Module 1 : Traffic Stream Characteristics

Lecture 01 : Fundamental Parameters of Traffic Flow

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	Multiple Vehicles Time-space diagram can also be used to determine the fundamental parameters of traffic flow like speed, density and volume. It can also be used to find the derived characteristics like space headway and time headway. Figure 1 shows the time-space diagram for a set of vehicles traveling at constant speed. Density, by definition is the number of vehicles per unit length. From the figure, an observer looking into the stream can count 4 vehicles passing the stretch of road between $x_1$ and $x_2$ at time $t$. Hence, the density is given as $$k = \frac{4 ~vehicles}{x_2 - x_1}$$ (1) We can also find volume from this time-space diagram. As per the definition, volume is the number of vehicles counted for a particular interval of time. From the figure 1 we can see that 6 vehicles are present between the time $t_1$ and $t_2$. Therefore, the volume $q$ is given as $$q = \frac{3 ~vehicles}{t_2 - t_1}$$ (2) Again the averages taken at a specific location (i.e., time ranging over an interval) are called time means and those taken at an instant over a space interval are termed as space means. Another related definition which can be given based on the time-space diagram is the headway. Space headway is defined as the distance between corresponding points of two successive vehicles at any given time. Thus, the vertical gap between any two consecutive lines represents space headway. The reciprocal of density otherwise gives the space headway between vehicles at that time. Similarly, time headway is defined as the time difference between any two successive vehicles when they cross a given point. Thus, the horizontal gap between the vehicles represented by the lines gives the time headway. The reciprocal of flow gives the average time headway between vehicles at that point. Figure 1: Time space diagram for many vehicles