Module 1 : Traffic Stream Characteristics

Lecture 02 : Fundamental Relations of Traffic Flow

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	Fundamental relations of traffic flow The relationship between the fundamental variables of traffic flow, namely speed, volume, and density is called the fundamental relations of traffic flow. This can be derived by a simple concept. Let there be a road with length $v$ km, and assume all the vehicles are moving with $v$ km/hr.(Fig 1). Figure 1: Illustration of relation between fundamental parameters of traffic flow Let the number of vehicles counted by an observer at A for one hour be $n_1$. By definition, the number of vehicles counted in one hour is flow(q). Therefore, $$n_1 = q.$$ (1) Similarly, by definition, density is the number of vehicles in unit distance. Therefore number of vehicles $n_2$ in a road stretch of distance $v_1$ will be density $\times$ distance.Therefore, $$n_2 = k\times v.$$ (2) Since all the vehicles have speed $v$, the number of vehicles counted in 1 hour and the number of vehicles in the stretch of distance $v$ will also be same.(ie $n_1 = n_2$). Therefore, $$q = k\times v.$$ (3) This is the fundamental equation of traffic flow. Please note that, $v$ in the above equation refers to the space mean speed will also be same.