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Exactly Solvable Single Lane Highway Traffic Model With Tollbooths
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Exactly Solvable Single Lane Highway Traffic Model With Tollbooths
H. F. Chau1?, Hao Xu1,2 and L.-G. Liu2
1 Department of Physics, University of Hong Kong, Pokfulam Road, Hong Kong, China
2 Department of Physics, Zhongshan University, Guangzhou, Guangdong 510275, China
(February 1, 2008)
Tolls are collected on many highways as a means of traffic control and revenue generation. How-
ever, the presence of tollbooths on highway surely slows down traffic flow. Here, we investigate how
the presence of tollbooths affect the average car speed using a simple-minded single lane determin-
istic discrete traffic model. More importantly, the model is exactly solvable.
PACS numbers: 45.70.Vn, 05.60.-k, 89.40.+k
Modern computing power allows us to simulate highway and city traffic by looking at the microscopic behaviors of
all cars. Perhaps the most well-known model of this kind is the cellular automaton based Biham-Middleton-Levine
(BML) model of two-dimensional city traffic [1]. Numerical simulations of this model strongly suggest that a first
order phase transition from the full-speed phase to the completely jamming phase occurs as the car density of the
system increases. Moreover, this phase transition is primarily the result of the exclusion volume effect [1,2]. In spite
of its simplicity, very little rigorous result is known for the BML model [3].
Different generations and variations of the BML model have been investigated in the literature [4]. These gen-
eralizations focus on different aspects of the problem. They include the introduction of more realistic traffic rules
[5], study of the effects of over-passes and faulty traffic lights [6], application of cellular automaton based traffic
rules to single and multiple lane highway traffic [7] and investigation of higher dimensional traffic behaviors [8]. In
particular, Nagel and Schreckenberg [9] proposed a model
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