Module 1 : Traffic Stream Characteristics

Lecture 01 : Fundamental Parameters of Traffic Flow

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	Time-space diagram Time space diagram is a convenient tool in understanding the movement of vehicles. It shows the trajectory of vehicles in the form of a two dimensional plot. Time space diagram can be plotted for a single vehicle as well as multiple vehicles. They are discussed below. Single vehicle Taking one vehicle at a time, analysis can be carried out on the position of the vehicle with respect to time. This analysis will generate a graph which gives the relation of its position on a road stretch relative to time. This plot thus will be between distance $x$ and time $t$ and $x$ will be a functions the position of the vehicle for every t along the road stretch. This graphical representation of $x(t)$ in a $(t,x)$ plane is a curve which is called as a trajectory. The trajectory provide an intuitive, clear, and complete summary of vehicular motion in one dimension. Figure 1: Time space diagram for a single vehicle In figure 1(a), the the distance $x$ goes on increasing with respect to the origin as time progresses. The vehicle is moving at a smooth condition along the road way. In figure 1(b), the vehicle at first moves with a smooth pace after reaching a position reverses its direction of movement. In figure 1(c), the vehicle in between becomes stationary and maintains the same position. From the figure, steeply increasing section of $x(t)$ denote a rapidly advancing vehicle and horizontal portions of $x(t)$ denote a stopped vehicle while shallow sections show a slow-moving vehicle. A straight line denotes constant speed motion and curving sections denote accelerated motion; and if the curve is concave downwards it denotes acceleration. But a curve which is convex upwards denotes deceleration.