An enhanced SPSA algorithm for the calibration of Dynamic Traffic Assignment models

Simultaneous perturbation stochastic approximation (SPSA) is an efficient and well established optimization method that approximates gradients from successive objective function evaluations. It is especially attractive for high-dimensional problems and has been successfully applied to the calibration of Dynamic Traffic Assignment (DTA) models. This paper presents an enhanced SPSA algorithm, called Weighted SPSA (W-SPSA), which incorporates the information of spatial and temporal correlation in a traffic network to limit the impact of noise and improve convergence and robustness. W-SPSA appears to outperform the original SPSA algorithm by reducing the noise generated by uncorrelated measurements in the gradient approximation, especially for DTA models of sparsely correlated large-scale networks and a large number of time intervals. Comparisons between SPSA and W-SPSA have been performed through rigorous synthetic tests and the application of W-SPSA for the calibration of real world DTA networks is demonstrated with a case study of the entire expressway network in Singapore.     

Calibration of traffic flow models using a memetic algorithm

A Memetic Algorithm (MA) for the calibration of microscopic traffic flow simulation models is proposed in this study. The proposed MA includes a combination of genetic and simulated annealing algorithms. The genetic algorithm performs the exploration of the search space and identifies a zone where a possible global solution could be located. After this zone has been found, the simulated annealing algorithm refines the search and locates an optimal set of parameters within that zone. The design and implementation of this methodology seeks to enable the generalized calibration of microscopic traffic flow models. Two different Corridor Simulation (CORSIM) vehicular traffic systems were calibrated for this study. All parameters after the calibration were within reasonable boundaries. The calibration methodology was developed independently of the characteristics of the traffic flow models. Hence, it is easily used for the calibration of any other model. The proposed methodology has the capability to calibrate all model parameters, considering multiple performance measures and time periods simultaneously. A comparison between the proposed MA and the Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm was provided; results were similar between the two. However, the effort required to fine-tune the MA was considerably smaller when compared to the SPSA. The running time of the MA-based calibration was larger when it was compared to the SPSA running time. The MA still required some knowledge of the model in order to set adequate optimization parameters. The perturbation of the parameters during the mutation process must have been large enough to create a measurable change in the objective function, but not too large to avoid noisy measurements.     

A copula-based approach to accommodate the dependence among microscopic traffic variables

Developing microscopic traffic simulation models requires the knowledge of probability distributions of microscopic traffic variables. Although previous studies have proposed extensive mathematical distributions for describing traffic variables (e.g., speed, headway, vehicle length, etc.), these studies usually consider microscopic traffic observations to be independent variables and distributions for these variables are investigated separately. As a result, some traditional approaches consider microscopic traffic variables as independent inputs to the traffic simulation process and these methods may ignore the possible dependence among different traffic variables.The objectives of this paper are to investigate the dependence structure among microscopic traffic variables and to examine the applicability of the copula approach to the joint modeling of these variables. Copulas are functions that relate multivariate distribution functions of random variables to their one-dimensional marginal distribution functions. The concept of copulas has been well recognized in the statistics field and recently has been introduced in transportation studies. The proposed copula approach is applied to the 24-h traffic data collected on IH-35 in Austin, Texas. The preliminary data analysis indicates that there exists dependence among microscopic traffic variables. Moreover, the modeling and simulation results suggest that copula models can adequately accommodate and accurately reproduce the dependence structure revealed by the traffic observations. Overall, the findings in this paper provide a framework for generating multiple microscopic traffic variables simultaneously by considering their dependence.     

Adaptive cruise control design for active congestion avoidance

We present an adaptive cruise control (ACC) strategy where the acceleration characteristics, that is, the driving style automatically adapts to different traffic situations. The three components of the concept are the ACC itself, implemented in the form of a car-following model, an algorithm for the automatic real-time detection of the traffic situation based on local information, and a strategy matrix to adapt the driving characteristics (that is, the parameters of the ACC controller) to the traffic conditions. Optionally, inter-vehicle and infrastructure-to-car communication can be used to improve the accuracy of determining the traffic states. Within a microscopic simulation framework, we have simulated the complete concept on a road section with an on-ramp bottleneck, using empirical loop-detector data for an afternoon rush-hour as input for the upstream boundary. We found that the ACC vehicles improve the traffic stability and the dynamic road capacity. While traffic congestion in the reference scenario was completely eliminated when simulating a proportion of 25% ACC vehicles, travel times were already significantly reduced for much lower penetration rates. The efficiency of the proposed driving strategy even for low market penetrations is a promising result for a successful application in future driver assistance systems.     

Optimization-based assisted calibration of traffic simulation models

Use of traffic simulation has increased in recent decades; and this high-fidelity modelling, along with moving vehicle animation, has allowed transportation decisions to be made with better confidence. During this time, traffic engineers have been encouraged to embrace the process of calibration, in which steps are taken to reconcile simulated and field-observed performance. According to international surveys, experts, and conventional wisdom, existing (non-automated) methods of calibration have been difficult or inadequate. There has been extensive research on improved calibration methods, but many of these efforts have not produced the flexibility and practicality required by real-world engineers. With this in mind, a patent-pending (US 61/859,819) architecture for software-assisted calibration was developed to maximize practicality, flexibility, and ease-of-use. This architecture is called SASCO (i.e. Sensitivity Analysis, Self-Calibration, and Optimization). The original optimization method within SASCO was based on “directed brute force” (DBF) searching; performing exhaustive evaluation of alternatives in a discrete, user-defined search space. Simultaneous Perturbation Stochastic Approximation (SPSA) has also gained favor as an efficient method for optimizing computationally expensive, “black-box” traffic simulations, and was also implemented within SASCO. This paper uses synthetic and real-world case studies to assess the qualities of DBF and SPSA, so they can be applied in the right situations. SPSA was found to be the fastest method, which is important when calibrating numerous inputs, but DBF was more reliable. Additionally DBF was better than SPSA for sensitivity analysis, and for calibrating complex inputs. Regardless of which optimization method is selected, the SASCO architecture appears to offer a new and practice-ready level of calibration efficiency.     

Dynamic traffic routing in a network with adaptive signal control

In real traffic networks, travellers’ route choice is affected by traffic control strategies. In this research, we capture the interaction between travellers’ route choice and traffic signal control in a coherent framework. For travellers’ route choice, a VANET (Vehicular Ad hoc NETwork) is considered, where travellers have access to the real-time traffic information through V2V/V2I (Vehicle to Vehicle/Vehicle to Infrastructure) infrastructures and make route choice decisions at each intersection using hyper-path trees. We test our algorithm and control strategy by simulation in OmNet++ (A network communication simulator) and SUMO (Simulation of Urban MObility) under several scenarios. The simulation results show that with the proposed dynamic routing, the overall travel cost significantly decreases. It is also shown that the proposed adaptive signal control reduces the average delay effectively, as well as reduces the fluctuation of the average speed within the whole network.     

Optimization of mixed cycle length traffic signals

Mixed cycle length operation has been recommended for networks where individual intersections process considerably different traffic volumes. The signals to operate at lower or higher cycle lengths are determined heuristically. This paper demonstrates that the use of mixed cycle lengths as given by the heuristic is inferior to operation under a common cycle length. This contradicts findings in earlier studies, and the difference in conclusion is due to the use of updated optimization methodology. A procedure for incorporating the allocation of mixed cycle lengths into the global optimization of all signal timing variables by a genetic algorithm is proposed. The mixed cycle length timing plans obtained from this procedure are an improvement over those determined heuristically. Mixed cycle length operation is found to be of a more limited application than indicated in previous studies. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

c-SPSA: Cluster-wise simultaneous perturbation stochastic approximation algorithm and its application to dynamic origin–destination matrix estimation

The simultaneous perturbation stochastic approximation (SPSA) algorithm has been used in the literature for the solution of the dynamic origin–destination (OD) estimation problem. Its main advantage is that it allows quite general formulations of the problem that can include a wide range of sensor measurements. While SPSA is relatively simple to implement, its performance depends on a set of parameters that need to be properly determined. As a result, especially in cases where the gradient of the objective function changes quickly, SPSA may not be as stable and even diverge. A modification of the SPSA algorithm, referred to as c-SPSA, is proposed which applies the simultaneous perturbation approximation of the gradient within a small number of carefully constructed “homogeneous” clusters one at a time, as opposed to all elements at once. The paper establishes the theoretical properties of the new algorithm with an upper bound for the bias of the gradient estimate and shows that it is lower than the corresponding SPSA bias. It also proposes a systematic approach, based on the k-means algorithm, to identify appropriate clusters. The performance of c-SPSA, with alternative implementation strategies, is evaluated in the context of estimating OD flows in an actual urban network. The results demonstrate the efficiency of the proposed c-SPSA algorithm in finding better OD estimates and achieve faster convergence and more robust performance compared to SPSA with fewer overall number of function evaluations.     

Short‐term traffic flow prediction with linear conditional Gaussian Bayesian network

Traffic flow prediction is an essential part of intelligent transportation systems (ITS). Most of the previous traffic flow prediction work treated traffic flow as a time series process only, ignoring the spatial relationship from the upstream flows or the correlation with other traffic attributes like speed and density. In this paper, we utilize a linear conditional Gaussian (LCG) Bayesian network (BN) model to consider both spatial and temporal dimensions of traffic as well as speed information for short‐term traffic flow prediction. The LCG BN allows both continuous and discrete variables, which enables the consideration of categorical variables in traffic flow prediction. A microscopic traffic simulation dataset is used to test the performance of the proposed model compared to other popular approaches under different predicting time intervals. In addition, the authors investigate the importance of spatial data and speed data in flow prediction by comparing models with different levels of information. The results indicate that the prediction accuracy will increase significantly when both spatial data and speed data are included. Copyright © 2016 John Wiley & Sons, Ltd.     

The treatment of uncertainty in the dynamic origin–destination estimation problem using a fuzzy approach

Regardless of existing types of transportation and traffic model and their applications, the essential input to these models is travel demand, which is usually described using origin–destination (OD) matrices. Due to the high cost and time required for the direct development of such matrices, they are sometimes estimated indirectly from traffic measurements recorded from the transportation network. Based on an assumed demand profile, OD estimation problems can be categorized into static or dynamic groups. Dynamic OD demand provides valuable information on the within-day fluctuation of traffic, which can be employed to analyse congestion dissipation. In addition, OD estimates are essential inputs to dynamic traffic assignment (DTA) models. This study presents a fuzzy approach to dynamic OD estimation problems. The problems are approached using a two-level model in which demand is estimated in the upper level and the lower level performs DTA via traffic simulation. Using fuzzy rules and the fuzzy C-Mean clustering approach, the proposed method treats uncertainty in historical OD demand and observed link counts. The approach employs expert knowledge to model fitted link counts and to set boundaries for the optimization problem by defining functions in the fuzzification process. The same operation is performed on the simulation outputs, and the entire process enables different types of optimization algorithm to be employed. The Box-complex method is utilized as an optimization algorithm in the implementation of the approach. Empirical case studies are performed on two networks to evaluate the validity and accuracy of the approach. The study results for a synthetic network and a real network demonstrate the robust performance of the proposed method even when using low-quality historical demand data.     

Assessment and prediction of the impact of road transport on ambient concentrations of particulate matter PM10

The main challenge facing the air quality management authorities in most cities is meeting the air quality limits and objectives in areas where road traffic is high. The difficulty and uncertainties associated with the estimation and prediction of the road traffic contribution to the overall air quality levels is the major contributing factor. In this paper, particulate matter (PM₁₀) data from 10 monitoring sites in London was investigated with a view to estimating and developing Artificial Neural Network models (ANN) for predicting the impact of the road traffic on the levels of PM₁₀ concentration in London. Twin studies in conjunction with bivariate polar plots were used to identify and estimate the contribution of road traffic and other sources of PM₁₀ at the monitoring sites. The road traffic was found to have contributed between 24% and 62% of the hourly average roadside PM₁₀ concentrations. The ANN models performed well in predicting the road contributions with their R-values ranging between 0.6 and 0.9, FAC2 between 0.6 and 0.95, and the normalised mean bias between 0.01 and 0.11. The hourly emission rates of the vehicles were found to be the most contributing input variables to the outputs of the ANN models followed by background PM₁₀, gaseous pollutants and meteorological variables respectively.     

Local online kernel ridge regression for forecasting of urban travel times

Accurate and reliable forecasting of traffic variables is one of the primary functions of Intelligent Transportation Systems. Reliable systems that are able to forecast traffic conditions accurately, multiple time steps into the future, are required for advanced traveller information systems. However, traffic forecasting is a difficult task because of the nonlinear and nonstationary properties of traffic series. Traditional linear models are incapable of modelling such properties, and typically perform poorly, particularly when conditions differ from the norm. Machine learning approaches such as artificial neural networks, nonparametric regression and kernel methods (KMs) have often been shown to outperform linear models in the literature. A bottleneck of the latter approach is that the information pertaining to all previous traffic states must be contained within the kernel, but the computational complexity of KMs usually scales cubically with the number of data points in the kernel. In this paper, a novel kernel-based machine learning (ML) algorithm is developed, namely the local online kernel ridge regression (LOKRR) model. Exploiting the observation that traffic data exhibits strong cyclic patterns characterised by rush hour traffic, LOKRR makes use of local kernels with varying parameters that are defined around each time point. This approach has 3 advantages over the standard single kernel approach: (1) It allows parameters to vary by time of day, capturing the time varying distribution of traffic data; (2) It allows smaller kernels to be defined that contain only the relevant traffic patterns, and; (3) It is online, allowing new traffic data to be incorporated as it arrives. The model is applied to the forecasting of travel times on London’s road network, and is found to outperform three benchmark models in forecasting up to 1 h ahead.     

Integrated expression method for technical mapping of traffic parameters using RGB color model

In the field of traffic flow, speed, density, time, and distance are fundamental variables analyzed to predict traffic conditions. Reliable sources of information are gauged using tested mathematical approaches that have been developed. However, a fundamental diagram that could serve as a basis for expression techniques has not been devised. Red–green–blue (RGB) color modeling was used to overcome this limitation in traffic flow. The purpose of this study is to provide a way to understand traffic flow conditions based on features of three traffic flow elements simultaneously. The limitation of three‐dimensional expressions in two‐dimensional paper was extended to multi‐dimensional information. Information on speed, density, and flow were combined into a single RGB color and given the name RGB flow‐density space time‐distance space. This cancels out the effect of each individual's vehicular trajectories and contains five major components of a specific road section. The new gizmo aims to provide information on traffic flow conditions in transition and to stimulate further approaches related to the predictions and understanding of traffic flow. Copyright © 2016 John Wiley & Sons, Ltd.     

A spatiotemporal correlative k-nearest neighbor model for short-term traffic multistep forecasting

The k-nearest neighbor (KNN) model is an effective statistical model applied in short-term traffic forecasting that can provide reliable data to guide travelers. This study proposes an improved KNN model to enhance forecasting accuracy based on spatiotemporal correlation and to achieve multistep forecasting. The physical distances among road segments are replaced with equivalent distances, which are defined by the static and dynamic data collected from real road networks. The traffic state of a road segment is described by a spatiotemporal state matrix instead of only a time series as in the original KNN model. The nearest neighbors are selected according to the Gaussian weighted Euclidean distance, which adjusts the influences of time and space factors on spatiotemporal state matrices. The forecasting accuracies of the improved KNN and of four other models are compared, and experimental results indicate that the improved KNN model is more appropriate for short-term traffic multistep forecasting than the other models are. This study also discusses the application of the improved KNN model in a time-varying traffic state.     

Recent developments in traffic flow modeling using macroscopic fundamental diagram

ABSTRACT

This paper presents an overview of the recent developments in traffic flow modelling and analysis using macroscopic fundamental diagram (MFD) as well as their applications. In recent literature, various aggregated traffic models have been proposed and studied to analyse traffic flow while enhancing network efficiency. Many of these studies have focused on models based on MFD that describes the relationship between aggregated flow and aggregated density of transport networks. The analysis of MFD has been carried out based on experimental data collected from sensors and GPS, as well as simulation models. Several factors are found to influence the existence and shape of MFD, including traffic demand, network and signal settings, and route choices. As MFD can well express the traffic dynamics of large urban transport networks, it has been extensively applied to traffic studies, including the development of network-wide control strategies, network partitioning, performance evaluation, and road pricing. This work also presents future extensions and research directions for MFD-based traffic modelling and applications.     

The existence, uniqueness and computation of an arc-based dynamic network user equilibrium formulation

In this paper, a dynamic user equilibrium traffic assignment model with simultaneous departure time/route choices and elastic demands is formulated as an arc-based nonlinear complementarity problem on congested traffic networks. The four objectives of this paper are (1) to develop an arc-based formulation which obviates the use of path-specific variables, (2) to establish existence of a dynamic user equilibrium solution to the model using Brouwer's fixed-point theorem, (3) to show that the vectors of total arc inflows and associated minimum unit travel costs are unique by imposing strict monotonicity conditions on the arc travel cost and demand functions along with a smoothness condition on the equilibria, and (4) to develop a heuristic algorithm that requires neither a path enumeration nor a storage of path-specific flow and cost information. Computational results are presented for a simple test network with 4 arcs, 3 nodes, and 2 origin–destination pairs over the time interval of 120 periods.     

A new approach to evaluating on-road public transport priority projects: balancing the demand for limited road-space

Despite widespread growth in on-road public transport priority schemes, road management authorities have few tools to evaluate the impacts of these schemes on all road users. This paper describes a methodology developed in Melbourne, Australia to assist the road management authority, VicRoads, evaluate trade-offs in the use of its limited road-space for new bus and tram priority projects. The approach employs traffic micro-simulation modelling to assess road-space re-allocation impacts, travel behaviour modelling to assess changes in travel patterns and a social cost benefit framework to evaluate impacts. The evaluation considers a comprehensive range of impacts including the environmental benefits of improved public transport services. Impacts on public transport reliability improvements are also considered. Although improved bus and tram reliability is a major rationale for traffic priority its use in previous evaluations is rare. The paper critiques previous approaches, describes the proposed method and explores some of the results found in its application. A major finding is that despite a more comprehensive approach to measuring the benefits of bus and tram priority, road-space reallocation is difficult to economically justify in road networks where public transport usage is low and car usage high. Strategies involving the balanced deployment of bus and tram priority measures where the allocation of time and space to PT minimises negative traffic impacts is shown to improve the overall management of road-space. A discussion of the approach is also provided including suggestions for further methodology development.

A new fuzzy approach to estimate the O–D matrix from link volumes

Abstract

Estimation of the origin–destination (O–D) trip demand matrix plays a key role in travel analysis and transportation planning and operations. Many researchers have developed different O–D matrix estimation methods using traffic counts, which allow simple data collection as opposed to the costly traditional direct estimation methods based on home and roadside interviews.

In this paper, we present a new fuzzy model to estimate the O–D matrix from traffic counts. Since link data only represent a snapshot situation, resulting in inconsistency of data and poor quality of the estimated O–Ds, the proposed method considers the link data as a fuzzy number that varies within a certain bandwidth. Shafahi and Ramezani's fuzzy assignment method is improved upon and used to assign the estimated O–D matrix, which causes the assigned volumes to be fuzzy numbers similar to what is proposed for observed link counts. The shortest path algorithm of the proposed method is similar to the Floyd–Warshall algorithm, and we call it the Fuzzy Floyd–Warshall Algorithm. A new fuzzy comparing index is proposed by improving the fuzzy comparison method developed by Dubois and Prade to estimate and compare the distance between the assigned and observed link volumes. The O–D estimation model is formulated as a convex minimization problem based on the proposed fuzzy index to minimize the fuzzy distance between the observed and assigned link volumes. A gradient-based method is used to solve the problem. To ensure the original O–D matrix does not change more than necessary during the iterations, a fuzzy rule-based approach is proposed to control the matrix changes.     

Short-term speed predictions exploiting big data on large urban road networks

Big data from floating cars supply a frequent, ubiquitous sampling of traffic conditions on the road network and provide great opportunities for enhanced short-term traffic predictions based on real-time information on the whole network. Two network-based machine learning models, a Bayesian network and a neural network, are formulated with a double star framework that reflects time and space correlation among traffic variables and because of its modular structure is suitable for an automatic implementation on large road networks. Among different mono-dimensional time-series models, a seasonal autoregressive moving average model (SARMA) is selected for comparison. The time-series model is also used in a hybrid modeling framework to provide the Bayesian network with an a priori estimation of the predicted speed, which is then corrected exploiting the information collected on other links. A large floating car data set on a sub-area of the road network of Rome is used for validation. To account for the variable accuracy of the speed estimated from floating car data, a new error indicator is introduced that relates accuracy of prediction to accuracy of measure. Validation results highlighted that the spatial architecture of the Bayesian network is advantageous in standard conditions, where a priori knowledge is more significant, while mono-dimensional time series revealed to be more valuable in the few cases of non-recurrent congestion conditions observed in the data set. The results obtained suggested introducing a supervisor framework that selects the most suitable prediction depending on the detected traffic regimes.