An alternative model in traffic flow equations

The kinetic theory for traffic flow equations can be approached using the Grad’s method. This method, which is derived from the kinetic gas theory, was developed for the Paveri-Fontana equation when a special desired velocity model is assumed. A closure relation for the set of macroscopic equations is found when the density, the average velocity and the velocity variance are the relevant variables chosen to describe the system. Simulation results are also shown and a qualitative comparison with other models in the literature is presented.     

A dual decomposition method for sector capacity constrained traffic flow optimization

An aggregate air traffic flow model based on a multicommodity network is used for traffic flow management in the National Airspace System. The problem of minimizing the total travel time of flights in the National Airspace System of the United States, subject to sector capacity constraints, is formulated as an Integer Program. The resulting solution achieves optimal delay control. The Integer Program implemented for the scenarios investigated has billions of variables and constraints. It is relaxed to a Linear Program for computational efficiency. A dual decomposition method is applied to solve the large scale Linear Program in a computationally tractable manner. A rounding algorithm is developed to map the Linear Program solution to a physically acceptable result, and is implemented for the entire continental United States. A 2-h traffic flow management problem is solved with the method.     

A shockwave profile model for traffic flow on congested urban arterials

In this paper a new traffic flow model for congested arterial networks, named shockwave profile model (SPM), is presented. Taking advantage of the fact that traffic states within a congested link can be simplified as free-flow, saturated, and jammed conditions, SPM simulates traffic dynamics by analytically deriving the trajectories of four major shockwaves: queuing, discharge, departure, and compression waves. Unlike conventional macroscopic models, in which space is often discretized into small cells for numerical solutions, SPM treats each homogeneous road segment with constant capacity as a section; and the queuing dynamics within each section are described by tracing the shockwave fronts. SPM is particularly suitable for simulating traffic flow on congested signalized arterials especially with queue spillover problems, where the steady-state periodic pattern of queue build-up and dissipation process may break down. Depending on when and where spillover occurs along a signalized arterial, a large number of queuing patterns may be possible. Therefore it becomes difficult to apply the conventional approach directly to track shockwave fronts. To overcome this difficulty, a novel approach is proposed as part of the SPM, in which queue spillover is treated as either extending a red phase or creating new smaller cycles, so that the analytical solutions for tracing the shockwave fronts can be easily applied. Since only the essential features of arterial traffic flow, i.e., queue build-up and dissipation, are considered, SPM significantly reduces the computational load and improves the numerical efficiency. We further validated SPM using real-world traffic signal data collected from a major arterial in the Twin Cities. The results clearly demonstrate the effectiveness and accuracy of the model. We expect that in the future this model can be applied in a number of real-time applications such as arterial performance prediction and signal optimization.     

An improved cellular automata model for heterogeneous work zone traffic

This paper aims to develop an improved cellular automata (ICA) model for simulating heterogeneous traffic in work zone. The proposed ICA model includes the forwarding rules to update longitudinal speeds and positions of work zone vehicles. The randomization probability parameter used by the ICA is formulated as a function of the activity length, the transition length and the volumes of different types of vehicles traveling across work zone. Compared to the existing cellular automata models, the ICA model possesses a novel and realistic lateral speed and position updating rule so that the simulation of vehicle’s lateral movement in work zone is close to the reality. The ICA model is calibrated and validated microscopically and macroscopically by using the real work zone data. Comparisons of field data and ICA for trajectories, speed and speed–flow relationship in work zone show very close agreement. Finally, the proposed ICA model is applied to estimate traffic delay occurred in work zone.     

Validation of traffic flow models with respect to the spatiotemporal evolution of congested traffic patterns

We propose a quantitative approach for calibrating and validating key features of traffic instabilities based on speed time series obtained from aggregated data of a series of neighboring stationary detectors. The approach can be used to validate models that are calibrated by other criteria with respect to their collective dynamics. We apply the proposed criteria to historic traffic databases of several freeways in Germany containing about 400 occurrences of congestions thereby providing a reference for model calibration and quality assessment with respect to the spatiotemporal dynamics. First tests with microscopic and macroscopic models indicate that the criteria are both robust and discriminative, i.e., clearly distinguishes between models of higher and lower predictive power.     

Evidence of convective instability in congested traffic flow: A systematic empirical and theoretical investigation

An extended open system such as traffic flow is said to be convectively unstable if perturbations of the stationary state grow but propagate in only one direction, so they eventually leave the system. By means of data analysis, simulations, and analytical calculations, we give evidence that this concept is relevant for instabilities of congested traffic flow. We analyze detector data from several hundred traffic jams and propose estimates for the linear growth rate, the wavelength, the propagation velocity, and the severity of the associated bottleneck that can be evaluated semi-automatically. Scatter plots of these quantities reveal systematic dependencies. On the theoretical side, we derive, for a wide class of microscopic and macroscopic traffic models, analytical criteria for convective and absolute linear instabilities. Based on the relative positions of the stability limits in the fundamental diagram, we divide these models into five stability classes which uniquely determine the set of possible elementary spatiotemporal patterns in open systems with a bottleneck. Only two classes, both dominated by convective instabilities, are compatible with observations. By means of approximate solutions of convectively unstable systems with sustained localized noise, we show that the observed spatiotemporal phenomena can also be described analytically. The parameters of the analytical expressions can be inferred from observations, and also (analytically) derived from the model equations.     

Increase in particle number emissions from motor vehicles due to interruption of steady traffic flow

We assess the increase in particle number emissions from motor vehicles driving at steady speed when forced to stop and accelerate from rest. Considering the example of a signalized pedestrian crossing on a two-way single-lane urban road, we use a complex line source method to calculate the total emissions produced by a specific number and mix of light petrol cars and diesel passenger buses and show that the total emissions during a red light is significantly higher than during the time when the light remains green. Replacing two cars with one bus increased the emissions by over an order of magnitude.     

Heterogeneous traffic flow modelling for an arterial using grid based approach

A grid based modelling approach akin to cellular automata (CA) is adopted for heterogeneous traffic flow simulation. The road space is divided into a grid of equally sized cells. Moreover, each vehicle type occupies one or more cell as per its size unlike CA traffic flow model where each vehicle is represented by a single cell. Model needs inputs such as vehicle size, its maximum speed, acceleration, deceleration, probability constants, and arrival pattern. The position and speed of the vehicles are assumed to be discrete. The speed of each vehicle changes according to its interactions with other vehicles, following some stochastic rules depending on the circumstances. The model is calibrated and validated using real data and VISSIM. The results indicate that grid based model can reasonably well simulate complex heterogeneous traffic as well as offers higher computational efficiency needed for real time application.     

Analytical and grid-free solutions to the Lighthill-Whitham-Richards traffic flow model

In this article, we propose a computational method for solving the Lighthill-Whitham-Richards (LWR) partial differential equation (PDE) semi-analytically for arbitrary piecewise-constant initial and boundary conditions, and for arbitrary concave fundamental diagrams. With these assumptions, we show that the solution to the LWR PDE at any location and time can be computed exactly and semi-analytically for a very low computational cost using the cumulative number of vehicles formulation of the problem. We implement the proposed computational method on a representative traffic flow scenario to illustrate the exactness of the analytical solution. We also show that the proposed scheme can handle more complex scenarios including traffic lights or moving bottlenecks. The computational cost of the method is very favorable, and is compared with existing algorithms. A toolbox implementation available for public download is briefly described, and posted at http://traffic.berkeley.edu/project/downloads/lwrsolver.     

Cellpath: Fusion of cellular and traffic sensor data for route flow estimation via convex optimization

A new convex optimization framework is developed for the route flow estimation problem from the fusion of vehicle count and cellular network data. The issue of highly underdetermined link flow based methods in transportation networks is investigated, then solved using the proposed concept of cellpaths for cellular network data. With this data-driven approach, our proposed approach is versatile: it is compatible with other data sources, and it is model agnostic and thus compatible with user equilibrium, system-optimum, Stackelberg concepts, and other models. Using a dimensionality reduction scheme, we design a projected gradient algorithm suitable for the proposed route flow estimation problem. The algorithm solves a block isotonic regression problem in the projection step in linear time. The accuracy, computational efficiency, and versatility of the proposed approach are validated on the I-210 corridor near Los Angeles, where we achieve 90% route flow accuracy with 1033 traffic sensors and 1000 cellular towers covering a large network of highways and arterials with more than 20,000 links. In contrast to long-term land use planning applications, we demonstrate the first system to our knowledge that can produce route-level flow estimates suitable for short time horizon prediction and control applications in traffic management. Our system is open source and available for validation and extension.     

Integrated feedback ramp metering and mainstream traffic flow control on motorways using variable speed limits

Ramp metering (RM) is the most direct and efficient tool for the motorway traffic flow management. However, because of the usually short length of the on-ramps, RM is typically deactivated to avoid interference of the created ramp queue with adjacent street traffic. By the integration of local RM with mainstream traffic flow control (MTFC) enabled via variable speed limits (VSL), control operation upstream of active bottlenecks could be continued even if the on-ramp is full or if the RM lower bound has been reached. Such integration is proposed via the extension of an existing local cascade feedback controller for MTFC-VSL by use of a split-range-like scheme that allows different control periods for RM and MTFC-VSL. The new integrated controller remains simple yet efficient and suitable for field implementation. The controller is evaluated in simulation for a real motorway infrastructure (a ring-road) fed with real (measured) demands and compared to stand-alone RM or MTFC-VSL, both with feedback and optimal control results. The controller’s performance is shown to meet the specifications and to approach the optimal control results for the investigated scenario.     

The prigogine-herman kinetic model predicts widely scattered traffic flow data at high concentrations

The classical derivation of a traffic stream model (e.g. speed/concentration relation) from the equilibrium solutions of the Prigogine–Herman kinetic equation invokes the nontrivial assumption that the underlying distribution of desired speeds is nonzero for vanishingly small speeds. In this paper we investigate the situation when this assumption does not hold. It is found that the Prigogine–Herman kinetic equation has a one-parameter family of equilibrium solutions, and hence an associated traffic stream model, only for traffic concentrations below some critical value; at higher concentrations there is a two-parameter family of solutions, and hence a continuum of mean velocities for each concentration. This result holds for both constant values of the passing probability and the relaxation time, and for values that depend on concentration in the manner assumed by Prigogine and Herman. It is hypothesized that this result reflects the well-known tendency toward substantial scatter in observational data of traffic flow at high concentrations.     

Norm approximation method for handling traffic count inconsistencies in path flow estimator

Path flow estimator (PFE) is a one-stage network observer proposed to estimate path flows and hence origin–destination (O–D) flows from traffic counts in a transportation network. Although PFE does not require traffic counts to be collected on all network links when inferring unmeasured traffic conditions, it does require all available counts to be reasonably consistent. This requirement is difficult to fulfill in practice due to errors inherited in data collection and processing. The original PFE model handles this issue by relaxing the requirement of perfect replication of traffic counts through the specification of error bounds. This method enhances the flexibility of PFE by allowing the incorporation of local knowledge, regarding the traffic conditions and the nature of traffic data, into the estimation process. However, specifying appropriate error bounds for all observed links in real networks turns out to be a difficult and time-consuming task. In addition, improper specification of the error bounds could lead to a biased estimation of total travel demand in the network. This paper therefore proposes the norm approximation method capable of internally handling inconsistent traffic counts in PFE. Specifically, three norm approximation criteria are adopted to formulate three L_p-PFE models for estimating consistent path flows and O–D flows that simultaneously minimize the deviation between the estimated and observed link volumes. A partial linearization algorithm embedded with an iterative balancing scheme and a column generation procedure is developed to solve the three L_p-PFE models. In addition, the proposed L_p-PFE models are illustrated with numerical examples and the characteristics of solutions obtained by these models are discussed.     

Hybrid artificial neural network and locally weighted regression models for lane-based short-term urban traffic flow forecasting

ABSTRACT

In recent years, there has been considerable research interest in short-term traffic flow forecasting. However, forecasting models offering a high accuracy at a fine temporal resolution (e.g. 1 or 5?min) and lane level are still rare. In this study, a combination of genetic algorithm, neural network and locally weighted regression is used to achieve optimal prediction under various input and traffic settings. The genetically optimized artificial neural network (GA-ANN) and locally weighted regression (GA-LWR) models are developed and tested, with the former forecasting traffic flow every 5-min within a 30-min period and the latter for forecasting traffic flow of a particular 5-min period of each for four lanes of an urban arterial road in Beijing, China. In particular, for morning peak and off-peak traffic flow prediction, the GA-ANN 5-min traffic flow model results in average errors of 3–5% and most 95th percentile errors of 7–14% for each of the four lanes; for the peak and off-peak time traffic flow predictions, the GA-LWR 5-min traffic flow model results in average errors of 2–4% and most 95th percentile errors are lower than 10% for each of the four lanes. When compared to previous models that usually offer average errors greater than 6–15%, such empirical findings should be of interest to and instrumental for transportation authorities to incorporate in their city- or state-wide Advanced Traveller Information Systems (ATIS).     

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.     

Capacity drops at merges: An endogenous model

The Newell-Daganzo merge model is not only very simple but also accurately reproduces experimental findings. However, the capacity downstream of the merge is an exogenous variable in the model. This is a serious limitation for merges that behave as active bottlenecks because their downstream capacity is a direct consequence of the merging behavior. This paper proposes an analytical model that extends the Newell-Daganzo model by incorporating, endogenously, the capacity drop related to the merging process. Two cases are investigated depending on the traffic states on the on-ramp. The model properties are analyzed and a sensitivity analysis is performed to quantify the relative contribution of the each parameter in the capacity drop. Finally, the extended Newell-Daganzo model is validated with experimental data coming from an active merge bottleneck on the M6 freeway in UK.     

A stochastic model of traffic flow: Theoretical foundations

In a variety of applications of traffic flow, including traffic simulation, real-time estimation and prediction, one requires a probabilistic model of traffic flow. The usual approach to constructing such models involves the addition of random noise terms to deterministic equations, which could lead to negative traffic densities and mean dynamics that are inconsistent with the original deterministic dynamics. This paper offers a new stochastic model of traffic flow that addresses these issues. The source of randomness in the proposed model is the uncertainty inherent in driver gap choice, which is represented by random state dependent vehicle time headways. A wide range of time headway distributions is allowed. From the random time headways, counting processes are defined, which represent cumulative flows across cell boundaries in a discrete space and continuous time conservation framework. We show that our construction implicitly ensures non-negativity of traffic densities and that the fluid limit of the stochastic model is consistent with cell transmission model (CTM) based deterministic dynamics.     

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.     

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.