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.     

A traffic flow simulator for network reliability assessment

This paper investigates the transportation network reliability based on the information provided by detectors installed on some links. A traffic flow simulator (TFS) model is formulated for assessing the network reliability (in terms of travel time reliability), in which the variation of perceived travel time error and the fluctuations of origin-destination (OD) demand are explicitly considered. On the basis of prior OD demand and partial updated detector data, the TFS can estimate the link flows for the whole network together with link/path travel times, and their variance and covariance. The travel time reliability by OD pair can also be assessed and the OD matrix can be updated simultaneously. A Monte Carlo based algorithm is developed to solve the TFS model. The application of the proposed TFS model is illustrated by a numerical example.     

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.     

A phenomenological model for dynamic traffic flow in networks

A macroscopic model for dynamic traffic flow is presented. The main goal of the model is the real time simulation of large freeway networks with multiple sources and sinks. First, we introduce the model in its discrete formulation and consider some of its properties. It turns out, that our non-hydrodynamical ansatz for the flows results in a very advantageous behavior of the model. Next the fitting conditions at junctions of a traffic network are discussed. In the following sections we carry out a continuous approximation of our discrete model in order to derive stationary solutions and to consider the stability of the homogeneous one. It turns out, that for certain conditions unstable traffic flow occurs. In a subsequent section, we compare the stability of the discrete model and the corresponding continuous approximation. This confirms in retrospection the close similarities of both model versions. Finally we compare the results of our model with the results of another macroscopic model, that was recently suggested by Kerner and Konhäuser [Phys. Rev. E 48, 2335–2338 (1993)].     

On some traffic equilibrium theory paradoxes

We consider the asymmetric equilibrium problem with fixed demands in a transportation network where the travel cost on each link may depend on the flow on this as well as other links of the network and we study how the travellers' cost is affected by changes in the travel demand or addition of new routes. Assuming that the travel cost functions are strongly monotone, we derive formulas which express, under certain conditions, how a change in travel demand associated with a particular origin-destination (O / D) pair will affect the travelers' cost for any O / D pair. We then use these formulas to show that an increase in the travel demand associated with a particular O / D pair (all other remaining fixed) always results in an increase in the travelers' cost on that O / D pair, however, the travelers' cost on other O / D pairs may decrease. We then derive formulas yielding, under certain conditions, the change in travelers' cost on every O / D pair induced by the addition of a new path. These can be used to determine, whether Braess' paradox occurs in the network. We then show that when a new path is added, the travelers' cost associated with the particular O / D pair joined by this path will decrease (hence Braess' paradox does not occur) if a test matrix is positive semidefinite.     

Short-term traffic flow rate forecasting based on identifying similar traffic patterns

The ability to timely and accurately forecast the evolution of traffic is very important in traffic management and control applications. This paper proposes a non-parametric and data-driven methodology for short-term traffic forecasting based on identifying similar traffic patterns using an enhanced K-nearest neighbor (K-NN) algorithm. Weighted Euclidean distance, which gives more weight to recent measurements, is used as a similarity measure for K-NN. Moreover, winsorization of the neighbors is implemented to dampen the effects of dominant candidates, and rank exponent is used to aggregate the candidate values. Robustness of the proposed method is demonstrated by implementing it on large datasets collected from different regions and by comparing it with advanced time series models, such as SARIMA and adaptive Kalman Filter models proposed by others. It is demonstrated that the proposed method reduces the mean absolute percent error by more than 25%. In addition, the effectiveness of the proposed enhanced K-NN algorithm is evaluated for multiple forecast steps and also its performance is tested under data with missing values. This research provides strong evidence suggesting that the proposed non-parametric and data-driven approach for short-term traffic forecasting provides promising results. Given the simplicity, accuracy, and robustness of the proposed approach, it can be easily incorporated with real-time traffic control for proactive freeway traffic management.     

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.     

A porous flow approach to modeling heterogeneous traffic in disordered systems

A continuum model that describes a disordered, heterogeneous traffic stream is presented. Such systems are widely prevalent in developing countries where classical traffic models cannot be readily applied. The characteristics of such systems are unique since drivers of smaller vehicles exploit their maneuverability to move ahead through lateral gaps at lower speeds. At higher speeds, larger vehicles press their advantage of greater motive power. The traffic stream at the microscopic level is disordered and defines a porous medium. Each vehicle is considered to move through a series of pores defined by other vehicles. A speed-density relationship that explicitly considers the pore space distribution is presented. This captures the considerable dynamics between vehicle classes that are overlooked when all classes are converted to a reference class (usually Passenger Car Equivalents) as is traditionally done. Using a finite difference approximation scheme, traffic evolution for a two-class traffic stream is shown.     

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 note on a graphical interpretation of wave and shockwave velocities of a traffic stream

This note gives simple equations for wave and shockwave velocities, using a graphical interpretation of speed-intercepts on the speed-concentration and speed-flow curves.     

A clustering based traffic flow prediction method with dynamic spatiotemporal correlation analysis

Transportation - There are significant spatiotemporal correlations among the traffic flows of neighboring road sections in the road network. Correctly identifying such correlations makes an...     

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.     

Evaluation of green wave policy in real-time railway traffic management

In order to face the expected growth of transport demand in the next years, several new traffic control policies have been proposed and analyzed both to generate timetables and to effectively manage the traffic in real-time. In this paper, a detailed optimization model is used to analyze one such policy, called green wave, which consists in letting trains wait at the stations to avoid speed profile modifications in open corridors. Such policy is expected to be especially effective when the corridors are the bottleneck of the network. However, there is a lack of quantitative studies on the real-time effects of using this policy. To this end, this work shows a comparison of the delays obtained when trains are allowed or not to change their speed profile in open corridors. An extensive computational study is described for two practical dispatching areas of the Dutch railway network.     

Dynamic prediction of traffic volume through Kalman filtering theory

Two models employing Kalman filtering theory are proposed for predicting short-term traffic volume. Prediction parameters are improved using the most recent prediction error and better volume prediction on a link is achieved by taking into account data from a number of links. Based on data collected from a street network in Nagoya City, average prediction error is found to be less than 9% and maximum error less than 30%. The new models perform substantially (up to 80%) better than UTCS-2.     

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.     

An expert system for air traffic flow management

An expert system for the air traffic flow management (ATFM) problem is presented. Two main prototypes have been constructed, one for timetable rescheduling that attempts to modify airline timetables to smooth traffic peaks at airports during rush-hours and another for centralized flow control that works to forecast the place, time and magnitude of the congestion and to propose mitigative actions. Simulations for the Brazilian ATFM, including the principal 14 airports, show the potential usefulness of the expert system.     

On the kinematics and quantum dynamics of traffic flow

The hydrodynamic model of traffic flow is presented and interpreted. Traffic dimensions are defined for the dynamic entities of flow and the behaviour of congestive and dispersive flow is discussed dependent on the value of the local traffic transfer number, R. The wave equation is one example of dispersive flow, where quantum numbers define the condition of free flow at the endpoints of the link. The Schrödinger equation is defined and applied to the study of the cyclic work journey and the problem of traffic lights as an harmonic oscillator.     

Spillback congestion in dynamic traffic assignment: A macroscopic flow model with time-varying bottlenecks

In this paper, we propose a new model for the within-day Dynamic Traffic Assignment (DTA) on road networks where the simulation of queue spillovers is explicitly addressed, and a user equilibrium is expressed as a fixed-point problem in terms of arc flow temporal profiles, i.e., in the infinite dimension space of time’s functions. The model integrates spillback congestion into an existing formulation of the DTA based on continuous-time variables and implicit path enumeration, which is capable of explicitly representing the formation and dispersion of vehicle queues on road links, but allows them to exceed the arc length. The propagation of congestion among adjacent arcs will be achieved through the introduction of time-varying exit and entry capacities that limit the inflow on downstream arcs in such a way that their storage capacities are never exceeded. Determining the temporal profile of these capacity constraints requires solving a system of spatially non-separable macroscopic flow models on the supply side of the DTA based on the theory of kinematic waves, which describe the dynamic of the spillback phenomenon and yield consistent network performances for given arc flows. We also devise a numerical solution algorithm of the proposed continuous-time formulation allowing for “long time intervals” of several minutes, and give an empirical evidence of its convergence. Finally, we carry out a thorough experimentation in order to estimate the relevance of spillback modeling in the context of the DTA, compare the proposed model in terms of effectiveness with the Cell Transmission Model, and assess the efficiency of the proposed algorithm and its applicability to real instances with large networks.     

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.