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Showing papers on "Traffic wave published in 1977"


Book
01 Jun 1977
TL;DR: In this article, the authors present an overview of mathematical models in the physical sciences and their application in the field of traffic flow, including the following: Newton's Law, Newton's law as applied to a Spring-Mass System Gravity Oscillation of a SpringMass System Dimensions and Units Qualitative and Quantitative Behavior of a Two-Mass Oscillator Friction Oscillations of a Damped System Underdamped Oscillators Overdamped and Critically Damped Ocillations A Pendulum How Small is Small? A Dimensionless Time Variable Nonlinear Friction
Abstract: Foreword Preface to the classics edition Preface Part I. Mechanical Vibrations: Introduction to Mathematical Models in the Physical Sciences Newton's Law Newton's Law as Applied to a Spring-Mass System Gravity Oscillation of a Spring-Mass System Dimensions and Units Qualitative and Quantitative Behavior of a Spring-Mass System Initial Value Problem A Two-Mass Oscillator Friction Oscillations of a Damped System Underdamped Oscillations Overdamped and Critically Damped Oscillations A Pendulum How Small is Small? A Dimensionless Time Variable Nonlinear Frictionless Systems Linearized Stability Analysis of an Equilibrium Solution Conservation of Energy Energy Curves Phase Plane of a Linear Oscillator Phase Plane of a Nonlinear Pendulum Can a Pendulum Stop? What Happens if a Pendulum is Pushed Too Hard? Period of a Nonlinear Pendulum Nonlinear Oscillations with Damping Equilibrium Positions and Linearized Stability Nonlinear Pendulum with Damping Further Readings in Mechanical Vibrations Part II. Population Dynamics-Mathematical Ecology. Introduction to Mathematical Models in Biology Population Models A Discrete One-Species Model Constant Coefficient First-Order Difference Equations Exponential Growth Discrete Once-Species Models with an Age Distribution Stochastic Birth Processes Density-Dependent Growth Phase Plane Solution of the Logistic Equation Explicit Solution of the Logistic Equation Growth Models with Time Delays Linear Constant Coefficient Difference Equations Destabilizing Influence of Delays Introduction to Two-Species Models Phase Plane, Equilibrium, and linearization System of Two Constant Coefficient First-Order Differential Equations, Stability of Two-Species Equilibrium Populations Phase Plane of Linear Systems Predator-Prey Models Derivation of the Lotka-Volterra Equations Qualitative Solution of the Lotka- Volterra Equations Average Populations of Predators and Preys Man's Influence on Predator-Prey Ecosystems Limitations of the Lotka-Volterra Equation Two Competing Species Further Reading in Mathematical Ecology Part III. Traffic Flow. Introduction to Traffic Flow Automobile Velocities and a Velocity Field Traffic Flow and Traffic Density Flow Equals Density Times Velocity Conservation of the Number of Cars A Velocity-Density Relationship Experimental Observations Traffic Flow Steady-State Car-Following Models Partial Differential Equations Linearization A Linear Partial Differential Equation Traffic Density Waves An Interpretation of Traffic Waves A Nearly Uniform Traffic Flow Example Nonuniform Traffic - The Method of Characteristics After a Traffic Light Turns Green A Linear Velocity-Density Relationship An Example Wave Propagation of Automobile Brake Lights Congestion Ahead Discontinuous Traffic Uniform Traffic Stopped by a Red Light A Stationary Shock Wave The Earliest Shock Validity of Linearization Effect of a Red Light or an Accident Exits and Entrances Constantly Entering Cars A Highway Entrance Further reading in traffic flow Index.

131 citations


Journal ArticleDOI
TL;DR: In this paper, the authors collected responses from residents of 27 different sites in the Greater Manchester area and tested existing noise indices on this general sample of traffic flow situations to determine their efficacy in the prediction of community dissatisfaction to traffic noise.

18 citations


Journal ArticleDOI
TL;DR: The results of these experiments show that substantial savings in average total journey time could be obtained by the use of route control rather than area traffic control alone.

10 citations


Journal Article
TL;DR: In this article, a mathematical model is presented at the traffic pattern on two-lane highways having no structural obstacles to impede overtaking, based on a queueing analogy of the process of overtaking.
Abstract: A mathematical model is presented at the traffic pattern on two-lane highways having no structural obstacles to impede overtaking. The model is based on a queueing analogy of the process of overtaking. Calculations resulted in an indication of the real travel time distribution on a road of this type. This can be used to derive various parameters from which the quality of the traffic pattern can be discerned. The dependence of such parameters on the traffic volume and the fraction of trucks is shown by one example. The agreement of the model with empirical results can be demonstrated at some points. The model proposed in this work can be used as an aid in setting standards for the capacity of two-lane highways and in estimating the consequence of traffic control policies, e.g. speed limits, on such roads. /Author/

10 citations


Journal ArticleDOI
TL;DR: In this article, a mathematical model of the traffic pattern on two-lane highways having no structural obstacles to impede overtaking is presented, based on a queueing analogy of the process of overtaking.

8 citations


01 Jan 1977
TL;DR: The techniques of traffic control and traffic assignment have been combined to enable the calculation of mutually consistent signal timings and traffic assignments by means of an iterative procedure.
Abstract: In a signal-controlled road network, the average delay incurred by traffic is a function of the network cycle time and signal settings, and the traffic pattern in the network. Techniques exist for calculating signal timings to minimise average delay in the network for a particular choice of network cycle time and for a given traffic pattern. No allowance is made in these calculations, however, for likely consequent changes in the traffic pattern brought about by drivers endeavouring to minimise their journey time through the network. Techniques also exist for assigning traffic to routes through the network in such a way that each individual driver minimises his travel-time, provided that the travel-time on each link of the network is a suitable increasing function of the flow of traffic on that link. In the case of a signal-controlled network, these functions will depend in the first instance on the given signal settings at the particular downstream junction, and suitable expressions exist for the particular case of random arrivals of traffic at the junction. In general, however, and especially if a network of quite short links is being considered, the flow of traffic on a link is not random, because of platooning at the upstream junction. Use has been made of a general procedure for estimating the relationships between travel-time and traffic flow for all the links of a signal-controlled road network for any given signal timings in a form suitable for use in assignment calculations. The techniques of traffic control and traffic assignment have then been combined to enable the calculation of mutually consistent signal timings and traffic assignment by means of an iterative procedure. There will usually be, in principle, many solutions to such calculations for a given network and given origin-destination movements, and a case is described in which two quite distinct solutions have been found for a small realistic network, using as a starting point in each instance some preconceived initial assignment of traffic. If such distinct traffic patterns can be induced in practice, by implementing the corresponding signal timings, there will be scope for choosing between them on grounds such as safety and environment as well as delay to traffic. /Author/TRRL/

7 citations


Journal ArticleDOI
TL;DR: Schedule planning and a computer process which demonstrates how a given demand schedule can be smoothed down to a given target flow in an optimum way and also give an indication of the schedule-upset penalty involved is described.
Abstract: The application of the theory of queues to air traffic control is discussed, and the importance is noted of random perturbations due to late arrival of aircraft, and how traffic schedules in an airway network can best be adjusted to minimize delays due to congestion on certain routes. The theory of queues is explained and time varying queues are described. The randomness in air traffic systems, the effect of reduction in randomness, and the effect of randomness on the design of air traffic systems are discussed. Schedule planning and a computer process which demonstrates how a given demand schedule can be smoothed down to a given target flow in an optimum way and also give an indication of the schedule-upset penalty involved is described. An irregular schedule traffic fed into a node where there is a single constraint is discussed as well as a more complex air traffic system with many constraints. The optimization of the system and further improvements are also discussed.

7 citations


Journal ArticleDOI
TL;DR: Ways of using the techniques to best advantage in assessing the traffic capacity of signal-controlled junctions and in calculating signal settings to maximize capacity or to minimize delay are described.

7 citations


01 Apr 1977
TL;DR: The simulation model based on the knowledge of the interaction behaviour of driver-vehicle-elements in a traffic stream allows to quantify the relation between macroscopic parameters of traffic flow, for example, between traffic density and mean speed.
Abstract: The structure of a model is described for digital simulation of traffic flow on a two-lane highway with traffic moving in opposing directions. The model is based on the knowledge of the interaction behaviour of driver-vehicle-elements in a traffic stream. The simulation model allows to quantify the relation between macroscopic parameters of traffic flow, for example, between traffic density and mean speed. The results fit quite well to respective values of measurement. Thus, the simulation model may be considered as a suitable device to determine the capacity of existing highways. An extension of this model will allow forecasting of traffic flow characteristics on highways still in the state of projection. /Author/

1 citations


Journal Article
TL;DR: In this article, a simulation model of bus priority was developed at the University of Bradford, England to aid in determining the overall travel effects of the bus priority scheme on the highway.
Abstract: This paper describes a simulation model of bus priority developed at the University of Bradford, England. Two digital computer simulation models were developed to aid in determining the overall travel effects of bus priority. Observations of traffic flow on the highway were carried out to determine the characteristics of speed and headway distributions. A microscopic Monte Carlo simulation model was used that assigned each vehicle entering the section of the highway under study to a lane and to a vehicle type. A comparison was made between the travel times of buses and non bus vehicles by running the priority and nonpriority models under identical traffic flows and signal settings. The study concluded that the use of these two speed and flow relationships allowed overall passenger travel time savings to be calculated for various proportions of buses in the traffic flow. Since the introduction of the bus-priority scheme, field observations have verified the validity of the model.

1 citations