The introduction of connected and autonomous vehicles will bring changes to the highway driving environment. Connected vehicle technology provides real-time information about the surrounding traffic condition and the traffic management center’s decisions. Such information is expected to improve drivers’ efficiency, response, and comfort while enhancing safety and mobility. Connected vehicle technology can also further increase efficiency and reliability of autonomous vehicles, though these vehicles could be operated solely with their on-board sensors, without communication. While several studies have examined the possible effects of connected and autonomous vehicles on the driving environment, most of the modeling approaches in the literature do not distinguish between connectivity and automation, leaving many questions unanswered regarding the implications of different contemplated deployment scenarios. There is need for a comprehensive acceleration framework that distinguishes between these two technologies while modeling the new connected environment. This study presents a framework that utilizes different models with technology-appropriate assumptions to simulate different vehicle types with distinct communication capabilities. The stability analysis of the resulting traffic stream behavior using this framework is presented for different market penetration rates of connected and autonomous vehicles. The analysis reveals that connected and autonomous vehicles can improve string stability. Moreover, automation is found to be more effective in preventing shockwave formation and propagation under the model’s assumptions. In addition to stability, the effects of these technologies on throughput are explored, suggesting substantial potential throughput increases under certain penetration scenarios.

Influence of connected and autonomous vehicles on traffic flow stability and throughput

Certain aspects of traffic flow measurements imply the existence of a phase transition. Models known from chaos and fractals, such as nonlinear analysis of coupled differential equations, cellular automata, or coupled maps, can generate behavior which indeed resembles a phase transition in the flow behavior. Other measurements point out that the same behavior could be generated by geometrical constraints of the scenario. This paper looks at some of the empirical evidence, but mostly focuses on different modeling approaches. The theory of traffic jam dynamics is reviewed in some detail, starting from the well-established theory of kinematic waves and then veering into the area of phase transitions. One aspect of the theory of phase transitions is that, by changing one single parameter, a system can be moved from displaying a phase transition to not displaying a phase transition. This implies that models for traffic can be tuned so that they display a phase transition or not.This paper focuses on microscopic modeling, i.e., coupled differential equations, cellular automata, and coupled maps. The phase transition behavior of these models, as far as it is known, is discussed. Similarly, fluid-dynamical models for the same questions are considered. A large portion of this paper is given to the discussion of extensions and open questions, which makes clear that the question of traffic jam dynamics is, albeit important, only a small part of an interesting and vibrant field. As our outlook shows, the whole field is moving away from a rather static view of traffic toward a dynamic view, which uses simulation as an important tool.

Still Flowing: Approaches to Traffic Flow and Traffic Jam Modeling

Obtaining accurate information about current and near-term future traffic flows of all links in a traffic network has a wide range of applications, including traffic forecasting, vehicle navigation devices, vehicle routing, and congestion management. A major problem in getting traffic flow information in real time is that the vast majority of links is not equipped with traffic sensors. Another problem is that factors affecting traffic flows, such as accidents, public events, and road closures, are often unforeseen, suggesting that traffic flow forecasting is a challenging task. In this paper, we first use a dynamic traffic simulator to generate flows in all links using available traffic information, estimated demand, and historical traffic data available from links equipped with sensors. We implement an optimization methodology to adjust the origin-to-destination matrices driving the simulator. We then use the real-time and estimated traffic data to predict the traffic flows on each link up to 30 min ahead. The prediction algorithm is based on an autoregressive model that adapts itself to unpredictable events. As a case study, we predict the flows of a traffic network in San Francisco, CA, USA, using a macroscopic traffic flow simulator. We use Monte Carlo simulations to evaluate our methodology. Our simulations demonstrate the accuracy of the proposed approach. The traffic flow prediction errors vary from an average of 2% for 5-min prediction windows to 12% for 30-min windows even in the presence of unpredictable events.

Traffic Flow Prediction for Road Transportation Networks With Limited Traffic Data

Based on the previous literature review, this paper builds a short-term traffic speed forecasting model using Support Vector Machine (SVM) regression theory (referred as SVM model in this paper). Besides the advantages of the SVM model, it also has some limitations. Perhaps the biggest one lies in choice of the appropriate kernel function for the practical problem; how to optimize the parameters efficiently and effectively presents another one. Unfortunately, these limitations are still research topics in current literature. This paper puts an effort to investigate these limitations. In order to find the effective way to choose the appropriate and suitable kernel function, this paper constructs a new kernel function using a wavelet function to capture the non-stationary characteristics of the short-term traffic speed data. In order to find the efficient way to identify the model structure parameters, this paper uses the Phase Space Reconstruction theory to identify the input space dimension. To take the advantage of these components, the paper proposes a short-term traffic speed forecasting hybrid model (Chaos–Wavelet Analysis-Support Vector Machine model, referred to as C-WSVM model in this paper). The real traffic speed data is applied to evaluate the performance and practicality of the model and the results are encouraging. The theoretical advantage and better performance from the study indicate that the C-WSVM model has good potential to be developed and is feasible for short-term traffic speed forecasting study.

Short-term traffic speed forecasting hybrid model based on Chaos–Wavelet Analysis-Support Vector Machine theory

This paper deals with the problem of predicting traffic flows and updating these predictions when information about OD pairs and/or link flows becomes available. To this end, a Bayesian network is built which is able to take into account the random character of the level of total mean flow and the variability of OD pair flows, together with the random violation of the balance equations for OD pairs and link flows due to extra incoming or exiting traffic at links or to measurement errors. Bayesian networks provide the joint density of all unobserved variables and in particular the corresponding conditional and marginal densities, which allow not only joint predictions, but also probability intervals. The influence of congested traffic can also be taken into consideration by combination of the traffic assignment rules (as SUE, for example) with the Bayesian network model proposed. Some examples illustrate the model and show its practical applicability.

Predicting traffic flow using Bayesian networks

This paper deals with two mathematically similar problems in transport network analysis: trip matrix estimation and traffic signal optimisation on congested road networks. These two problems are formulated as bi-level programming problems with stochastic user equilibrium assignment as the second-level programming problem. We differentiate two types of solutions in the combined matrix estimation and stochastic user equilibrium assignment problem (or the combined signal optimisation and stochastic user equilibrium assignment problem): one is the solution to the bi-level programming problem and the other the mutually consistent solution where the two sub-problems in the combined problem are solved simultaneously. In this paper, we shall concentrate on the bi-level programming approach, although we shall also consider mutually consistent solutions so as to contrast the two types of solutions. The purpose of the paper is to present a solution algorithm for the two bi-level programming problems and to test the algorithm on several networks.

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A bi-level programming approach for trip matrix estimation and traffic control problems with stochastic user equilibrium link flows

This paper investigates the stability of the classical car-following model (for example, Chandler et al., Operations Research, 6, 165–184, 1958; Herman et al., Operations Research, 7, 86–106, 1959; Wilhelm and Schmidt, Transportation Engineering Journal (ASCE) 99, 923–933, 1973). Conditions for local and asymptotic stability as defined in the references cited are established for the linear model. These differ from those in the literature in two ways. First, it will be shown that, in the autonomous model when the product of the coefficient of proportionality α and the reaction time τ is less than or equal to 1/e, there exist oscillatory solutions with higher frequencies than 2π, although there are none with lower frequencies. Secondly, asymptotic stability is considered along with local stability. The derived condition for asymptotic stability is both necessary and sufficient. In addition, the condition depends on the frequency of the forcing term, with the sufficient condition ατ 1 2 for the asymptotic stability found in the literature being included as a special case. The nonlinear model is considered by linearization and numerical integrations. Some practical values of parameters are tested for the stability of the model. The analyses in this paper are extended to consider different values of α and τ for different drivers in the line.

Stability analysis of the classical car-following model

In this paper we investigate the dynamic behavior of road traffic flows in an area represented by an origin-destination (O-D) network. Probably the most widely used model for estimating the distribution of O-D flows is the gravity model, [J. de D. Ortuzar and L. G. Willumsen, Modelling Transport (Wiley, New York, 1990)] which originated from an analogy with Newton's gravitational law. The conventional gravity model, however, is static. The investigation in this paper is based on a dynamic version of the gravity model proposed by Dendrinos and Sonis by modifying the conventional gravity model [D. S. Dendrinos and M. Sonis, Chaos and Social-Spatial Dynamics (Springer-Verlag, Berlin, 1990)]. The dynamic model describes the variations of O-D flows over discrete-time periods, such as each day, each week, and so on. It is shown that when the dimension of the system is one or two, the O-D flow pattern either approaches an equilibrium or oscillates. When the dimension is higher, the behavior found in the model includes equilibria, oscillations, periodic doubling, and chaos. Chaotic attractors are characterized by (positive) Liapunov exponents and fractal dimensions.(c) 1998 American Institute of Physics.

Chaos in a dynamic model of traffic flows in an origin-destination network.

This paper addresses the problem of estimating an Origin–Destination (O–D) matrix with platoon dispersion from fully disaggregate data: that is, the passage times of vehicles at the entries and exits or the origins and destinations of a network. Given a list of entry times and a list of exiting times, a fully disaggregate method or a matching method tries to match each pair of entry–exiting times such that the resultant journey times for each O–D pair fit the given distributions best. Bell et al., 1991 formulated the problem of finding the most likely set of matches as a 0–1 assignment problem. In this paper, two estimators will be considered: maximum likelihood estimator and the matching-Furness technique. It will be shown that the maximum likelihood estimation can be formulated more generally as a transportation problem. The matching-Furness method is investigated by use of simulated traffic data and is applied to a set of real data collected on the Brescia–Padova motorway network in Italy. The matching-Furness method gives consistently better estimates than the least squares estimator ( Cremer and Keller, 1987 ) and the linked static-dynamic correlation model ( Keller and Ploss, 1987 ). The method is therefore suitable for off-line estimations for general networks.

The evaluation and application of a fully disaggregate method for trip matrix estimation with platoon dispersion

This paper deals with two problems in transport network planning and control: trip matrix estimation and traffic signal optimisation. These two problems have both been formulated as bi-level programming problems with the User Equilibrium assignment as the second-level programming problem. One currently used method for solving the two problems consists of alternate optimisation of the two sub-problems until mutually consistent solutions are found. However, this alternate procedure does not converge to the solution of the bi-level programming problem. In this paper, a new algorithm will be developed and will be applied to two road networks.

Xiaoyan Zhang

Papers

A bi-level programming approach for trip matrix estimation and traffic control problems with stochastic user equilibrium link flows

Stability analysis of the classical car-following model

Chaos in a dynamic model of traffic flows in an origin-destination network.

The evaluation and application of a fully disaggregate method for trip matrix estimation with platoon dispersion

An algorithm for the solution of bi-level programming problems in transport network analysis