Introduction to the Theory of Traffic Flow

ISBN-13: 9783642648052 / Angielski / Miękka / 2012 / 204 str.

Wilhelm Leutzbach

Opis

This book describes a coherent approach to the explanation of the movement of individual vehicles or groups of vehicles. To avoid possible misunderstandings, some preliminary remarks are called for. 1. This is intended to be a textbook. It brings together methods and approaches that are widely distributed throughout the literature and that are therefore difficult to assess. Text citations of sources have been avoided; literature references are listed together at the end of the book. 2. The book is intended primarily for students of engineering. It describes the theoretical background necessary for an understanding of the methods by which links in a road network are designed and dimensioned or by which traffic is controlled; the methods themselves are not dealt with. It may also assist those actually working in such sectors to interpret the results of traffic flow measure ments more accurately than has hitherto been the case. 3. The book deals with traffic flow on links between nodes, and not at nodes themselves. Many readers will probably regret this, since nodes are usually the bottlenecks which limit the capacity of the road network. A book dedicated to the node would be the obvious follow-up. A separation of link and node is justified, however, partly because the quantity of material has to be kept within reasonable bounds and partly because the treatment of traffic flow at nodes requires additional mathematical techniques (in particular, those relating to queueing theory)."

Spis treści

I. The Motion of a Single Vehicle.- I.1. Kinematics of a Single Vehicle.- I.1.1 Time-dependent Description.- I.1.1.1 Motion as a Function of Time.- I.1.1.2 Motion as a Function of Distance.- I.1.1.3 Motion as a Function of Speed.- I.1.2 Distance-dependent Description.- I.1.3 Graphical Transformations.- I.2. Statistics of the Motion of an Individual Vehicle.- I.2.1 Means and Variances of Speeds.- I.2.2 The Relationship Between the Parameters of Time-dependent and Distance-dependent Motion.- I.2.3 The Distribution of Acceleration.- II. The Motion of Several Vehicles on a Road.- II.1. Distributions and Their Parameters.- II.2. Parameters for Describing a Traffic Stream.- II.2.1 Discrete Flows and Local Measurements.- II.2.2 Discrete Flows and Instantaneous Measurements.- II.2.3 Speed Distributions.- II.2.3.1 The Instantaneous Speed Distribution.- II.2.3.2 The Local Speed Distribution.- II.2.3.3 The Speed Distribution as Seen by a Moving Observer.- II.2.3.4 Parameters of Speed Distributions for Non-constant Speeds.- II.2.4 Headway Distributions.- II.2.5 Lane Occupancy.- II.2.6 Relationship Between Parameters.- II.2.6.1 Fundamental Considerations.- II.2.6.2 The Effects of the Method of Measurement.- II.2.6.2.1 Local Measurements and Measurement Intervals.- II.2.6.2.2 Instantaneous Measurement and Measurement Intervals.- II.2.6.2.3 Quasi-local Measurements.- II.2.6.2.4 Quasi-instantaneous Measurements.- II.2.6.2.5 The Generalized Relationship.- II.2.6.2.6 Journey Time Measurement.- II.2.6.2.6.1 Observations Made from a Moving Vehicle.- II.2.6.2.6.2 Determination of q and r from Traffic Counts at the End of a Link.- II.2.6.3 Empirical Relationships.- II.2.6.3.1 Speed and Volume.- II.2.6.3.2 Speed and Density.- II.2.6.3.3 Volume and Density: The Fundamental Diagram.- II.2.6.3.4 The Dynamic Fundamental Diagram.- II.2.6.3.5 Influences on the Shape of the Fundamental Diagram.- II.3 Description of the States of Traffic.- II.3.1 Freely Flowing Traffic.- II.3.1.1 Parameters as Functions of Time and Distance.- II.3.1.2 Overtaking in Freely Flowing Traffic.- II.3.2 Partly Constrained Traffic.- II.3.2.1 Queueing Theory Models for Two-Lane Rural Roads.- II.3.2.2 The Kinetic Theory.- II.3.2.3 A Multi-phase Model of Traffic Flow.- II.3.2.4 Observed Lane Changing Behaviour.- II.3.3 The Constrained Traffic.- II.3.3.1 Deterministic Spacing Models.- II.3.3.1.1 Constant Spacing.- II.3.3.1.2 Spacing as a Function of Speed.- II.3.3.1.3 Car Following Models.- II.3.3.1.4 Macroscopic Verification of Microscopic Models.- II.3.3.1.4.1 Integration of the Car Following Equation.- II.3.3.1.4.2 The Influence of Exponential Terms in the Car Following Equation on the Shape of the Fundamental Diagram.- II.3.3.2 Psycho-Physical Spacing Models.- II.3.3.3 Continuum Theory.- II.3.3.3.1 The Fundamental Equation and the Continuum Equation.- II.3.3.3.2 Shockwaves.- II.3.3.3.3 Kinematic Waves or Characteristics.- II.3.3.3.4 Form of the Fundamental Diagram II.- II.3.3.3.5 The Application of Continuum Theory to a Multi-lane Carriageway.- II.3.3.3.6 Generalization of the Continuum Theory.- II.3.3.3.7 A Dynamic Continuum Model.- II.3.3.3.8 Derivation of the Continuum Model from a Kinetic Model.- References.- List of Symbols.