Some errors in macroscopic traffic models based on car following models

The macroscopic traffic flow models developed from the car following models of Gazis et al. (1961) are shown to have a flaw in that they do not meet certain of the boundary conditions that researchers have said that they do. This does not affect many existing models but, nevertheless, should be cleared up.     

Derivation of delays based on input-output analysis

In a recent paper Michalpoulos and Pisharody (1981) contend that traditional input-output analysis results in substantial overestimation of delays, and they develop an alternate, more laborious, calculation method. This premise is incorrect since input-output analysis is nothing more than a simple accounting method, which by definition gives exact results. It should give results consistent with the more laborious method proposed by those authors.     

Robust calibration of macroscopic traffic simulation models using stochastic collocation

The predictions of a well-calibrated traffic simulation model are much more valid if made for various conditions. Variation in traffic can arise due to many factors such as time of day, work zones and weather. Calibration of traffic simulation models for traffic conditions requires larger datasets to capture the stochasticity in traffic conditions. In this study we use datasets spanning large time periods to incorporate variability in traffic flow, speed for various time periods. However, large data poses a challenge in terms of computational effort. With the increase in number of stochastic factors, the numerical methods suffer from the curse of dimensionality. In this study, we propose a novel methodology to address the computational complexity due to the need for the calibration of simulation models under highly stochastic traffic conditions. This methodology is based on sparse grid stochastic collocation, which, treats each stochastic factor as a different dimension and uses a limited number of points where simulation and calibration are performed. A computationally efficient interpolant is constructed to generate the full distribution of the simulated flow output. We use real-world examples to calibrate for different times of day and conditions and show that this methodology is much more efficient that the traditional Monte Carlo-type sampling. We validate the model using a hold out dataset and also show the drawback of using limited data for the calibration of a macroscopic simulation model. We also discuss the drawbacks of the predictive ability of a single calibrated model for all the conditions.     

High-resolution numerical relaxation approximations to second-order macroscopic traffic flow models

A novel numerical approach for the approximation of several, widely applied, macroscopic traffic flow models is presented. A relaxation-type approximation of second-order non-equilibrium models, written in conservation or balance law form, is considered. Using the relaxation approximation, the nonlinear equations are transformed to a semi-linear diagonilizable problem with linear characteristic variables and stiff source terms. To discretize the resulting relaxation system, low- and high-resolution reconstructions in space and implicit–explicit Runge–Kutta time integration schemes are considered. The family of spatial discretizations includes a second-order MUSCL scheme and a fifth-order WENO scheme, and a detailed formulation of the scheme is presented. Emphasis is given on the WENO scheme and its performance for solving the different traffic models. To demonstrate the effectiveness of the proposed approach, extensive numerical tests are performed for the different models. The computations reported here demonstrate the simplicity and versatility of relaxation schemes as solvers for macroscopic traffic flow models.     

Simplified transport models based on traffic counts

Having accepted the need for the development of simpler and less cumbersome transport demand models, the paper concentrates on one possible line for simplification: estimation of trip matrices from link volume counts. Traffic counts are particularly attractive as a data basis for modelling because of their availability, low cost and nondisruptive character. It is first established that in normal conditions it may be possible to find more than one trip matrix which, when loaded onto a network, reproduces the observed link volumes. The paper then identifies three approaches to reduce this underspecification problem and produce a unique trip matrix consistent with the counts. The first approach consists of assuming that trip-making behaviour can be explained by a gravity model whose parameters can be calibrated from the traffic counts. Several forms of this gravity model have been put forward and they are discussed in Section 3. The second approach uses mathematical programming techniques associated to equilibrium assignment problems to estimate a trip matrix in congested areas. This method can also be supplemented by a special distribution model developed for small areas. The third approach relies on entropy and information theory considerations to estimate the most likely trip matrix consistent with the observed flows. A particular feature of this group is that they can include prior, perhaps outdated, information about the matrix.These three approaches are then compared and their likely areas for application identified. Problems for further research are discussed and finally an assessment is made of the possible role of these models vis-a-vis recent developments in transport planning.     

A variational formulation for higher order macroscopic traffic flow models of the GSOM family

The GSOM (Generic second order modelling) family of traffic flow models combines the LWR model with dynamics of driver-specific attributes and can be expressed as a system of conservation laws. The object of the paper is to show that a proper Lagrangian formulation of the GSOM model can be recast as a Hamilton–Jacobi equation, the solution of which can be expressed as the value function of an optimal control problem. This value function is interpreted as the position of vehicles, and the optimal trajectories of the optimal control formulation can be identified with the characteristics. Further the paper analyzes the initial and boundary conditions, proposes a generalization of the inf-morphism and the Lax–Hopf formulas to the GSOM model, and considers numerical aspects.     

Automatic calibration of fundamental diagram for first‐order macroscopic freeway traffic models

Despite its importance in macroscopic traffic flow modeling, comprehensive method for the calibration of fundamental diagram is very limited. Conventional empirical methods adopt a steady state analysis of the aggregate traffic data collected from measurement devices installed on a particular site without considering the traffic dynamics, which renders the simulation may not be adaptive to the variability of data. Nonetheless, determining the fundamental diagram for each detection site is often infeasible. To remedy these, this study presents an automatic calibration method to estimate the parameters of a fundamental diagram through a dynamic approach. Simulated flow from the cell transmission model is compared against the measured flow wherein an optimization merit is conducted to minimize the discrepancy between model‐generated data and real data. The empirical results prove that the proposed automatic calibration algorithm can significantly improve the accuracy of traffic state estimation by adapting to the variability of traffic data when compared with several existing methods under both recurrent and abnormal traffic conditions. Results also highlight the robustness of the proposed algorithm. The automatic calibration algorithm provides a powerful tool for model calibration when freeways are equipped with sparse detectors, new traffic surveillance systems lack of comprehensive traffic data, or the case that lots of detectors lose their effectiveness for aging systems. Furthermore, the proposed method is useful for off‐line model calibration under abnormal traffic conditions, for example, incident scenarios. Copyright © 2015 John Wiley & Sons, Ltd.     

Development of network restructuring models for improved air traffic forecasts

Current air traffic forecast methods employed by the United States Federal Aviation Administration function under the assumption that the structure of the network of routes operated by airlines will not change; that is, no new routes will be added nor existing ones removed. However, in reality the competitive nature of the airline industry is such that new routes are routinely added between cities possessing significant passenger demand; city-pairs are also removed. Such phenomena generates a gap between the forecasted and actual state of the US Air Transportation System in the long term, providing insufficient situational awareness to major stakeholders and decision-makers in their consideration of major policy and technology changes. To address this gap, we have developed and compared three algorithms that forecast the likelihood of un-connected city-pairs being connected by service in the future, primarily based on the nodal characteristics of airports in the US network. Validation is performed by feeding historical data to each algorithm and then comparing the accuracy and precision of new city-pairs forecasted using knowledge of actual new city-pairs that developed. While an Artificial Neural Network produces superior precision, fitness function and logistic regression algorithms provide good representation of the distribution of new route types as well as greater flexibility for modeling future scenarios. However, these latter two algorithms face difficulty in resolving differences among the large number of ‘spoke’ airports in the network – additional parameters that may be able to differentiate them are currently under review. These insights gained are valuable stepping stones for exploiting knowledge of restructuring in the service route network to improve overall forecasts that drive policy and technology decision-making.     

A generic class of first order node models for dynamic macroscopic simulation of traffic flows

Node models for macroscopic simulation have attracted relatively little attention in the literature. Nevertheless, in dynamic network loading (DNL) models for congested road networks, node models are as important as the extensively studied link models. This paper provides an overview of macroscopic node models found in the literature, explaining both their contributions and shortcomings. A formulation defining a generic class of first order macroscopic node models is presented, satisfying a list of requirements necessary to produce node models with realistic, consistent results. Defining a specific node model instance of this class requires the specification of a supply constraint interaction rule and (optionally) node supply constraints. Following this theoretical discussion, specific macroscopic node model instances for unsignalized and signalized intersections are proposed. These models apply an oriented capacity proportional distribution of the available supply over the incoming links of a node. A computationally efficient algorithm to solve the node models exactly is included.     

On the macroscopic stability of freeway traffic

A simple model of traffic flow is used to analyze the spatio-temporal distribution of flow and density on closed-loop homogeneous freeways with many ramps, which produce inflows and allow outflows. As we would expect, if the on-ramp demand is space-independent then this distribution tends toward uniformity in space if the freeway is either: (i) uncongested; or (ii) congested with queues on its on-ramps and enough inflow to cause the average freeway density to increase with time. In all other cases, however, including any recovery phase of a rush hour where the freeway’s average density declines, the distribution of flow and density quickly becomes uneven. This happens even under conditions of perfect symmetry, where the percentage of vehicles exiting at every off ramp is the same. The flow-density deviations from the average are shown to grow exponentially in time and propagate backwards in space with a fixed wave speed. A consequence of this type of instability is that, during recovery, gaps of uncongested traffic will quickly appear in the unevenly congested stream, reducing average flow. This extends the duration of recovery and invariably creates clockwise hysteresis loops on scatter-plots of average system flow vs. density during any rush hour that oversaturates the freeway. All these effects are quantified with formulas and verified with simulations. Some have been observed in real networks. In a more practical vein, it is also shown that the negative effects of instability diminish (i.e., freeway flows increase) if (a) some drivers choose to exit the freeway prematurely when it is too congested and/or (b) freeway access is regulated in a certain traffic-responsive way. These two findings could be used to improve the algorithms behind VMS displays for driver guidance (finding a), and on-ramp metering rates (finding b).     

Characterization and prediction of air traffic delays

This paper presents a new class of models for predicting air traffic delays. The proposed models consider both temporal and spatial (that is, network) delay states as explanatory variables, and use Random Forest algorithms to predict departure delays 2–24 h in the future. In addition to local delay variables that describe the arrival or departure delay states of the most influential airports and links (origin–destination pairs) in the network, new network delay variables that characterize the global delay state of the entire National Airspace System at the time of prediction are proposed. The paper analyzes the performance of the proposed prediction models in both classifying delays as above or below a certain threshold, as well as predicting delay values. The models are trained and validated on operational data from 2007 and 2008, and are evaluated using the 100 most-delayed links in the system. The results show that for a 2-h forecast horizon, the average test error over these 100 links is 19% when classifying delays as above or below 60 min. Similarly, the average over these 100 links of the median test error is found to be 21 min when predicting departure delays for a 2-h forecast horizon. The effects of changes in the classification threshold and forecast horizon on prediction performance are studied.     

Determination of traffic delays from shock-wave analysis

The traffic shock-wave theory of Lighthill and Whitham is applied to a general incident, i.e. a moving incident with filtering (overtakings). It is shown that individual and total delays and the related costs can be determined simply by graphical means. A formulation, which is independent of any particular macroscopic theory of traffic flow, is obtained for the total delay upstream of the incident. It is shown to be identical to that obtained by using deterministic queuing theory. Simple incidents such as a red traffic signal light and a slow truck in a no passing zone are shown to be special cases.     

A family of macroscopic node models

The family of macroscopic node models which comply to a set of basic requirements is presented and analysed. Such models are required in macro-, mesoscopic traffic flow models, including dynamic network loading models for dynamic traffic assignment. Based on the behaviour of drivers approaching and passing through intersections, the model family is presented. The headway and the turn delay of vehicles are key variables. Having demand and supply as input creates a natural connection to macroscopic link models. Properties like the invariance principle and the conservation of turning fractions are satisfied. The inherent non-uniqueness is analysed by providing the complete set of feasible solutions. The node models proposed by Tampère et al. (2011), Flötteröd and Rohde (2011) and Gibb (2011) are members of the family. Furthermore, two new models are added to the family. Solution methods for all family members are presented, as well as a qualitative and quantitative comparison. Finally, an outlook for the future development of empirically verified models is given.     

Mixed manual/semi-automated traffic: a macroscopic analysis

The use of advanced technologies and intelligence in vehicles and infrastructure could make the current highway transportation system much more efficient. Semi-automated vehicles with the capability of automatically following a vehicle in front as long as it is in the same lane and in the vicinity of the forward looking ranging sensor are expected to be deployed in the near future. Their penetration into the current manual traffic will give rise to mixed manual/semi-automated traffic. In this paper, we analyze the fundamental flow–density curve for mixed traffic using flow–density curves for 100% manual and 100% semi-automated traffic. Assuming that semi-automated vehicles use a time headway smaller than today’s manual traffic average due to the use of sensors and actuators, we have shown using the flow–density diagram that the traffic flow rate will increase in mixed traffic. We have also shown that the flow–density curve for mixed traffic is restricted between the flow–density curves for 100% manual and 100% semi-automated traffic. We have presented in a graphical way that the presence of semi-automated vehicles in mixed traffic propagates a shock wave faster than in manual traffic. We have demonstrated that the presence of semi-automated vehicles does not change the total travel time of vehicles in mixed traffic. Though we observed that with 50% semi-automated vehicles a vehicle travels 10.6% more distance than a vehicle in manual traffic for the same time horizon and starting at approximately the same position, this increase is marginal and is within the modeling error. Lastly, we have shown that when shock waves on the highway produce stop-and-go traffic, the average delay experienced by vehicles at standstill is lower in mixed traffic than in manual traffic, while the average number of vehicles at standstill remains unchanged.     

Properties of a well-defined macroscopic fundamental diagram for urban traffic

A field experiment in Yokohama (Japan) revealed that a macroscopic fundamental diagram (MFD) linking space-mean flow, density and speed exists on a large urban area. It was observed that when the highly scattered plots of flow vs. density from individual fixed detectors were aggregated the scatter nearly disappeared and points grouped along a well defined curve. Despite these and other recent findings for the existence of well-defined MFDs for urban areas, these MFDs should not be universally expected. In this paper we investigate what are the properties that a network should satisfy, so that an MFD with low scatter exists. We show that the spatial distribution of vehicle density in the network is one of the key components that affect the scatter of an MFD and its shape. We also propose an analytical derivation of the spatial distribution of congestion that considers correlation between adjacent links. We investigate the scatter of an MFD in terms of errors in the probability density function of spatial link occupancy and errors of individual links’ fundamental diagram (FD). Later, using real data from detectors for an urban arterial and a freeway network we validate the proposed derivations and we show that an MFD is not well defined in freeway networks as hysteresis effects are present. The datasets in this paper consist of flow and occupancy measures from 500 fixed sensors in the Yokohama downtown area in Japan and 600 loop detectors in the Twin Cities Metropolitan Area Freeway network in Minnesota, USA.     

Trajectory data reconstruction and simulation-based validation against macroscopic traffic patterns

This paper shows that the behavior of driver models, either individually or entangled in stochastic traffic simulation, is affected by the accuracy of empirical vehicle trajectories. To this aim, a “traffic-informed” methodology is proposed to restore physical and platoon integrity of trajectories in a finite time–space domain, and it is applied to one NGSIM I80 dataset. However, as the actual trajectories are unknown, it is not possible to verify directly whether the reconstructed trajectories are really “nearer” to the actual unknowns than the original measurements. Therefore, a simulation-based validation framework is proposed, that is also able to verify indirectly the efficacy of the reconstruction methodology. The framework exploits the main feature of NGSIM-like data that is the concurrent view of individual driving behaviors and emerging macroscopic traffic patterns. It allows showing that, at the scale of individual models, the accuracy of trajectories affects the distribution and the correlation structure of lane-changing model parameters (i.e. drivers heterogeneity), while it has very little impact on car-following calibration. At the scale of traffic simulation, when models interact in trace-driven simulation of the I80 scenario (multi-lane heterogeneous traffic), their ability to reproduce the observed macroscopic congested patterns is sensibly higher when model parameters from reconstructed trajectories are applied. These results are mainly due to lane changing, and are also the sought indirect validation of the proposed data reconstruction methodology.     

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.     

An analytical approximation for the macroscopic fundamental diagram of urban traffic

This paper shows that a macroscopic fundamental diagram (MFD) relating average flow and average density must exist on any street with blocks of diverse widths and lengths, but no turns, even if all or some of the intersections are controlled by arbitrarily timed traffic signals. The timing patterns are assumed to be fixed in time. Exact analytical expressions in terms of a shortest path recipe are given, both, for the street’s capacity and its MFD. Approximate formulas that require little data are also given.For networks, the paper derives an upper bound for average flow conditional on average density, and then suggests conditions under which the bound should be tight; i.e., under which the bound is an approximate MFD. The MFD’s produced with this method for the central business districts of San Francisco (California) and Yokohama (Japan) are compared with those obtained experimentally in earlier publications.     

Efficiency evaluation and PM emission reallocation of China ports based on improved DEA models

The emission of particulate matter (PM) and other atmospheric pollutants in port operations and shipping have caused a huge negative impact on the environment. Consequently, how to evaluate the environmental efficiency of ports and put forward corresponding countermeasures on this basis is becoming a more important issue than ever before from the perspectives of the government, academia, and society. We construct three data envelopment analysis (DEA) models to evaluate the environmental efficiency of ports under the circumstances of environmental control, non-environmental control and PM emission through inter-ports cooperation. The innovation of the DEA models constructed in this paper lies in: (1) Setting environmental control parameters to uniformly manipulate the situations of environmental control and non-environmental control, etc.; (2) Allowing non-equal proportional change of input index, expected output and non-expected output index; (3) Setting preference coefficients for ports to admit favorable decisions; (4) Providing a distance formula of expected output for PM emission reallocation. Further, data from 11 major ports in China are collected to compare the expected output under different PM emission standards assuming the situation of environmental control and non-environmental control, port cooperation, and non-cooperative sewage discharge. The empirical results show that: (1) Ports in the eastern China (Shanghai, Ningbo, and Nanjing) have higher port efficiency; (2) Port cooperation can improve the overall expected output but it will lose its edge with the improvement of PM emission standards. (3) Ports follow the same trend of output loss regardless of favorable decisions. In the end, the author makes a summary, puts forward relevant policy suggestions and makes the recommendation for future research.     

Pedestrian detection for traffic safety based on Accumulate Binary Haar features and improved deep belief network algorithm

ABSTRACT

In order to improve traffic safety and protect pedestrians, an improved and efficient pedestrian detection method for auto driver assistance systems is proposed. Firstly, an improved Accumulate Binary Haar (ABH) feature extraction algorithm is proposed. In this novel feature, Haar features keep only the ordinal relationship named by binary Haar features. Then, the feature brings in the idea of a Local Binary Pattern (LBP), assembling several neighboring binary Haar features to improve discriminating power and reduce the effect of illumination. Next, a pedestrian classification method based on an improved deep belief network (DBN) classification algorithm is proposed. An improved method of input is constructed using a Restricted Bolzmann Machine (RBM) with T distribution function visible layer nodes, which can convert information on pedestrian features to a Bernoulli distribution, and the Bernoulli distribution can then be used for recognition. In addition, a middle layer of the RBM structure is created, which achieves data transfer between the hidden layer structure and keeps the key information. Finally, the cost-sensitive Support Vector Machine (SVM) classifier is used for the output of the classifier, which could address the class-imbalance problem. Extensive experiments show that the improved DBN pedestrian detection method is better than other shallow classic algorithms, and the proposed method is effective and sufficiently feasible for pedestrian detection in complex urban environments.