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Rec1 2015 Ramp Metering Problem
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CEE 501 Recitation 1: Ramp Metering (A Linear Modeling Example)
Below is a stretch of the freeway consisting of a mainline (broken into 4 sections, plus an
upstream section) and 4 entry ramps and 3 exit ramps that are the main means of access to and
from the six nodes (labeled 0,1,2,3,4,5) depicted as 8-pointed banners in the figure:
Question
Determine ramp metering rates for entry ramps 1,2,3, and 4 that will maximize the total
number of vehicles served (i.e., maximize throughput in the system) while guaranteeing that
the speed along sections 1, 3 and 4 will not be less than 35 mph, and the speed along section
2 will not be less than 30 mph, during the peak hour.
Peak hour volumes to and from the various nodes are given in the table below:
Design Hour Flows (vph)
To
From
Node Totals
0 1 2 3 4 5
Node 0 N.A. N.A. 230 230 230 3,910 4,600
1 N.A. N.A. 200 40 80 480 800
2 N.A. N.A. N.A. 60 30 510 600
Entry R
amp 1
Entry R
amp 2
Entry R
amp 3
Entry R
amp 4
1 2 3
0
4
Section 1 Section 2 Section 3
Section 4
Direction of Flow5
Upstream
Section
Entry R
amp 1
Entry R
amp 2
Entry R
amp 3
Entry R
amp 4
1 2 3
0
4
Section 1 Section 2 Section 3
Section 4
Direction of Flow5
Upstream
Section
2
3 N.A. N.A. N.A. N.A. 80 720 800
4 N.A. N.A. N.A. N.A. N.A. 600 600
5 N.A. N.A. N.A. N.A. N.A. N.A. N.A.
Totals N.A. N.A. 430 330 420 6,220 7,400
N.A. = Not Applicable
Assume that the minimum practical ramp metering rate is 180 vph (i.e., metering headways
greater than 20 seconds will not be tolerated by motorists).
Question 2:
If the demand at Section 2 is reduced to 100, i.e., D2=100. Determine ramp metering rates for
entry ramps 1,2,3, and 4.
The flow-density relationships (fundamental diagrams) for each of the labeled sections are
given in the accompanying Figures.:
Section 1 Flow Density Relationship
0
1000
2000
3000
4000
5000
6000
0 50 100 150 200 250 300 350 400
Density (vpm)
Vo
lum
e (
vp
h)
3
Section 2 Flow Density Relationship
0
1000
2000
3000
4000
5000
6000
0 50 100 150 200 250 300 350 400
Density (vpm)
Vo
lum
e (
vp
h)
Section 3 Flow Density Relationship
0
1000
2000
3000
4000
5000
6000
0 50 100 150 200 250 300 350 400
Density (vpm)
Vo
lum
e (
vp
h)
4
Section 4 Flow Density Relationship
0
1000
2000
3000
4000
5000
6000
0 50 100 150 200 250 300 350 400
Density (vpm)
Vo
lum
e (
vp
h)
