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CIVL 262 C Introduction to Transportation System

Tutorial Quiz 3 27 Feb2009

Name : Student ID :
General flow models

QUESTION 1

For simplicity one proposes a double linear relationship with an optimal flow rate between flow rate and density of traffic on Freeway 261. Based on past observation data, the q-k relationship is shown in the following figure.

A 3m-long weight sensitive loop detector is installed to measure flow on Freeway 261, which can distinguish up to 3 vehicle types. The observation of the detector on at clock hour 10:00a.m. to 11:00a.m. on Feb 1, 2001 is listed in the table.

Type
Vehicle
Average vehicle length (m)
Average coverage time over the loop (sec)
Vehicle Composition by volume (%)

1
Private car
6
0.600
30

2
Coach/Bus
10
1.300
30

3
Container Trailer
12
1.125
40




Find the density of that observation hour on Freeway 261.

Solution:
Part 1 Speed Mean Speed vs
From the table, the average vehicle speeds are:
Type 1:

Type 2:

Type 3:

Thus the space mean speed =


Part 2 Density k
In next step, the density is calculated from the known value of vs. Two methods are illustrated.

Method 1
From the figure, the q-k relationship is:

,
Using the fundamental relationship we get

.

Hence, the v-k diagram is
Thus, when the speed is 45 km/hr, the density of the traffic is 31.25 veh/km.

Method 2
Recall that a straight line passing through and in q-k graph has a slope of vs. Thus, by constructing a line with a slope v from origin and finding out the intersection, i.e. solving gives .





125

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