A Similitude Theory for Modeling Traffic Flow Dynamics

Similitude theory, particularly dimension analysis, is a common tool for testing scaled-down engineering models and is widely used in vehicle dynamics and other engineering fields. However, it is barely employed in scaling traffic flow dynamics. In this paper, dimension analysis is adopted to scale car-following dynamics. Under the guidance of the similitude theory, a scaled downvehicle test bed is built where seven cars are running on a circular track at a maximum speed initially and congestion emerges after a period of time. In other words, a phantom traffic jam appears in our similitude test bed without any bottlenecks. The fundamental diagrams drawn from the experimental results show that our test bed has the capability of generating traffic hysteresis that is commonly observed in the field. Therefore, the design of this test bed can be used to simulate traffic dynamics to a certain degree and will pave the way for scaled-down connected and automated vehicle systems development.