Module 4 : Macroscopic And Mesoscopic Traffic Flow Modeling

Lecture 17 : Traffic Flow Modeling Analogies

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	Model framework Assumptions The traffic flow is similar to the flow of fluids and the traffic state is described based on speed, density and flow. However the traffic flow can be modelled as a one directional compressible fluid. The two important assumptions of this modelling approach are: The traffic flow is conserved, or in other words vehicles are not created or destroyed. The continuity or conservation equation can be applied. There is one to one relationship between speed and density as well as flow and density. The difficulty with this assumption is that although intuitively correct, in some cases this can lead to negative speed and density. Further, for a given density there exists many speed values are actually measured. These assumptions are valid only at equilibrium condition, that is, when the speed is a function of density. However, equilibrium can be rarely observed in practice and therefore hard to get Speed-density relationship. These are some of the limitations of continuous modelling. The advantages of the continuous modelling are: Better than input output models because flow and density are set as a function of time and distance. Compressibility: ie., flow is assumed to be a function of density. Solving the continuity equation (or flow conservation equation) and the state equation (speed-density and flow-density) are basic traffic flow equations ($q = k.v$). By using the equation that define $q$, $k$, and $v$ at any location $x$ and time $t$, we can evaluate the system using measures of effectiveness such as delays, travel time etc.