Blake Cicenas
PHYS 714
Traffic Circle and Roundabout Information
By
Blake Cicenas
PROBLEM A: Designing a Traffic Circle
Many cities and communities have traffic circles—from large ones with many lanes in the circle (such as at the Arc de Triomphe in Paris and the Victory Monument in Bangkok) to small ones with one or two lanes in the circle. Some of these traffic circles position a stop sign or a yield sign on every incoming road that gives priority to traffic already in the circle; some position a yield sign in the circle at each incoming road to give priority to incoming traffic; and some position a traffic light on each incoming road (with no right turn allowed on a red light). Other designs may also be possible.
First I did a little basic research on the subject. I visited the Insurance for Highway Safety Website[1]and a Roundabout Design Website[2] which gave me a basis to start with. According to these two websites, they claim that roundabouts are safer and more efficient than regular traffic lights and stop signs. And they also give a few diagrams and tips on the best types of roundabouts. However, they did not give any mathematical modeling tips.
So the next step was to examine the math behind traffic circles. The first issue that had to be dealt with is the approach to the problem. First on the suggestion of David, I readTraffic Circlesby Chris Raastad, Igor Tolkov, and Ian Zemke[3]which was a paper written for the mathematical modeling contest under Professor Morrow at the University of Washington. This paper introduced me to the basics of the Bandomodel; however, I wanted to improve on this by combining it with another field.
The first method involved geophysical processes and two books, Introduction to the Physics of Cohesive Sediment in the Marine Environment by Johan C. Winterwerp and Walther G. M. van Kesteren and Fluid Physics in Geology: An introduction to Fluid Motions on Earth’s Surface and Within Its Crust by David Jon Furbish, were examined. In particular, I had hoped to examine the physics of eddies and vortices and then relate to them to the fluid like flow of a traffic circle modeled by Bando. However, there was very little information in the two geo-fluid mechanical books that were in the WSU library and the articles contained in the databases were scant. Therefore a different approach was needed and it was found with the article Models for highway Traffic and their connections to thermodynamics by Hans Weber, Reinhard Mahnke, Julia Hinkel, and Anesot[4]. This article took the Bando model and examined traffic jams with respect to thermodynamics. In particular, they looked at traffic jams being a dense liquid fluid and flowing traffic being in a gas phase. Then using their given equations, they used the acceleration to create potential energy which is then used to create a pseudo Hamiltonian. Once the Hamiltonian is completed, the Monte Carlo simulation can be applied. Then some of the results were integrated using the Runge-Kutta method. Because of the complexity of this article and my scant background knowledge, much time has been devoted to understanding the article. I have outlined a process that I need to follow in order to understand this article enough to figure out if I want to use it or not. Attached to each of the points are the footnotes of websites visited so that the reader can easily follow my progress.
I. Understand the given Bando equations and their parameters(completed)
II. Understand what a Hamiltonian[5] is(incomplete)
A. Relearn Langrage’s Theorem[6](incomplete)
III. Understand what the Motel Carlo Method[7] is(incomplete)
IV. Learn what the Runge-Kutta method[8] is (incomplete)
In addition to the websites listed, I also examined the texts The Fundamentals of Physics by Halliday, Resnick & Walker, Calculus by Larson, Hostetler and Edwards, A First Course in Differential Equations by Dennis G. Zill, and Modern Physics for Scientists and Engineers by John R. Taylor, Chris D. Zafiratos and Michale A Dubson. Articles obtained by not yet examined are An Improved Car-Following Model for Multiphase Vehicular Traffic Flow and Numerical Tests by LI Zhi-Peng,† GONG Xiao-Bo, and LIU Yun-Cai obtained from Communications in Theoretical Physics; Phase transition in a difference equation model of trafficflow by Takashi Nagatani, Ken Nakanishi and Heike Emmerich obtained from the Journal of Physics and Math and an article written by three mathematicians[9] that I only contain because somebody with more mathematical knowledge might understand what is going on. I have also contained my pencil and paper ramblings in my feeble attempts to understand the thermo dynamical article.
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