Module 1 : Traffic Stream Characteristics

Lecture 02 : Fundamental Relations of Traffic Flow

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Numerical Example

The results of a speed study is given in the form of a frequency distribution table. Find the time mean speed and space mean speed.

speed range	frequency
2-5	1
6-9	4
10-13	0
14-17	7

Solution

No.	speed range	average speed ($v_i$)	volume of flow ($q_i$)	$v_iq_i$	$\frac{q_i}{v_i}$
1	2-5	3.5	1	3.5	2.29
2	6-9	7.5	4	30.0	0.54
3	10-13	11.5	0	0	0
4	14-17	15.5	7	108.5	0.45
	total		12	142	3.28

The time mean speed and space mean speed can be found out from the frequency table given below. First, the average speed is computed, which is the mean of the speed range. For example, for the first speed range, average speed, $v_i = \frac{2+5}{2}$ = 3.5 seconds. The volume of flow $q_i$ for that speed range is same as the frequency. The terms $v_i.q_i$ and $\frac{q_i}{v_i}$ are also tabulated, and their summations given in the last row. Time mean speed can be computed as, $v_t = \frac{\Sigma{q_iv_i}}{\Sigma q_i} = \frac{142}{12} = 11.83.$ Similarly, space mean speed can be computed as, $v_s = \frac{\Sigma{q_i}}{\Sigma{\frac{q_i}{v_i}}} = \frac{12}{3.28} = 3.65.$