Stochasticity of freeway operational capacity and chance-constrained ramp metering

The notion of capacity is essential to the planning, design, and operations of freeway systems. However, in the practice freeway capacity is commonly referred as a theoretical/design value without consideration of operational characteristics of freeways. This is evident from the Highway Capacity Manual (HCM) 2000 in that no influence from downstream traffic is considered in the definition of freeway capacity. In contrast to this definition, in this paper, we consider the impact of downstream traffic and define freeway operational capacity as the maximum hourly rate at which vehicles can be expected to traverse a point or a uniform section of a roadway under prevailing traffic flow conditions. Therefore freeway operational capacity is not a single value with theoretical notion. Rather, it changes under different traffic flow conditions. Specifically, this concept addresses the capacity loss during congested traffic conditions. We further study the stochasticity of freeway operational capacity by examining loop detector data at three specifically selected detector stations in the Twin Cities’ area. It is found that values of freeway operational capacity under different traffic flow conditions generally fit normal distributions. In recognition of the stochastic nature of freeway capacity, we propose a new chance-constrained ramp metering strategy, in which, constant capacity value is replaced by a probabilistic one that changes dynamically depending on real-time traffic conditions and acceptable probability of risk determined by traffic engineers. We then improve the Minnesota ZONE metering algorithm by applying the stochastic chance constraints and test the improved algorithm through microscopic traffic simulation. The evaluation results demonstrate varying degrees of system improvement depending on the acceptable level of risk defined.     

Discrete dynamic models for freeway incident detection systems

This paper considers the problem of freeway incident detection within the general framework of computer‐based freeway surveillance and control. A new approach to the detection of freeway traffic incidents is presented based on a discrete‐time stochastic model of the form ARIMA (0, 1, 3) that describes the dynamics of traffic occupancy observations. This approach utilizes real‐time estimates of the variability in traffic occupancies as detection thresholds, thus eliminating the need for threshold calibration and lessening the problem of false‐alarms. Because the moving average parameters of the ARIMA (0, 1, 3) model change over time, these parameters can be updated occasionally. The performance of the developed detection algorithm has been evaluated in terms of detection rate, false‐alarm rate, and average time‐lag to detection, using a total of 1692 minutes of occupancy observations recorded during 50 representative traffic incidents.     

Cooperative traffic control of a mixed network with two urban regions and a freeway

Currently most optimization methods for urban transport networks (i) are suited for networks with simplified dynamics that are far from real-sized networks or (ii) apply decentralized control, which is not appropriate for heterogeneously loaded networks or (iii) investigate good-quality solutions through micro-simulation models and scenario analysis, which make the problem intractable in real time. In principle, traffic management decisions for different sub-systems of a transport network (urban, freeway) are controlled by operational rules that are network specific and independent from one traffic authority to another. In this paper, the macroscopic traffic modeling and control of a large-scale mixed transportation network consisting of a freeway and an urban network is tackled. The urban network is partitioned into two regions, each one with a well-defined Macroscopic Fundamental Diagram (MFD), i.e. a unimodal and low-scatter relationship between region density and outflow. The freeway is regarded as one alternative commuting route which has one on-ramp and one off-ramp within each urban region. The urban and freeway flow dynamics are formulated with the tool of MFD and asymmetric cell transmission model, respectively. Perimeter controllers on the border of the urban regions operating to manipulate the perimeter interflow between the two regions, and controllers at the on-ramps for ramp metering are considered to control the flow distribution in the mixed network. The optimal traffic control problem is solved by a Model Predictive Control (MPC) approach in order to minimize total delay in the entire network. Several control policies with different levels of urban-freeway control coordination are introduced and tested to scrutinize the characteristics of the proposed controllers. Numerical results demonstrate how different levels of coordination improve the performance once compared with independent control for freeway and urban network. The approach presented in this paper can be extended to implement efficient real-world control strategies for large-scale mixed traffic networks.     

Optimization of mainline traffic via an adaptive co-ordinated ramp-metering control model with dynamic OD estimation

Frequently implemented at freeway accesses to streamline traffic, ramp-metering control strategy is often implemented during rush hours in heavily congested areas. This paper presents a novel ramp-metering control model capable of optimizing mainline traffic by providing metering rates for accesses within the control segments. Based on Payne's continuum traffic stream model, a linear dynamic model with a quadratic objective function is constructed for integrated-responsive ramp-metering control. Incorporating on-line origin–destination (OD) estimation of co-ordinated interchanges into the proposed model increases efficiency of the control. In addition, an iterative algorithm is proposed to obtain the optimal solution. Simulation results demonstrate the robustness of the proposed model and its ability to streamline freeway traffic while avoiding traffic congestion.     

Using high-resolution event-based data for traffic modeling and control: An overview

Research on using high-resolution event-based data for traffic modeling and control is still at early stage. In this paper, we provide a comprehensive overview on what has been achieved and also think ahead on what can be achieved in the future. It is our opinion that using high-resolution event data, instead of conventional aggregate data, could bring significant improvements to current research and practices in traffic engineering. Event data records the times when a vehicle arrives at and departs from a vehicle detector. From that, individual vehicle’s on-detector-time and time gap between two consecutive vehicles can be derived. Such detailed information is of great importance for traffic modeling and control. As reviewed in this paper, current research has demonstrated that event data are extremely helpful in the fields of detector error diagnosis, vehicle classification, freeway travel time estimation, arterial performance measure, signal control optimization, traffic safety, traffic flow theory, and environmental studies. In addition, the cost of event data collection is low compared to other data collection techniques since event data can be directly collected from existing controller cabinet without any changes on the infrastructure, and can be continuously collected in 24/7 mode. This brings many research opportunities as suggested in the paper.     

Stochastic cell transmission model (SCTM): A stochastic dynamic traffic model for traffic state surveillance and assignment

The paper proposes a first-order macroscopic stochastic dynamic traffic model, namely the stochastic cell transmission model (SCTM), to model traffic flow density on freeway segments with stochastic demand and supply. The SCTM consists of five operational modes corresponding to different congestion levels of the freeway segment. Each mode is formulated as a discrete time bilinear stochastic system. A set of probabilistic conditions is proposed to characterize the probability of occurrence of each mode. The overall effect of the five modes is estimated by the joint traffic density which is derived from the theory of finite mixture distribution. The SCTM captures not only the mean and standard deviation (SD) of density of the traffic flow, but also the propagation of SD over time and space. The SCTM is tested with a hypothetical freeway corridor simulation and an empirical study. The simulation results are compared against the means and SDs of traffic densities obtained from the Monte Carlo Simulation (MCS) of the modified cell transmission model (MCTM). An approximately two-miles freeway segment of Interstate 210 West (I-210W) in Los Ageles, Southern California, is chosen for the empirical study. Traffic data is obtained from the Performance Measurement System (PeMS). The stochastic parameters of the SCTM are calibrated against the flow-density empirical data of I-210W. Both the SCTM and the MCS of the MCTM are tested. A discussion of the computational efficiency and the accuracy issues of the two methods is provided based on the empirical results. Both the numerical simulation results and the empirical results confirm that the SCTM is capable of accurately estimating the means and SDs of the freeway densities as compared to the MCS.     

Time of day intervals partition for bus schedule using GPS data

Time of day partition of bus operating hours is a prerequisite of bus schedule design. Reasonable partition plan is essential to improve the punctuality and level of service. In most mega cities, bus vehicles have been equipped with global positioning system (GPS) devices, which is convenient for transit agency to monitor bus operations. In this paper, a new algorithm is developed based on GPS data to partition bus operating hours into time of day intervals. Firstly, the impacts of passenger demand and network traffic state on bus operational performance are analyzed. Then bus dwell time at stops and inter-stop travel time, which can be attained based on GPS data, are selected as partition indexes. For buses clustered in the same time-of-day interval, threshold values of differences in dwell time at stops and inter-stop travel time are determined. The buses in the same time-of-day interval should have adjacent dispatching numbers, which is set as a constraint. Consequently, a partition algorithm with three steps is developed. Finally, a bus route in Suzhou China is taken as an example to validate the algorithm. Three partition schemes are given by setting different threshold values for the two partition indexes. The present scheme in practice is compared with the three proposed schemes. To balance the number of ToD intervals and partition precision, a Benefit Evaluation Index is proposed, for a better time-of-day interval plan.     

RENAISSANCE – A unified macroscopic model-based approach to real-time freeway network traffic surveillance

The paper presents a unified macroscopic model-based approach to real-time freeway network traffic surveillance as well as a software tool RENAISSANCE that has been recently developed to implement this approach for field applications. RENAISSANCE is designed on the basis of stochastic macroscopic freeway network traffic flow modeling, extended Kalman filtering, and a number of traffic surveillance algorithms. Fed with a limited amount of real-time traffic measurements, RENAISSANCE enables a number of freeway network traffic surveillance tasks, including traffic state estimation and short-term traffic state prediction, travel time estimation and prediction, queue tail/head/length estimation and prediction, and incident alarm. The traffic state estimation and prediction lay the operating foundation of RENAISSANCE since RENAISSANCE bases the other traffic surveillance tasks on its traffic state estimation or prediction results. The paper first introduces the utilized stochastic macroscopic freeway network traffic flow model and a real-time traffic measurement model, upon which the complete dynamic system model of RENAISSANCE is established with special attention to the handling of some important model parameters. The algorithms for the various traffic surveillance tasks addressed are described along with the functional architecture of the tool. A simulation test was conducted via application of RENAISSANCE to a hypothetical freeway network example with a sparse detector configuration, and the testing results are presented in some detail. Final conclusions and future work are outlined.     

A recursive, cell processing model for predicting freeway travel times

Travel time information influences driver behaviour and can contribute to reducing congestion and improving network efficiency. Consequently many road authorities disseminate travel time information on road side signs, web sites and radio traffic broadcasts. Operational systems commonly rely on speed data obtained from inductive loop detectors and estimate travel times using simple algorithms that are known to provide poor predictions particularly on either side of the peak period. This paper presents a new macroscopic model for predicting freeway travel times which overcomes the limitations of operational ‘instantaneous’ speed models by drawing on queuing theory to model the processing of vehicles in sections or cells of the freeway. The model draws on real-time speed, flow and occupancy data and is formulated to accommodate varying geometric conditions, the relative distribution of vehicles along the freeway, variations in speed limits, the impact of ramp flows and fixed or transient bottlenecks. Field validation of the new algorithm was undertaken using data from two operational freeways in Melbourne, Australia. Consistent with the results of simulation testing, the validation confirmed that the recursive model provided a substantial improvement in travel time predictions when compared to the model currently used to provide real-time travel time information to motorists in Melbourne.     

Traffic state estimation and uncertainty quantification based on heterogeneous data sources: A three detector approach

This study focuses on how to use multiple data sources, including loop detector counts, AVI Bluetooth travel time readings and GPS location samples, to estimate macroscopic traffic states on a homogeneous freeway segment. With a generalized least square estimation framework, this research constructs a number of linear equations that map the traffic measurements as functions of cumulative vehicle counts on both ends of a traffic segment. We extend Newell’s method to solve a stochastic three-detector problem, where the mean and variance estimates of cell-based density and flow can be analytically derived through a multinomial probit model and an innovative use of Clark’s approximation method. An information measure is further introduced to quantify the value of heterogeneous traffic measurements for improving traffic state estimation on a freeway segment.     

A phase-based smoothing method for accurate traffic speed estimation with floating car data

In this paper, a novel freeway traffic speed estimation method based on probe data is presented. In contrast to other traffic speed estimators, it only requires velocity data from probes and does not depend on any additional data inputs such as density or flow information. In the first step the method determines the three traffic phases free flow, synchronized flow, and Wide Moving Jam (WMJ) described by Kerner et al. in space and time. Subsequently, reported data is processed with respect to the prevailing traffic phase in order to estimate traffic velocities. This two-step approach allows incorporating empirical features of phase fronts into the estimation procedure. For instance, downstream fronts of WMJs always propagate upstream with approximately constant velocity, and downstream fronts of synchronized flow phases usually stick to bottlenecks. The second step assures the validity of measured velocities is limited to the extent of its assigned phase. Effectively, velocity information in space-time can be estimated more distinctively and the result is therefore more accurate even if the input data density is low.The accuracy of the proposed Phase-Based Smoothing Method (PSM) is evaluated using real floating car data collected during two traffic congestions on the German freeway A99 and compared to the performance of the Generalized Adaptive Smoothing Method (GASM) as well as a naive algorithm. The quantitative and qualitative results show that the PSM reconstructs the congestion pattern more accurately than the other two. A subsequent analysis of the computational efficiency and sensitivity demonstrates its practical suitability.     

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.     

Two-class freeway traffic regulation to reduce congestion and emissions via nonlinear optimal control

The objective of this paper is the regulation of freeway traffic by means of optimal control techniques. A first innovative aspect of the proposed approach is the adopted objective function in which, besides the reduction of traffic congestion (which is typically considered in traffic control schemes), the minimization of traffic emissions is also included. Moreover, a multi-class framework is defined in which two classes of vehicles (cars and trucks) are explicitly modelled, and specific control actions for each vehicle class are sought. This results in the formulation of a multi-objective optimal control problem which is described in the paper and for which a specific solution algorithm is developed and used. The algorithm exploits a specific version of the feasible direction algorithm whose effectiveness is demonstrated in the paper by means of simulation results.     

Long distance truck tracking from advanced point detectors using a selective weighted Bayesian model

Truck flow patterns are known to vary by season and time-of-day, and to have important implications for freight modeling, highway infrastructure design and operation, and energy and environmental impacts. However, such variations cannot be captured by current truck data sources such as surveys or point detectors. To facilitate development of detailed truck flow pattern data, this paper describes a new truck tracking algorithm that was developed to estimate path flows of trucks by adopting a linear data fusion method utilizing weigh-in-motion (WIM) and inductive loop point detectors. A Selective Weighted Bayesian Model (SWBM) was developed to match individual vehicles between two detector locations using truck physical attributes and inductive waveform signatures. Key feature variables were identified and weighted via Bayesian modeling to improve vehicle matching performance. Data for model development were collected from two WIM sites spanning 26 miles in California where only 11 percent of trucks observed at the downstream site traversed the whole corridor. The tracking model showed 81 percent of correct matching rate to the trucks declared as through trucks from the algorithm. This high accuracy showed that the tracking model is capable of not only correctly matching through vehicles but also successfully filtering out non-through vehicles on this relatively long distance corridor. In addition, the results showed that a Bayesian approach with full integration of two complementary detector data types could successfully track trucks over long distances by minimizing the impacts of measurement variations or errors from the detection systems employed in the tracking process. In a separate case study, the algorithm was implemented over an even longer 65-mile freeway section and demonstrated that the proposed algorithm is capable of providing valuable insights into truck travel patterns and industrial affiliation to yield a comprehensive truck activity data source.     

Modelling and real-time control of traffic flow on the southern part of Boulevard Peripherique in Paris: Part I: Modelling

A microscopic mathematical model of freeway traffic flow is applied to a 6 km stretch of the Boulevard Périphérique in Paris including several on-ramps and off-ramps. The model is validated on the basis of real traffic flow measurements selected under a broad spectrum of traffic conditions. The mathematical model is capable of describing complicated traffic phenomena with considerable accuracy. A simulation program which is developed on the basis of the modelling equations may be used as a tool for testing of control strategies. Development and testing of control strategies is the strategies is the subject of a subsequent paper.     

Dynamic user equilibrium with side constraints for a traffic network: Theoretical development and numerical solution algorithm

This paper investigates a traffic volume control scheme for a dynamic traffic network model which aims to ensure that traffic volumes on specified links do not exceed preferred levels. The problem is formulated as a dynamic user equilibrium problem with side constraints (DUE-SC) in which the side constraints represent the restrictions on the traffic volumes. Travelers choose their departure times and routes to minimize their generalized travel costs, which include early/late arrival penalties. An infinite-dimensional variational inequality (VI) is formulated to model the DUE-SC. Based on this VI formulation, we establish an existence result for the DUE-SC by showing that the VI admits at least one solution. To analyze the necessary condition for the DUE-SC, we restate the VI as an equivalent optimal control problem. The Lagrange multipliers associated with the side constraints as derived from the optimality condition of the DUE-SC provide the traffic volume control scheme. The control scheme can be interpreted as additional travel delays (either tolls or access delays) imposed upon drivers for using the controlled links. This additional delay term derived from the Lagrange multiplier is compared with its counterpart in a static user equilibrium assignment model. If the side constraint is chosen as the storage capacity of a link, the additional delay can be viewed as the effort needed to prevent the link from spillback. Under this circumstance, it is found that the flow is incompressible when the link traffic volume is equal to its storage capacity. An algorithm based on Euler’s discretization scheme and nonlinear programming is proposed to solve the DUE-SC. Numerical examples are presented to illustrate the mechanism of the proposed traffic volume control scheme.     

Evaluation of ramp control algorithms using microscopic traffic simulation

Ramp metering has emerged as an effective freeway control measure to ensure efficient freeway operations. A number of algorithms have been developed in recent years to ensure an effective use of ramp metering. As the performance of ramp metering depends on various factors (e.g. traffic volume, downstream traffic conditions, queue override policy etc), these algorithms should be evaluated under a wide range of traffic conditions to check their applicability and performance and to ensure their successful implementation. In view of the expenses of and confounding effects in field testing, simulation plays an important role in the evaluation of such algorithms. This paper presents an evaluation study of two ramp metering algorithms: ALINEA and FLOW. ALINEA is a local control algorithm and FLOW is an area wide coordinated algorithm. The purpose of the study is to use microscopic simulation to evaluate systematically how the level of traffic demand, queue spillback handling policy and downstream bottleneck conditions affect the performance of the algorithms. It is believed that these variables have complex interactions with ramp metering. MITSIM microscopic traffic simulator is used to perform the empirical study. The study consists of two stages. In the first stage, key input parameters for the algorithms were identified and calibrated. The calibrated parameters were then used for the second stage, where the performance of the algorithms were compared with respect to three traffic variables mentioned above using an orthogonal fraction of experiments. Regression analysis was used to identify the impacts of some of the interactions among experimental factors on the algorithms' performance, which is not otherwise possible with a tabular analysis. These results provide insights which may be helpful for design and calibration of more efficient ramp control algorithms.     

Real-time freeway traffic state estimation based on extended Kalman filter: Adaptive capabilities and real data testing

This paper reports on real data testing of a real-time freeway traffic state estimator, with a particular focus on its adaptive capabilities. The pursued general approach to the real-time adaptive estimation of complete traffic state in freeway stretches or networks is based on stochastic macroscopic traffic flow modeling and extended Kalman filtering. One major innovative feature of the traffic state estimator is the online joint estimation of important model parameters (free speed, critical density, and capacity) and traffic flow variables (flows, mean speeds, and densities), which leads to three significant advantages of the estimator: (1) avoidance of prior model calibration; (2) automatic adaptation to changing external conditions (e.g. weather and lighting conditions, traffic composition, control measures); (3) enabling of incident alarms. These three advantages are demonstrated via suitable real data testing. The achieved testing results are satisfactory and promising for subsequent applications.     

Modeling the effects of traveler information on freeway origin–destination demand prediction

The primary focus of this research is to develop an approach to capture the effect of travel time information on travelers’ route switching behavior in real-time, based on on-line traffic surveillance data. It also presents a freeway Origin–Destination demand prediction algorithm using an adaptive Kalman Filtering technique, where the effect of travel time information on users’ route diversion behavior has been explicitly modeled using a dynamic, aggregate, route diversion model. The inherent dynamic nature of the traffic flow characteristics is captured using a Kalman Filter modeling framework. Changes in drivers’ perceptions, as well as other randomness in the route diversion behavior, have been modeled using an adaptive, aggregate, dynamic linear model where the model parameters are updated on-line using a Bayesian updating approach. The impact of route diversion on freeway Origin–Destination demands has been integrated in the estimation framework. The proposed methodology is evaluated using data obtained from a microscopic traffic simulator, INTEGRATION. Experimental results on a freeway corridor in northwest Indiana establish that significant improvement in Origin–Destination demand prediction can be achieved by explicitly accounting for route diversion behavior.