DSES-6620 Simulation Modeling Analysis
Ernesto Gutierrez-Miravete
Final Project:
Traffic Light Hold-Ups
An Adventure Down the Berlin Turnpike
Submitted by:
Jim Henriques
December 2000
ABSTRACT
The Berlin Turnpike consists of many traffic lights. Every morning people drive down it
and have to stop at these traffic lights. A selected portion of the Berlin Turnpike is
modeled in the simulation software package ProModel. Tests were performed in an
attempt to find the speed that will result in the least amount of waiting time at red lights.
Along with the overall time it takes to go through the system will help determine the
optimal speed to travel during the morning commute on the Berlin Turnpike.
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TABLE OF CONTENTS
An Adventure Down the Berlin Turnpike .......................................................................... 1
1. Introduction ................................................................................................................. 4
1.1 Objective ................................................................................................................. 4
1.2 Scope ....................................................................................................................... 5
1.3 Requirements .......................................................................................................... 5
2. Implementation ........................................................................................................... 5
2.1 Data Collection ....................................................................................................... 6
2.1.1 Distance Collection ......................................................................................... 6
2.1.2 Traffic Light Data Collection.......................................................................... 6
2.2 Model Design .......................................................................................................... 7
2.2.1 Locations ......................................................................................................... 7
2.2.2 Entities ............................................................................................................ 7
2.2.3 Processing ....................................................................................................... 8
2.2.4 Arrivals ........................................................................................................... 8
2.3 Integration ............................................................................................................... 8
2.3.1 Assumptions.................................................................................................... 9
2.4 Testing the System .................................................................................................. 9
2.4.1 Test 1 ............................................................................................................... 9
2.4.2 Test 2 ............................................................................................................. 10
3. Results ....................................................................................................................... 10
3.1 Results: Test 1 ....................................................................................................... 11
3.2 Results: Test 2 ....................................................................................................... 11
3.3 Verification ........................................................................................................... 11
3.4 Validation .............................................................................................................. 12
4. Conclusion ................................................................................................................ 12
5. Appendix A: Distances Between Traffic Lights ....................................................... 14
6. AppenDix B: Traffic Light Times ............................................................................ 15
7. Appendix C: Test 1 Results ...................................................................................... 16
8. Appendix D: Test 2 Results ...................................................................................... 18
9. Appendix E: Sample Output and Trace file of System, Test 2 ................................. 19
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1.
INTRODUCTION
Every morning countless people drive down the Berlin Turnpike in order to get to school,
work, or just to run errands. These people all drive at different speeds, speeds that they
are comfortable with. Some people are not in a hurry and drive at a slower pace while
others wish to think that they are participating at the Indianapolis 500 and drive as fast as
they possibly can. The one equalizing factor between these drivers is that they must obey
traffic lights. Very often it seems that no matter what the speed of the driver is, two
travelers going different speeds, through the timing of the traffic lights, end up at the
same destination at relatively the same time. The Berlin Turnpike has been modeled to
simulate the morning commuter traffic light patters to help gain insight into the optimal
constant speed on should drive to get to their destination as safely and effectively as
possible. This includes the time it takes to get there versus the amount of time one is
waiting at a red light.
1.1
Objective
The goal of this system is to determine the optimal speed to travel down the Berlin
Turnpike during the morning rush hour commute. This includes taking into consideration
how much time a commuter is actually waiting at a traffic light, and monitoring the
percentage of time the vehicle is moving over the entire travel time. The optimal speed
will be decided by the amount of time a vehicle is moving versus the amount of time it is
stopped at a light. This will be correlated to the overall time of the commute.
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1.2
Scope
A portion of the Berlin Turnpike will be modeled in this system. The starting point to this
system will be one mile away from the Turnpike. After this first mile, the Berlin
Turnpike will be used for the commute. The portion of the Berlin Turnpike to be modeled
will be from the first light in Berlin northward to the end of the Berlin Turnpike, where
route 15 begins. It will consist in all of 27 traffic lights.
1.3
Requirements
In order to portray an accurate representation of the Berlin Turnpike some pieces of
information would be needed. The distances between each light would be necessary in
order to model it correctly. The other main requirement is learning how the traffic lights
work. Determining how long each traffic light on the Berlin Turnpike stays green, red
and yellow. Also a working knowledge of a software package to simulate this system is
necessary. In this case, the software package that will be used is ProModel 4.22.
2.
IMPLEMENTATION
In order to accomplish this system a plan needed to be developed. The plan identified
what would be needed to fulfill the requirements. Once each step was identified, they
were prioritized. The steps included collecting all pertinent data, developing a computer
model, integrate the data collected into the system and then analyze the data from the
model.
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2.1
Data Collection
There were two main pieces of data collection require for this system. The first was the
distance between each traffic light and the second was the cycles of the traffic lights
during rush hour.
2.1.1 Distance Collection
The distances between the lights were recorded while driving down the Turnpike. Using
a car odometer, the distances after going under each light were recorded. These distances
are listed in Appendix A.
2.1.2 Traffic Light Data Collection
The traffic lights cycles were obtained from the Connecticut Department of
Transportation (DOT). Each light had its own blueprint and listed out how long they were
green during the rush hour commute. With these blueprints it was determined how much
time it was green, red and yellow on each side of the intersection. An employee at the
DOT gave information on how to read them correctly. Each light has a different cycle
depending on the time of day. Since this simulation was for a morning commute, the
morning cycle was used (6:00 am – 9:00 am). That cycle then gives a number of how
many seconds the light is green and the percentage of the time. There was also a section
that showed how long it was yellow, and how long all of the lights were all red at the
same time. In most cases the lights were yellow for 5 seconds, and the lights would all be
red during the transitions for a period of 2 seconds. Although sometimes this data varied
those are the average figures. All of the competing sides of the lights green times and the
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2-second transition period were added up to give a total wait time at each light. This data
would later be used as the downtime of the lights in the model. This data can be found in
Appendix B.
2.2
Model Design
Before using the data recorded a design of the system needed to be defined. Using
ProModel test systems were developed. Once the concept was proven, integrating the
recorded data to the system would be possible.
2.2.1 Locations
It was decided that each traffic light would have to be a location as well as the stretch of
road between each traffic light. This was done since a location is allowed to have a
downtime. Each light would be given a downtime according to the amount of time it was
scheduled to be red. The stretches between the lights were queues. This was done since
they could be given a distance, and the speed was determined by the entity. A conveyor
was also an option, but they have their own speed and the volume of them would make it
difficult to test different speeds quickly.
2.2.2 Entities
The only entity in this system was the vehicle that travels the system. A speed could be
associated with the vehicle, which made it easy to change the speeds for testing optimal
speeds.
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2.2.3 Processing
The processing was fairly simple in concept but tedious in implementing. The entity of
the vehicle was to move from one location to the next in succession. It would go from
Light_1 to Queue_1 and from Queue_1 to Light_2, and so on throughout the whole
system.
2.2.4 Arrivals
To test different times of the system a delay for arriving to the first location was used.
Since the traffic lights cycles started at 6:00, a delay could be added to simulate someone
driving through at any time. For instance by having a “First Time” of 90 minutes, it
would simulate a ride down the Turnpike at 7:30.
2.3
Integration
After the test system was developed with only two traffic lights and made up downtimes
the real system could be created. Due to the high amount of locations, the Student
Version of ProModel could not be used. Instead the Professional version was used. First
the queues were created and given the correct attributes according to the data recorded for
the distances between each light. The next part was to decipher the blueprints from the
DOT. Each light location was then given a downtime of the calculated wait times from
the collected data. A frequency was then set for how often it should be down. This time
was the total green time plus the wait time. Once each light was finished the system was
run.
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2.3.1 Assumptions
The assumptions made this is model were as follows:
 No other cars present on the road
 Braking and acceleration times could be averaged in constant speed
 Distance under traffic light were negligible
 Traffic light patterns occur as accurately as designed in blueprint
 Car can maintain a constant speed
 All speeds used are safe and within reason
 No traffic violations such as speeding or running a yellow light
 Yellow lights would be run up to one second before they turned red.
2.4
Testing the System
With the system completed with all of the data collected a few different tests were run.
The first test was to try different times of the morning. The second test was sending a
vehicle through the system every minute for a two hour period, essentially between 6:008:00 am. Several different speeds were used, ranging from 35 mph, up to 70 mph, in
different intervals.
2.4.1 Test 1
The first test used for different start times, 6:00, 6:30, 7:00 and 7:30 in the morning. Each
time was used with twelve different speeds. The output of the system gave a total time of
the vehicle in the system and the percentage that it was moving, and the percentage it was
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stopped at a light. The table below shows a portion of the output. The full results can be
found in Appendix C
Time of Day
6:00
6:30
7:00
7:30
Fastest Time
70 mph (17.17 minutes/ 76.17%)
70 mph (20.31 minutes/ 64.41%)
70 mph (17.32 minutes/ 75.52%)
70 mph (17.27 minutes/ 75.73%
Best Utilization
60 mph (17.25 minutes/ 84.36%)
35 mph (25.61 minutes/ 85.39%)
35 mph (25.65 minutes/ 85.28%)
35 mph (25.68 minutes/ 85.17%)
Table 1. Best of Test 1 (minutes/utilization)
2.4.2 Test 2
The second test took an average of the morning rush hour commute. A vehicle was
inserted into the system every minute over a two-hour time period. At the end of the
simulation the average time and utilization was taken. Again, the same speeds were used
as in the first test. As shown in Table 1, again, the fastest speed of 70 mph resulted in the
fastest time, and the slowest speed, 35 mph, resulted in the best utilization. The full resul
ts can be found in Appendix D.
3.
RESULTS
The results of the two tests show similar results. It appears that the faster one travels, the
quicker one gets to the destination. However the utilization went down at the quickest
time. The task then became finding the best utilization that correlate with the best speed.
In many cases, the difference in time between 70 mph and 60 mph was only a few
seconds, while the utilization difference was over 8% in favor of going the slower speed.
Since the best utilization was normally 35 mph, it took ultimately too long to travel, so it
was ruled out as optimal speed. At the other end of the spectrum, normally the utilization
was not that great at the fastest speed, but some of the slower speeds only took a few
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seconds less and their utilization’s were a few points higher and therefore they were
selected to be the optimal speeds.
3.1
Results: Test 1
Table 2 below shows the best speed and utilization for the four times selected in Test 1.
Time of Day
6:00
6:30
7:00
7:30
Speed
60 mph
60 mph
65 mph
63 mph
Time in System
17.25
20.31
17.35
17.32
Utilization
84.36%
71.63%
79.3%
81.16%
Table 2. Optimal Speeds From Test 1
From this data it appears that leaving at 6:00 in the morning and driving a constant speed
of 60 mph would be the most effective. A sample output file for this system can be found
in Appendix E.
3.2
Results: Test 2
The results for Test 2 show the average time in the system a vehicle going a constant
speed would go. At any time during the rush hour commute it appears that going a
constant speed of 63 mph would deliver the best speed and utilization combination of
18.95 minutes and 75.02% utilization.
3.3
Verification
The system went through two verification periods. The first was during the initial design
of the system. Once the test version performed as expected it was expanded into the final
system. Once the final system was finished many test were run. A few minor defects
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were found and quickly corrected. The system was setup to watch a car stop at a light
with a known stop time. The car ran to the light and stopped for the appropriate amount
of time and then continued. Since the system was of a basic setup repeated over and over
again, since the small test worked, it is assumed the rest of the system will fall into place
as the small test did. After watching the complete system run this was proven true.
3.4
Validation
These number correspond fairly well with the actual amount of driving time it normally
takes on this particular part of the Berlin Turnpike during the rush hour commute.
Unfortunately it is not possible to perform this test in an actual car at the conditions as in
the model. It has been attempted to go a constant speed but other traffic often is in the
way thus ruining the experiment. Although it does seem like the system is producing
logical travel times.
4.
CONCLUSION
The Berlin Turnpike was modeled well. It can be quickly calculated at any given point in
the morning commute how fast one should drive for the optimal results. Unfortunately,
there is some disappointment in the results that were gathered. It seemed that the faster
one drove the quicker one got to their destination, regardless of the utilization. It was
hoped that perhaps it could be proved that going slower could still take less time than
going faster. While often it only a few seconds or a minute difference, it was always less
time to go faster. Of course more can be looked into just the utilization of the system. For
example over a long period of time a worse utilization may require a driver to use more
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gas, and have more maintenance done to one’s car. If the cost of driving a car could be
linked to the utilization number this experiment may still prove going slower
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5.
APPENDIX A: DISTANCES BETWEEN TRAFFIC LIGHTS
Feet
5280
2640
4224
1056
792
2904
3696
2640
3168
1056
3168
1320
1848
1320
792
2112
528
2112
1320
792
1056
24.571
1848
264
5808
528
2112
Miles
1.00
0.50
0.80
0.20
0.15
0.55
0.70
0.50
0.60
0.20
0.60
0.25
0.35
0.25
0.15
0.40
0.10
0.40
0.25
0.15
0.20
0.00
0.35
0.05
1.10
0.10
0.40
Accumlated Miles
0.00
1.50
2.30
2.50
2.65
3.20
3.90
4.40
5.00
5.20
5.80
6.05
6.40
6.65
6.80
7.20
7.30
7.70
7.95
8.10
8.30
8.30
8.65
8.70
9.80
9.90
10.30
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6.
APPENDIX B: TRAFFIC LIGHT TIMES
LightTotal
# Cycle Time (SEC)
Downtime (SEC) Uptime (SEC)
1
92
72
20
2
82
39
43
3
92
46
46
4
92
42
50
5
80
38
42
6
92
40
52
7
92
45
47
8
91
45
46
9
92
44
48
10
92
41
51
11
120
73
47
12
118
61
57
13
97
52
45
14
97
40
57
15
80
37
43
16
82
18
64
17
100
57
43
18
77
23
54
19
100
58
42
20
92
23
69
21
133.5
39.5
94
22
101
47
54
23
98
55
43
24
106
51
55
25
106
51
55
26
104
43
61
27
106
51
55
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7.
APPENDIX C: TEST 1 RESULTS
Time:
6:00
MPH
Total Time
Total Time (Minutes) % Moving % Stopped
35
27.35
79.98
20.02
40
24.57
80.11
19.89
45
22.72
79.11
20.89
50
22.65
73.3
26.7
53
20.85
76.28
23.72
55
19.06
81.22
18.78
57
19.04
79.24
20.76
60
17.25
84.36
15.64
63
17.23
81.63
18.37
65
17.21
79.95
20.05
67
17.20
78.37
21.63
70
17.18
76.17
23.83
Time
6:30
MPH
35
40
45
50
53
55
57
60
63
65
67
70
Total Time (Minutes) % Moving % Stopped
25.62
85.39
14.61
25.62
76.82
23.18
25.62
70.15
29.85
23.85
69.61
30.39
23.85
66.68
33.32
23.85
64.92
35.08
23.85
63.27
36.73
20.32
71.63
28.37
20.32
69.21
30.79
20.32
67.73
32.27
20.32
66.34
33.66
20.32
64.41
35.59
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Time
Time
7:00
MPH
35
40
45
50
53
55
57
60
63
65
67
70
7:30
MPH
35
40
45
50
53
55
57
60
63
65
67
70
Total Time (Minutes)
25.65
24.63
24.55
22.72
22.67
22.66
22.64
19.12
19.10
17.35
17.34
17.33
Total Time (Minutes)
25.68
24.67
22.82
22.75
20.95
20.93
20.91
20.88
17.33
17.31
17.30
17.28
% Moving
85.28
79.89
73.2
73.09
70.12
68.32
66.64
76.12
73.63
79.3
77.72
75.52
% Moving
85.17
79.78
78.76
72.98
75.92
73.98
72.17
69.68
81.16
79.49
77.92
75.73
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% Stopped
14.72
20.11
26.8
26.91
29.88
31.68
33.36
23.88
26.37
20.7
22.28
24.48
% Stopped
14.83
20.22
21.24
27.02
24.08
26.02
27.83
30.32
18.84
20.51
22.08
24.27
8.
APPENDIX D: TEST 2 RESULTS
Average Time Throughout 2-hour Period
Speed
Time (sec)
Time (min) Moving %
35
26.82
73.68
40
25.18
81.96
45
24.16
78.55
50
22.34
74.82
53
21.21
74.9
55
20.44
75.57
57
20.08
76.39
60
19.57
75.78
63
18.96
75.02
65
18.72
74.79
67
18.51
74.1
70
17.95
73.5
Stopped %
26.32
18.04
21.45
25.18
25.1
24.43
23.61
24.22
24.98
25.21
25.9
26.5
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9.
APPENDIX E: SAMPLE OUTPUT AND TRACE FILE OF SYSTEM, TEST 2
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