Journal ArticleDOI
An Operational Analysis of Traffic Dynamics
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In this paper, the authors studied the dynamics of a line of traffic composed of n vehicles, where the movements of the vehicles are controlled by an idealized ''law of separation'' which specifies that each vehicle must maintain a certain prescribed following distance from the preceding vehicle.Abstract:
The dynamics of a line of traffic composed of n vehicles is studied mathematically. It is postulated that the movements of the several vehicles are controlled by an idealized ``law of separation.'' The law considered in the analysis specifies that each vehicle must maintain a certain prescribed ``following distance'' from the preceding vehicle. This distance is the sum of a distance proportional to the velocity of the following vehicle and a certain given minimum distance of separation when the vehicles are at rest. By the application of this postulated law to the motion of the column of vehicles, the differential equations governing the dynamic state of the system are obtained.The solution of the dynamical equations for several assumed types of motion of the leading vehicle is effected by the operational or Laplace transform method and the velocities and accelerations of the various vehicles are thus obtained. Consideration is given to the use of an electrical analog computer for studying the dynamical e...read more
Citations
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Journal ArticleDOI
Shock Waves on the Highway
TL;DR: In this article, a simple theory of traffic flow is developed by replacing individual vehicles with a continuous fluid density and applying an empirical relation between speed and density, which is a simple graph-shearing process for following the development of traffic waves.
Journal ArticleDOI
Traffic and related self-driven many-particle systems
Dirk Helbing,Dirk Helbing +1 more
TL;DR: This article considers the empirical data and then reviews the main approaches to modeling pedestrian and vehicle traffic, including microscopic (particle-based), mesoscopic (gas-kinetic), and macroscopic (fluid-dynamic) models.
Journal ArticleDOI
Statistical physics of vehicular traffic and some related systems
TL;DR: In this paper, a critical review of particle-hopping models of vehicular traffic is presented, focusing on the results obtained mainly from the so-called "particle hopping" models, particularly emphasizing those formulated in recent years using the language of cellular automata.
Journal ArticleDOI
Nonlinear Follow-the-Leader Models of Traffic Flow
TL;DR: A variety of nonlinear follow-the-leader models of traffic flow are discussed in this article in the light of available observational and experimental data, with emphasis placed on steady-state flow equations.
Journal ArticleDOI
Car-following: a historical review
Mark Brackstone,Mike McDonald +1 more
TL;DR: In this article, the authors assess the range of options available in the choice of car-following model, and assess just how far work has proceeded in our understanding of what, at times, would appear to be a simple process.
References
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Book
Methods of operations research
TL;DR: An exhibit honoring Hermann von Helmholtz, inventor of the ophthalmoscope, will be on display for six months at the Armed Forces Medical Museum, Washington, D. C.
Journal ArticleDOI
Methods of Operations Research.
Book
Applied Mathematics for Engineers and Physicists
Louis A. Pipes,Harold Mendlowitz +1 more
TL;DR: Applied mathematics for engineers and physicists as mentioned in this paper, applied mathematics for scientists and engineers, applied mathematics and physics for engineers, and applied mathematics in the field of computer science and engineering, etc.
Book
Tables of the incomplete gamma-function
TL;DR: In this paper, Tocher pointed out an error in the introduction to the above tables and pointed out that in a table on page xx the wrong argument has been inserted to the correct value of the function.