast to conventional practice, the new estimate significantly reduces velocity estimation errors when it is not possible to control for a wide range of vehicle lengths.