Module 4 : Macroscopic And Mesoscopic Traffic Flow Modeling

Lecture 19 : Traffic Progression Models

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Numerical Example 2

In a case study, the average travel time from the upstream point to 1st downward point (point in between upstream and downstream) was found out to be 22.8 seconds and from upstream point to downward point (end point) was found out to be 32.8 seconds , standard deviation is 5.951 and model time step duration is 10 sec. Find out the Robertson's model parameters and also the flow at downstream at different time steps where the upstream flows are as given below. $q_{10~sec} = 20, q_{20~sec} = 10, q_{30~sec} = 15, q_{40~sec} = 18, q_{50~sec} = 14, q_{60~sec} = 12$.

Solution

This problem is similar to the earlier problem. Only there are 2 downstream points given in this. For the first downstream point, upstream values of flow given in the problem will be used, whereas for the $2_{nd}$ downstream point, the flow from the $1_{st}$ downstream point is to be used. Hence at $1_{st}$ downstream point, flow in the first interval is zero and at the $2_nd$ downstream value, flow is zero for first 2 intervals. The calculations have been done in excel and the following shows the results.

Upstream Vol. for (in sec.)	No. of Vehicles
10	20
20	10
30	15
40	18
50	14
60	12
	0
	0
	0
	0
	89

Smoothing Factor F	0.783
Lag Time(For In Between Point)	20 sec
Lag Time(For End Point)	30 sec

Downstream Volume		Downstream Volume
At in between Point		At End Point
(in seconds)		(in seconds)
10	0	10	0.00
20	15.66	20	0.00
30	11.23	30	12.26
40	14.18	40	11.45
50	17.17	50	13.59
60	14.69	60	16.39
70	12.58	70	15.06
80	2.73	80	13.12
90	0.59	90	4.99
100	0.13	100	1.55
	0.00	110	0.44
	88.96	120	0.09
			88.84

Four graphs are plotted below. The first graph shows the upstream profile, the second shows the downstream profile at in between point, the third shows the downstream profile at the end point. The last graph shows the comparison of all the three.