Abstract
This paper demonstrates the limitation of the flow-based travel time functions. This paper presents a density-based travel time function and further develops a fundamental model of travel time dynamics that is built from a given fundamental traffic relationship and vehicle characteristics. The travel time dynamics produce an asymmetric one-sided coupled system of hyperbolic partial differential equations, where the first equation represents the macroscopic traffic dynamics. The existence of the solution for the mathematical model is then presented. The main contribution of this paper is the mathematical development and analysis of the real-time model of travel time. Moreover, this paper also shows various intelligent transportation system applications where travel time is an important factor and where this new model would be extremely useful and important.
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