Christina Clark & Jingkang Gao
ORF 467 Fall 2012
MyCity Final Report
The City of Pension Heaven: Land Use Characteristics
Character of Pension Heaven
Pension Heaven, a retirement utopia, is a self-sustaining city of population 250,000. The city sits on a
square plot of land of size 102.4 square miles, and it is divided into 75 rectangular zones (TAZs) of
various sizes, 10 of which are undeveloped (open space and lakes) and 65 are developed.
An unzoned river runs diagonally through the city. There are four zones for lakes; the largest lake
occupies 2.5 square miles and the other three lakes are 0.6 square miles in size. Each of the small lakes
borders an open space zone. The total area of water (river and lakes) is 14.2 square miles. The city also
contains 14 square miles of open space, most of which border the edges of the city. Thus nearly 30% of
the city is undeveloped.
Residential areas occupy about a third of the city and they are classified as light residential (~9%),
medium residential (~17%), and heavy residential (~9%).
Six zones allocated for education include one research university that does not provide housing to
students, two K-8 school districts, two high school districts, and one private day school. The university is
located between a strip of open land and the largest lake, which are utilized for university athletic
events. Each school district borders at least one residential zone.
There is an airport along the northern border of Pension Heaven. The net population flow for the airport
is zero. The airport occupies 4.8 square miles, which is based on a city of comparable size, St. Paul, MN,
which has population 290,000 and an airport of size 5.3 square miles.
One large park sized 1.4 square miles (comparable to Central Park, 1.3 square miles) borders a lake near
the center of the city. A much smaller park is located in the middle of a residential district in the eastern
part of the city.
A football stadium (capacity 100,000) and soccer stadium complex (capacity 100,000)—the complex
includes the stadiums and surrounding entertainment and retail as well as parking—is located along the
western edge of the city next to the large lake. A baseball stadium (capacity 40,000) and
basketball/hockey arena (capacity 20,000) complex (including surrounding parking and retail) is located
on the northeastern corner of the city. These sports complexes would be excessive for a normal
American city of 250,000 but appropriate for a retirement city where the elderly have the time and
financial means to attend sporting events almost daily.
The center of the city consists of a town hall zone—which includes the town hall and other government
office buildings—as well as a large retail zone, professional office zone, and light commercial zone. Our
public buildings include other types of government office buildings, police stations, and fire stations.
Most industrial zones (total area of about 5 square miles) are located along the river or in the outskirts
of the city. Industrial zones include not only factories and plants but also hospitals.
Land Use Map
1
2
3
4
5
6
2
8
9
10
11
12
13
14
15
16
37
17
18
19
20
21
22
23
24
25
26
27
28
29
41
5
39
7
40
6
7
8
74
9
42
43
44
10
11
12
11
13
45
12
46
13
47
14
16
14
48
15
zone cnt
river
0
lake
4
open space
6
light industrial
3
heavy industrial
2
light commercial
2
medium commercial
1
heavy commercial
1
9
10
49
50
17
15
18
19
20
light residential
15
medium residential
16
heavy residential
6
Recreation
2
stadium/arena
2
Public Buildings
1
Town Hall
1
Education
6
Retail
2
Restaurant
2
Professional Office
2
airport
1
51
16
52
17
21
18
22
53
19
54
20
23
55
56
21
24
25
57
22
26
27
28
29
30
23
58
24
31
59
25
60
32
61
63
27
62
64
34
65
67
75
30
68
70
71
72
33
35
66
29
32
Legend
73
8
31
32
4
6
28
31
38
5
26
30
2
3
3
4
7
1
1
69
36
Residential Zones
37
TOTAL ZONES
75
Zone Information
Zone # Area (sq mi) Land Use
TOTAL
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
75
0.9
4.8
1.6
2.5
0.6
4.2
2.1
0.8
2.1
1.4
0.4
0.9
0.6
0.2
0.6
0.6
1.2
0.6
1.2
0.8
2.1
1.8
0.6
1.5
1.6
0.3
0.3
0.3
0.3
0.3
0.5
0.8
0.6
0.3
0.6
2.1
0.1
0.4
0.4
0.1
0.6
0.6
2.4
1.6
0.3
0.6
1.5
2.5
1.5
1.0
0.9
2.0
1.2
3.0
1.5
1.8
1.6
2.8
1.0
1.6
1.2
0.8
0.6
1.4
0.5
0.8
0.8
1.6
1.2
3.2
0.8
0.9
0.6
4.2
0.8
9.9
102.4
light residential
airport
light residential
stadium/arena
light industrial
open space
medium commercial
light residential
open space
Recreation
medium residential
Restaurant
lake
light residential
light residential
medium residential
heavy commercial
medium residential
heavy residential
Education - High School
heavy residential
open space
lake
heavy industrial
medium residential
medium residential
medium residential
Recreation
medium residential
medium residential
light residential
Professional Office
light residential
light residential
light residential
open space
light residential
light residential
heavy industrial
light residential
open space
light residential
medium residential
heavy residential
medium residential
Town Hall
Professional Office
lake
medium residential
heavy residential
light commercial
Retail
Education - High School
stadium/arena
heavy residential
heavy residential
medium residential
medium residential
medium residential
medium residential
Restaurant
Public Buildings
lake
light industrial
light commercial
Retail
Education - Elementary School
medium residential
light industrial
open space
light residential
light residential
Education - Elementary School
Education - University
Education - Boarding/Day School
river
% of Land x‐coord y‐coord
0.88%
4.69%
1.56%
2.44%
0.59%
4.10%
2.05%
0.78%
2.05%
1.37%
0.39%
0.88%
0.59%
0.20%
0.59%
0.59%
1.17%
0.59%
1.17%
0.78%
2.05%
1.76%
0.59%
1.46%
1.56%
0.29%
0.29%
0.29%
0.29%
0.29%
0.49%
0.78%
0.59%
0.29%
0.59%
2.05%
0.10%
0.39%
0.39%
0.10%
0.59%
0.59%
2.34%
1.56%
0.29%
0.59%
1.46%
2.44%
1.46%
0.98%
0.88%
1.95%
1.17%
2.93%
1.46%
1.76%
1.56%
2.73%
0.98%
1.56%
1.17%
0.78%
0.59%
1.37%
0.49%
0.78%
0.78%
1.56%
1.17%
3.13%
0.78%
0.88%
0.59%
4.10%
0.78%
9.67%
100.00%
7
19
7
30
10
20
24
28
31
20
26
22
28
28
31
24
25
27
22
28
24
31
28
21
26
30
28
30
32
30
28
29
31
26
29
29
1
2
8
8
3
7
11
15
9
12
15
3
7
10
12
16
11
4
8
15
11
6
12
2
16
20
6
11
21
3
16
19
22
9
3
19
27
3
6
1
2
3
3
5
5
8
8
9
10
10
11
11
13
13
14
14
14
15
15
18
18
19
21
21
21
22
22
22
23
24
25
25
26
27
29
2
4
6
7
5
10
10
10
12
13
13
15
15
15
16
17
19
20
20
21
22
24
25
26
26
26
27
27
27
28
29
29
29
30
31
32
5
9
30
Summary Tables of Land Use
Color Key Land Use
water
open space
light industrial
heavy industrial
light commercial
medium commercial
heavy commercial
light residential
medium residential
heavy residential
Recreation
stadium/arena
Public Buildings
Town Hall
Education
Retail
Restaurant
Professional Office
airport
TOTALS
% of Land
Grid Count Area (sq. miles)
13.87%
14.2
142
13.67%
14
140
3.13%
3.2
32
1.86%
1.9
19
1.37%
1.4
14
2.05%
2.1
21
1.17%
1.2
12
8.79%
9
90
16.80%
17.2
172
8.98%
9.2
92
1.66%
1.7
17
5.37%
5.5
55
0.78%
0.8
8
0.59%
0.6
6
8.20%
8.4
84
2.73%
2.8
28
2.05%
2.1
21
2.25%
2.3
23
4.69%
4.8
48
100%
102.4
74.2
28.2
Developed
Undeveloped
Residential Zones
Light Residential
Medium Residential
Heavy Residential
Density
4456
6400
10850
TOTAL
Employment Zones
light industrial
heavy industrial
light commercial
medium commercial
heavy commercial
Restaurants
Retail
Town Hall
Airport
Education
Professional Office
Public Buildings
Stadium/Arena
Recreation
TOTAL
Residents
40100
110080
99820
250,000
Density
8500
20000
3000
9000
15000
300
300
200
300
400
3000
200
400
100
Employees
27200
38000
4200
18900
18000
630
840
120
1440
3360
6900
160
2200
170
122120
72.46%
27.54%
School Zones - Student Breakdown
Elementary (K-8) School District 1
Elementary (K-8) School District 2
High School 1 District 1
High School 2 District 2
Private Day School
University
TOTAL STUDENTS
Uniform density factor**
**factor used in P vector of HBS
5427
4784
2598
2743
2310
9273
27135
0.10854
Demographics and Quality of Life
As previously stated, Pension Heaven is a retirement city. A very large portion of the population consists
of retirees (we define retires as people age 65 or older), and the working population (we define working
population as age 22-65) is much older than the average working population in the United States. Our
workers bear children at the same rate as the American population as a whole but since they are older
most children no longer live with their parents. Thus the under-18-population ratio (11% of Pension
Heaven population) is much lower than that of the entire American population (about 30%); and the
over-65-population ratio (32%) is much larger than that of the entire American population (13%), hence
the city is named Pension Heaven. 52% of the population in Pension Heaven is female. Pension Heaven
attracts the elderly because of the small children population in that local taxes for education are very
low compared to other cities.
The population break down and age breakdown correspond as the following. Children population is the
same as the under 5 population. Student population consists of the 5-18 population (all 5-18 people
attend school) and 9273 university students. Workers include the 18-65 population minus the 9273
university student population and the 9616 unemployed population. *We define our unemployed
population not as people seeking work but cannot find work, but as anyone between 18 and 65 who is
not working. Thus our unemployment rate cannot be compared to the usual unemployment rates of
other cities; it would be much lower (very close to zero) if we defined unemployment as those seeking
work but cannot find it.
Workers in Pension Heaven work exclusively in Pension Heaven, and students attending all schools
reside in Pension Heaven. Residential density varies from 4,456 per square mile in light residential zones
(suburban-like areas) to 10,850 per square mile in heavy residential zones. In Pension Heaven there are
no workers in any residential zone.
The population per household number is consistent with that of the 2010 U.S. census. Pension Heaven
has 97,018 households; on average each household has 2.58 people. Although Pension Heaven is not
similar to the U.S. population in age distribution, the larger number of retirees (who are more likely to
be married, thus increasing number of people per household) offsets the small number of children per
household. The median household income is $100,000, significant higher than the U.S. median
household income of $52,000 in 2010 and provides a large consumer base for the stadiums and arenas.
The industrial and commercial areas, restaurants, stadiums and arenas, recreation, retail, and airport
zones serve all shopping, dining, and recreation needs of residents of Pension Heaven.
Population Breakdown
Children
Students
Workers
*Unemployed
Elderly
TOTAL
# OF WORKERS
Uniform density factor*
*factor used in P vector of HBW
People
10745
27135
122120
9616
80384
250000
122120
0.48848
Population Percentages by Age
age range
0-18
18-22
23-65
65+
total
US Census Data
total household (hh) pop
# of hh
avg hh pop
Pension H's # of hh
%
11.4%
3.71%
52.69%
32.15%
100.00%
#
28,607
9,273
131,736
80,384
250,000
300,758,215
116,716,292
2.58
97,018
Demand for Transportation: Trip Generation
Generating the Production and Attraction Vectors1
Home-Based Work (HBW) P&A Vectors
Production: this vector equals the corresponding zone’s residential population multiplied by the uniform
distribution constant (since an assumption we must make is that the home-to-work departures are
uniform across all zones). This constant was calculated by dividing the total number of workers by the
total population.
Attraction: this vector must equal the number of workers in each corresponding zone.
Work-Based Home (WBH) P&A Vectors
Production: because 80% of workers go home after work, this vector equals 0.8 multiplied by the total
number of workers in each corresponding zone.
Attraction: this vector therefore must equal 80% of workers that came from the residential zones. In
other words, this equals 0.8 multiplied by the HBW production vector.
Home-Based School (HBS) P&A Vectors
Production: just as we calculated the HBW production vector, this HBS production vector also is
uniformly distributed across the residential zones. Therefore, it equals each zone’s residential
population multiplied by this uniform distribution constant. The constant was calculated by dividing the
total number of students by the total population.
Attraction: this attraction vector equals the set number of students in each school zone, as dictated in
our Student Breakdown.
School-Based Home (SBH) P&A Vectors
Production: similar to the working population, 80% of the school populations go directly home.
Therefore, this production vector equals 0.8 multiplied by the school population (represented by the
attraction vector of HBS).
Attraction: also similar to the working population, this attraction vector must equal 80% of students that
originated from each residential zone. In other words, this vector equals 0.8 multiplied by the HBS
production vector.
Home-Based Other (HBO) P&A Vectors
Production: in Pension Heaven, 59.7% of residents go to school or work in the morning. When
calculating this HBO production vector we took into account two categories of persons making this trip;
we accounted for the remaining 40.3% who do not go to school or work, but also the workers and
students who return home then go back out to an "other" zone. Therefore, we decided that 85% of the
residential population was a reasonable estimate for this production vector.
Attraction: we determined this vector at our own discretion. These attraction values are estimates
based on each type of “other” zone.
1
see hyperlinks to Appendix for the Production and Attraction Vectors
Other-Based Home (OBH) P&A Vectors
Production: people must eventually return home after any number of trips to “other” zone(s).
Therefore, this production vector equals the sum of the HBO, SBO and WBO attraction vectors.
Attraction: the attraction vector here represents the people going home from “other” zones. It must
equal the number of people who left from home to "other" (the production vector of HBO) plus the
remaining 20% of people coming from work or school that didn't go directly home (0.2 times the HBW
production vector plus 0.2 times the HBS production vector).
School-Based Other (SBO) P&A Vectors
Production: this production vector accounts for the remaining 20% of students that did not go straight
home after school. Therefore, it equals 0.2 multiplied by the attraction vector of HBS (which as said
above, equals the number of students enrolled in each school).
Attraction: as dictated by the Gravity Model, this attraction vector must equal the production vector.
For consistency, this vector follows the same relative attractiveness among the "other" zones which was
estimated in the HBO attraction vector. So, a constant was determined to follow both these constraints
(found to equal .0255). Therefore this SBO attraction vector equals .0255 multiplied by the HBO
attraction vector.
Work-Based Other (WBO) P&A Vectors
Production: similar to SBO above, this production vector accounts for the remaining 20% of workers that
did not go straight home after work. Therefore, it equals 0.2 multiplied by the total number of workers
in each zone.
Attraction: again dictated by constraints of the Gravity Model and our estimated relative attractiveness
of each “other” zone, a constant was determined for this attraction vector (found to equal to 0.2).
Therefore, this WBO attraction vector equals 0.2 multiplied by the HBO attraction vector.
Other-Based Other (OBO) P&A Vectors
Production: logically, this OBO production vector must equal the OBO attraction vector for an equal flow
in and out of each “other” zone – else, there would be a net number of people remaining in a zone
which would compound over time (which is obviously impossible).
Attraction: this vector was also determined mostly by our discretion. Because all people must return
home eventually, we calculated this attraction vector by multiplying the OBH attraction vector by a
constant. In order to hold the constraint that there should be 1M trips per day (~4 per person), we chose
our constant to be 1.02. In practical terms, this means that on average every person who traveled an
"other" zone made 1.02 other-to-other trips. In other words, most people traveling to an "other" zone
from any origin will go to 2, sometimes 3 "other" zones.
Brief Summary of Each of the Trip Type-Purposes
HB-work trips directly connect residential zones and work zones. Work zones include light industrial,
heavy industrial, light commercial, medium commercial, heavy commercial, restaurants, retail, town
hall, airport, education, professional office, public buildings, stadium/arena, and recreation zones. All
122,120 workers who hold jobs make one daily trip in the morning to work. The average trip length is
3.51 miles.
HB-school trips directly connect residential zones to education zones. Since the university in Pension
Heaven does not offer housing to its students, all university students travel from residential zones to
school. All 27,135 students make one daily trip to school in the morning. The average trip length to
school is 4.11 miles.
HB-other trips directly connect residential zones to shopping, dining, and recreation areas. These zones
include stadiums/arenas, commercial zones, recreation, restaurants, and lakes. There were 212,500
trips made from home to SDR. These trips were made by the 80384 elderly, 9616 people not going to
work, and some of the workers and students who return home and then go shopping. The average trip
length to S/D/R zones is 4.49 miles.
Other-other trips shopping, dining, and recreation zones to each other. There are 246,639 daily such
trips. Of all trips made to S/D/R areas, 212,500 (directly from home) + 24,434 (home to work to S/D/R) +
5,427 (home to school to S/D/R) = 242,351 trips come from home at some point. This equals the total
number of other-HB trips (thus everyone who leaves home goes home) and roughly equals the 246,639
trips made from one S/D/R zone to another, which means every person who traveled to an S/D/R zone
made about one trip to another S/D/R zone. Unlike the above trip-types, we had to discount intrazonal
trips inside Other zones. To do so, we multiplied the diagonals of our D (distance) matrix by a factor of
100. Note that as a result, we had some trips longer than 15 miles – which is the upperbound of all our
other trips – but in later analysis below, it is evident that the number of trips over 15 miles is
insignificant compared to the number of trip lengths between 0 and 15 miles. The average other-other
trip length is 2.96 miles.
Demand for Transportation: Trip Distribution
Overview of Trip Array Generation2
The trip distribution for Pension City is based on the Gravity Model. This model is in fact similar to
Newton’s theory of gravity; it assumes that trips produced at an origin and attracted to a destination are
directly proportional to the total trip productions at the origin and the total attractions at the
destination. The calibrating term—in our case, the “friction factor” (F) – represents the reluctance or
impedance of persons to make trips of various duration or distances. The general friction factor
indicates that as travel times increase, travelers are increasingly less likely to make trips of such lengths.
Calibration of the gravity model involves adjusting the friction factor. The other adjustment factor
associated with the Gravity Model is the socioeconomic adjustment factor (K), but in our case we have
this factor equal to 1 and therefore has no impact.
A crucial consideration in following the Gravity Model is the “balancing” production and attraction
vectors. This means that the sum of the productions must equal the sum of the attractions for each triptype. In the trip distribution for Pension Heaven, the Gravity Model is as follows:
𝑇𝑖𝑗 =
𝐴𝑗 𝐹𝑖𝑗 𝐾𝑖𝑗
𝑥𝑃
∑𝑎𝑙𝑙 𝑧𝑜𝑛𝑒𝑠 𝐴𝑥 𝐹𝑖𝑗 𝐾𝑖𝑥 𝑖
Where:
𝑇𝑖𝑗 = trips produced in zone 𝑖 and attracted to 𝑗
𝑃𝑖 = total trip production in zone 𝑖
𝐴𝑗 = total trip attraction to zone 𝑗
𝐹𝑖𝑗 = friction factor; a calibration term for spatial separation between zones 𝑖𝑗
𝐾𝑖𝑗 = a socioeconomic adjustment factor for interchange 𝑖𝑗 = 1
𝑖 = origin zone
𝑛 = number of zones
We used this above Gravity Model to generate the TripArray matrices for all nine types of trips between
Home, Work, School, and Other. Our excel sheets are consistent in their calculations, as laid out below:
2
http://www.princeton.edu/~alaink/Orf467F12/The%20Gravity%20Model.pdf
𝐷 = distance between zones.
This was calculated as the
Cartesian distance between
the zone centroids multiplied
by 1.2 which is a factor
accepted as a good estimate
of the circuitry.
1
𝑇
P/Sum
𝑋 = [𝑃] ∗ [𝐴𝑖𝑛𝑝𝑢𝑡 ]
Sum = [𝐹] ∗ 𝐴
Ainput
𝐹 = 𝐷′2 = matrix of friction
factors, which we have
defined across all trip
purposes as the inverse of
the distance squared.
Y = [𝑃/𝑆𝑢𝑚] ∗ [𝐴𝑖𝑛𝑝𝑢𝑡 ]
𝐼 = identity matrix.
TripArray = 𝑌𝑖𝑗 ∗ 𝐹𝑖𝑗
𝑇
𝐴𝑜𝑢𝑡𝑝𝑢𝑡
[𝑃/𝑆𝑢𝑚]𝑇
TripLengthDistribution
= TripArrayij * D’ij
Error* (%)
Anew*=Adesired*Ainput/Cprevious
Cprevious
C = Aoutput
𝐴𝑖𝑛𝑝𝑢𝑡 𝑇
Adesired
P
Layout of Excel Sheets
𝐷′ = distance matrix D
multiplied by the adjustment
factor of √. 1. This adjustment
factor is applied to put the
distance between cells in terms of
miles (since the centroids are in
an improper coordinate system).
***
blue = constant matrix
**To compute the iterations dictated by the Gravity
Model, we used the colored vectors above.
TripMiles =
TripLengthDistributionij
TripArrayij
The following steps were followed for each of the nine TripArray matrices:
First, the P and A vectors created (as previously described) were used to begin the first iteration. The
next calculations as directed by cell formulas are for the remaining vectors and matrices in black text on
the previous page. The TripArray matrix equals the number of trips.
Because the Gravity Model is tightly constrained, the program will iterate until the number of trips
produced and attracted to each zone follow the input assumptions on all the trips. During the iterations
we perform (instructions written on each excel sheet), we are focusing on the Adesired vector – which is
equal to the original attraction vector first generated. Note that the green vector sum of the TripArray
columns is C = Aoutput, while the Cprevious vector keeps track of previous vector values in order to compare
iteration results. The vector Anew* becomes the new input attraction vector, Ainput. This vector is
calculated as shown above – by multiplying the elements of Adesired and Ainput divided by Cprevious. We
repeated this iteration process until C = Aoutput was close enough to Adesired that the resulting error was
less than 1%.
Finally once these iterations were complete, the TripArray matrices for each of the nine production and
attraction vectors were finalized and taken to equal the total number of trips.
Generated Trip Arrays
The generated 75x75 TripArrays are too large to properly format for this document. Please see
the attached excel for the corresponding trip-type tabs and the TripArray matrices.
1)
2)
3)
4)
5)
6)
7)
8)
9)
Home-Based Work (HBW)
Home-Based School (HBS)
Home-Based Other (HBO)
Work-Based Home (WBH)
Work-Based Other (WBO)
School-Based Home (SBH)
School-Based Other (SBO)
Other-Based Home (OBH)
Other-Based Other (OBO)
Summary of Trip Demands: trip-distance charts
Once all of the TripArray matrices were generated through the Gravity Model, we can equate3 the
PersonTrips distribution to the number of trips predicted. We ran the TripArrays through an R script to
print out only non-zero values and their corresponding TripMiles. This TripMiles4 value equals the
average number of miles per person which intuitively, as written above, equals the
TripLengthDistribution divided by the TripArray matrix. This TripLengthDistribution equals the number of
trips – or the TripArray cell values – multiplied by the corresponding D’ values.
From the script outputs for each of the nine trip types, we summed the total number of trips in each
mile range from 0 to 15. The values can be seen below:
TripMiles
HBW
HBO
HBS
OBO
WBO
SBO
WBH
SBH
OBH
Sum
-
1.0
8,116
9,357
389
14,387
8,951
6,496
313
10,956
58,964
2.0
35,671
49,999
5,529
106,962
614
1,451
28,532
4,414
57,195
290,366
3.0
20,713
24,048
4,380
30,822
838
224
16,537
3,496
27,398
128,456
4.0
16,548
18,458
4,285
34,043
5,795
418
13,230
3,427
20,960
117,164
5.0
12,731
26,367
4,229
23,964
1,261
506
10,190
3,383
30,010
112,642
6.0
9,121
18,286
2,809
13,736
2,235
369
7,306
2,248
20,736
76,846
7.0
7,692
27,977
2,066
8,682
1,342
625
6,161
1,659
31,857
88,061
8.0
5,650
12,681
1,311
6,286
2,328
516
4,528
1,049
14,376
48,725
9.0
1,928
10,343
957
3,935
576
904
1,546
770
11,793
32,752
10.0
2,194
6,992
525
1,987
61
206
1,760
423
7,963
22,110
11.0
1,155
5,276
306
756
247
160
927
246
6,008
15,081
12.0
369
1,156
182
380
173
36
296
147
1,301
4,041
13.0
165
759
156
298
0
0
132
126
881
2,517
14.0
51
532
11
25
4
13
41
9
612
1,298
15.0
16
268
376
13
307
979
Cum Sum
-
58,964
349,330
477,786
594,950
707,592
784,437
872,498
921,223
953,975
976,085
991,165
995,206
997,723
999,021
1,000,000
Cum Distribution
-
0.059
0.349
0.478
0.595
0.708
0.784
0.872
0.921
0.954
0.976
0.991
0.995
0.998
0.999
1.000
Total
122,120
212,500
27,135
246,639
24,424
5,427
97,696
21,708
242,351
1,000,000
assume that each trip is taken by one person
TripMiles equals the TripLength because of the same assumption that each trip is composed of one person. TM equals the true distance in
miles between zones, because the distance is multiplied by the number of trips to get the trip length. The trip length is then divided by the
number of people to get miles per person, and because the number of trips equals the number of people, the distance of the trip equals miles
per person
3
4
Below are the nine TripLength distributions for the number of trips vs. trip miles:
As expected, the shape of the Home-Based Work distribution is the same as the return trip home. The
two graphs differ in their Number of Trips – this makes sense, because only 80% of the HBW trips
become WBH trips. This distribution jumps quickly at low Trip Miles values, and quickly decreases as the
Trip Miles increases. This distribution seems logical, as often people choose their residence based on
proximity to place of work. We can see a steep s-curve in the cumulative distribution, and the right tail is
also is what we expect for this trip distribution.
Also as expected, the shape of the Home-Based School distribution is the same as the return trip home.
Just as above, the two graphs differ in their Number of Trips – which also makes sense, because only
80% of the HBS trips become SBH trips. The steep increase in number of trips at low Trip Miles makes
sense, as children attend the public school in their designated district. The tail of this distribution is less
severe than the above distribution for the work-commute—this, and the temporary flat line in the graph
could be explained by the distances people are willing to travel to take their children to the private day
school. In the cumulative distribution graph, we can again see an s-curve and a right tail – not as
extreme as the HBW right tail, which is accounted for by the above reasons.
The shape of the Home-Based Other distribution is very similar to the Other-Based Home, but not
identical, as accounted for by the people who made WBO and SBO trips. The shapes of the curves are
very alike, but this difference is easier seen in the Number of Trips scale. The steep immediate increase
in Number of Trips at low Trip Miles is also consistent with people’s preferences – as expected, people
will usually shop, eat or enjoy recreation near their home. The two jumps around five and seven Trip
Miles could be explained by Other zones at the edges of Pension Heaven for example, the two stadiums
on the outskirts of town that people are willing to make longer trips for. We see the expected s-curve in
the cumulative distribution, and see the difference again as accounted by the WBO and SBO trips.
The WBO distribution has the two most drastic jumps in Number of Trips. We expect every graph to
have the first significant, steep peak in the low Trip Miles values, but the second peek around four Trip
Miles is after a significant trough. This can logically be explained; those leaving work for Other zones (ie
a restaurant or commercial zone) would most likely prefer a zone close to their place of business –
purely out of convenience. The second peak could be explained by trips that workers have to make – in
other words, the zone is not selected based on proximity but on the specific, perhaps necessary,
destination. These two peaks are also seen in the drastic jumps of the s-curve in the cumulative
distribution graph.
The SBO distribution is unique in that after the first expected peak at low Trip Miles, the Number of Trips
increases. This could be explained by what types of Other zones are congregated around the six
different schools. For example, the school in zone 74 is far from the restaurant and retail zones as
compared to the other five schools. The cumulative distribution is still an s-curve, but is not as steep as
the previous charts. This is expected from the TripLength graph’s dispersion of trips.
This OBO distribution graph is essentially unimodel, with a large peak around two Trip Miles. This is not
out of place because the layout of Pension Heaven is such that most of the Other zones are clustered
around each other, as are the Residential and Work zones. Intrazonal trips inside Other zones were
discounted by multiplying diagonals of the D (distance) matrix by a factor of 100. Although some trips
were longer than 15 miles – the upperbound of all our other trip-types – the graphs below demonstrate
that the number of trips over 15 miles is insignificant compare to those between 0 and 15 miles. The
cumulative trips distribution only appears to be the steepest s-curve, but that is only a result of the
scaling; when we take the x-values between 0 and 15, the s-curve is more similar to previous
distributions.
*note that for comparison purposes in the tables below, we included any OBO trips over 15 miles long in
the 15 TripMiles.
TripLength Distribution Analysis
When we transform each trip-type into percentage of trips across the different trip lengths, we can better compare the different distributions.
The shapes are relatively similar among all the series with the slight exception of the OBO and WBO trips. The first peaks of OBO and WBO line
are both at low miles and account for the largest percent of their trip-type counts, which seems appropriate. People traveling from work-toother and other-to-other and more inclined to go to an Other zone in close proximity; both because of preference and also the clustering of
Other zones around Work zones and different Other zones.
TripLength
HBW
HBO
HBS
OBO
WBO
SBO
WBH
SBH
OBH
0
-
1
6.65%
4.40%
1.43%
5.83%
36.65%
6.65%
1.44%
4.52%
2
29.21%
23.53%
20.37%
43.37%
2.51%
26.74%
29.20%
20.33%
23.60%
3
16.96%
11.32%
16.14%
12.50%
3.43%
4.12%
16.93%
16.11%
11.30%
4
13.55%
8.69%
15.79%
13.80%
23.73%
7.71%
13.54%
15.79%
8.65%
5
10.42%
12.41%
15.59%
9.72%
5.16%
9.32%
10.43%
15.59%
12.38%
6
7.47%
8.61%
10.35%
5.57%
9.15%
6.80%
7.48%
10.35%
8.56%
7
6.30%
13.17%
7.61%
3.52%
5.49%
11.52%
6.31%
7.64%
13.15%
8
4.63%
5.97%
4.83%
2.55%
9.53%
9.50%
4.64%
4.83%
5.93%
9
1.58%
4.87%
3.53%
1.60%
2.36%
16.65%
1.58%
3.55%
4.87%
10
1.80%
3.29%
1.93%
0.81%
0.25%
3.79%
1.80%
1.95%
3.29%
11
0.95%
2.48%
1.13%
0.31%
1.01%
2.95%
0.95%
1.13%
2.48%
12
0.30%
0.54%
0.67%
0.15%
0.71%
0.66%
0.30%
0.68%
0.54%
13
0.13%
0.36%
0.58%
0.12%
0.00%
0.00%
0.14%
0.58%
0.36%
14
0.04%
0.25%
0.04%
0.01%
0.01%
0.25%
0.04%
0.04%
0.25%
15
0.01%
0.13%
0.15%
0.01%
0.13%
Total
100%
100%
100%
100%
100%
100%
100%
100%
100%
In the cumulative distribution graph below, we also see that the OBO and WBO curves are slightly different from the other distributions, in their
high occurrence of trips in the low mile category.
Cum TripLength
HBW
HBO
HBS
OBO
WBO
SBO
WBH
SBH
OBH
0
-
1
6.6%
4.4%
1.4%
5.8%
36.6%
6.6%
1.4%
4.5%
2
35.9%
27.9%
21.8%
49.2%
39.2%
26.7%
35.9%
21.8%
28.1%
3
52.8%
39.2%
37.9%
61.7%
42.6%
30.9%
52.8%
37.9%
39.4%
4
66.4%
47.9%
53.7%
75.5%
66.3%
38.6%
66.3%
53.7%
48.1%
5
76.8%
60.3%
69.3%
85.2%
71.5%
47.9%
76.8%
69.2%
60.5%
6
84.3%
68.9%
79.7%
90.8%
80.6%
54.7%
84.2%
79.6%
69.0%
7
90.6%
82.1%
87.3%
94.3%
86.1%
66.2%
90.5%
87.2%
82.2%
8
95.2%
88.1%
92.1%
96.9%
95.7%
75.7%
95.2%
92.1%
88.1%
9
96.8%
92.9%
95.6%
98.5%
98.0%
92.4%
96.8%
95.6%
93.0%
10
98.6%
96.2%
97.6%
99.3%
98.3%
96.1%
98.6%
97.6%
96.2%
11
99.5%
98.7%
98.7%
99.6%
99.3%
99.1%
99.5%
98.7%
98.7%
12
99.8%
99.3%
99.4%
99.7%
100.0%
99.8%
99.8%
99.4%
99.3%
13
99.9%
99.6%
100.0%
99.8%
100.0%
99.8%
99.9%
100.0%
99.6%
14
100.0%
99.9%
100.0%
99.8%
100.0%
100.0%
100.0%
100.0%
99.9%
15
100.0%
100.0%
100.0%
100.0%
100.0%
100.0%
100.0%
100.0%
100.0%
Total
100%
100%
100%
100%
100%
100%
100%
100%
100%
Appendix
Home-Based Work Work-Based Home Home-Based School
Zone
Land
UseUse
Area
Pop Workers
Workers P
P
A
P
A
Zone
Land
Area
Pop
A
1,567
1 light
residential
0.9 4,010
4,010
435
1 light
residential
0.9
- 1,959
1,152
2 airport
4.8
1,440
2 airport
4.8
- 1,440
1,440
2,786
3 light
residential
1.6 7,129
7,129
774
3 light
residential
1.6
- 3,482
800
4 stadium/arena
2.5
1,000
4 stadium/arena
2.5
- 1,000
1,000
4,080
5 light
industrial
0.6
5,100
5 light
industrial
0.6
- 5,100
5,100
6 open
space
4.2
6 open
space
4.2
- - 15,120
7 medium
commercial
2.1
18,900
7 medium
commercial
2.1
- 18,900
18,900
1,393
387
8 light
residential
0.8 3,564
3,564
8 light
residential
0.8
- 1,741
9 open
space
2.1
9 open
space
2.1
- - 112
10 10
Recreation
1.4
140
Recreation
1.4
- 140
140
1,000
278
medium
residential
0.4
- 1,251
11 11
medium
residential
0.4 2,560
2,560
216
Restaurant
0.9
- 270
270
12 12
Restaurant
0.9
270
0.6
- - 13 13
lakelake
0.6
348
97
residential
0.2
891
- 435
14 14
lightlight
residential
0.2
891
1,045
290
residential
0.6
- 1,306
15 15
lightlight
residential
0.6 2,673
2,673
1,501
417
medium
residential
0.6
- 1,876
16 16
medium
residential
0.6 3,840
3,840
14,400
heavy
commercial
1.2
- 18,000
18,000
17 17
heavy
commercial
1.2
18,000
1,501
417
medium
residential
0.6
- 1,876
18 18
medium
residential
0.6 3,840
3,840
5,088
1,413
heavy
residential
1.2
- 6,360
19 19
heavy
residential
1.2 13,020
13,020
256
2,598
Education--High
School
0.8
- 320
320
20 20
Education--High
School
0.8
320
8,904
2,473
heavy
residential
2.1
- 11,130
21 21
heavy
residential
2.1 22,785
22,785
open
space
1.8
- - 22 22
open
space
1.8
0.6
- - 23 23
lakelake
0.6
24,000
heavy
industrial
1.5
- 30,000
30,000
24 24
heavy
industrial
1.5
30,000
4,002
1,111
medium
residential
1.6
- 5,002
25 25
medium
residential
1.6 10,240
10,240
750
208
medium
residential
0.3
- 938
26 26
medium
residential
0.3 1,920
1,920
750
208
medium
residential
0.3
- 938
27 27
medium
residential
0.3 1,920
1,920
24
Recreation
0.3
- 3030
30
28 28
Recreation
0.3
750
208
medium
residential
0.3
- 938
29 29
medium
residential
0.3 1,920
1,920
750
208
medium
residential
0.3
- 938
30 30
medium
residential
0.3 1,920
1,920
871
242
residential
0.5
- 1,088
31 31
lightlight
residential
0.5 2,228
2,228
1,920
Professional
Office
0.8
- 2,400
2,400
32 32
Professional
Office
0.8
2,400
1,045
290
residential
0.6
- 1,306
33 33
lightlight
residential
0.6 2,673
2,673
522
145
residential
0.3
- 653
34 34
lightlight
residential
0.3 1,337
1,337
1,045
290
residential
0.6
- 1,306
35 35
lightlight
residential
0.6 2,673
2,673
open
space
2.1
- - 36 36
open
space
2.1
174
48
residential
0.1
446
- 218
37 37
lightlight
residential
0.1
446
696
193
residential
0.4
- 871
38 38
lightlight
residential
0.4 1,782
1,782
6,400
heavy
industrial
0.4
- 8,000
8,000
39 39
heavy
industrial
0.4
8,000
174
48
residential
0.1
446
- 218
40 40
lightlight
residential
0.1
446
open
space
0.6
- - 41 41
open
space
0.6
1,045
290
residential
0.6
- 1,306
42 42
lightlight
residential
0.6 2,673
2,673
6,002
1,667
medium residential
2.4 15,360
7,503
43 43
medium
residential
2.4 15,360
6,784
1,884
44 heavy residential
1.6 17,360
8,480
44 heavy residential
1.6 17,360
750
208
45 medium residential
0.3
1,920
938
45 medium residential
0.3
1,920
96
46 Town Hall
0.6
120
120
46 Town Hall
0.6
120
3,600
47 Professional Office
1.5
4,500
4,500
47 Professional Office
1.5
4,500
48 lake
2.5
48 lake
2.5
3,752
1,042
49 medium residential
1.5
9,600
4,689
49 medium residential
1.5
9,600
4,240
1,178
50 heavy residential
1.0 10,850
5,300
50 heavy residential
1.0 10,850
2,160
51 light commercial
0.9
2,700
2,700
51 light commercial
0.9
2,700
480
52 Retail
2.0
600
600
52 Retail
2.0
600
384
2,743
53 Education--High School
1.2
480
480
53 Education--High School
1.2
480
960
54 stadium/arena
3.0
1,200
1,200
54 stadium/arena
3.0
1,200
6,360
1,766
55 heavy residential
1.5 16,275
7,950
55 56
heavy
residential
1.5
16,275
7,632
2,120
heavy residential
1.8 19,530
9,540
56 57
heavy
residential
1.8
19,530
4,002
1,111
medium residential
1.6 10,240
5,002
57 58
medium
residential
1.6
10,240
7,003
1,945
medium residential
2.8 17,920
8,754
58 59
medium
residential
2.8
17,920
2,501
695
medium residential
1.0
6,400
3,126
59 60
medium
residential
1.0 10,240
6,400
4,002
1,111
medium
residential
1.6
- 5,002
60 61
medium
residential
1.6 10,240
288
Restaurant
1.2
360360
61 62
Restaurant
1.2
360
128
Public Buildings
0.8
- 160
160
62 63
Public
0.8
160
lakeBuildings
0.6
- 63 64
lakelight industrial
0.6
9,520
1.4
11,900
11,900
64 65
lightlight
industrial
1.4
11,900
1,200
commercial
0.5
1,500
1,500
65 66
lightRetail
commercial
0.5
1,500
192
0.8
240
240
66 67
Retail
0.8
240
256
4,784
Education--Elementary
0.8
- 320
320
67 68
Education--Elementary
0.8 10,240320
4,002
1,111
medium residential
1.6
5,002
68 69
medium
residential
1.6 10,240
8,160
light industrial
1.2
10,20010,200
69 70
lightopen
industrial
1.2
10,200
space
3.2
- 70 71
open
space
3.2 3,5641,393
387
light
residential
0.8
- 1,741
71 72
lightlight
residential
0.8 4,010
3,564
1,567
435
residential
0.9
- 1,959
72 73
lightEducation--Elementary
residential
0.9
4,010
192
5,427
0.6
240240
73 74
Education--Elementary
0.6
240
1,344
9,273
Education--University
4.2
1,680
1,680
74 Education--University
4.2
1,680
Education--Boarding/Day
75 75
Education--Boarding/Day
School
0.8
320
256
2,310
School
0.8
- 320
320
River
9.9
River
9.9
Total
102.4 250,000
250,000 122,120
122,120
Total
102.4
TotalOne-Ways
One-Ways
Total
122,120
122,120
97,696
97,696
27,135
27,135
Zone
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
Land Use
Area
Pop
light residential
0.9
4,010
airport
4.8
light residential
1.6
7,129
stadium/arena
2.5
light industrial
0.6
open space
4.2
medium commercial
2.1
light residential
0.8
3,564
open space
2.1
Recreation
1.4
medium residential
0.4
2,560
Restaurant
0.9
lake
0.6
light residential
0.2
891
light residential
0.6
2,673
medium residential
0.6
3,840
heavy commercial
1.2
medium residential
0.6
3,840
heavy residential
1.2 13,020
Education--High School
0.8
heavy residential
2.1 22,785
open space
1.8
lake
0.6
heavy industrial
1.5
medium residential
1.6 10,240
medium residential
0.3
1,920
medium residential
0.3
1,920
Recreation
0.3
medium residential
0.3
1,920
medium residential
0.3
1,920
light residential
0.5
2,228
Professional Office
0.8
light residential
0.6
2,673
light residential
0.3
1,337
light residential
0.6
2,673
open space
2.1
light residential
0.1
446
light residential
0.4
1,782
heavy industrial
0.4
light residential
0.1
446
open space
0.6
light residential
0.6
2,673
medium residential
2.4 15,360
heavy residential
1.6 17,360
medium residential
0.3
1,920
Town Hall
0.6
Professional Office
1.5
lake
2.5
medium residential
1.5
9,600
heavy residential
1.0 10,850
light commercial
0.9
Retail
2.0
Education--High School
1.2
stadium/arena
3.0
heavy residential
1.5 16,275
heavy residential
1.8 19,530
medium residential
1.6 10,240
medium residential
2.8 17,920
medium residential
1.0
6,400
medium residential
1.6 10,240
Restaurant
1.2
Public Buildings
0.8
lake
0.6
light industrial
1.4
light commercial
0.5
Retail
0.8
Education--Elementary
0.8
medium residential
1.6 10,240
light industrial
1.2
open space
3.2
light residential
0.8
3,564
light residential
0.9
4,010
Education--Elementary
0.6
Education--University
4.2
Education--Boarding/Day School
0.8
River
9.9
Total
102.4 250,000
Workers
1,440
1,000
5,100
18,900
140
270
18,000
320
30,000
30
2,400
8,000
120
4,500
2,700
600
480
1,200
360
160
11,900
1,500
240
320
10,200
240
1,680
320
P
School-Based Home
A
348
619
310
222
77
232
333
333
1,131
2,078
1,978
889
167
167
167
167
193
232
116
232
39
155
39
232
1,334
1,507
167
834
942
2,194
1,413
1,696
889
1,556
556
889
3,827
889
310
348
4,342
7,418
1,848
-
Home-Based Other Other-based Home
P
A
P
A
3,409
3,887
6,060
6,911
15,000
17,183
56,700
63,206
3,030
3,455
2,500
3,064
2,176
2,482
1,620
1,985
60
74
757
864
2,272
2,592
3,264
3,723
90,000 103,195
3,264
3,723
11,067
12,622
19,367
22,088
30
45
8,704
9,927
1,632
1,861
1,632
1,861
1,000
1,226
1,632
1,861
1,632
1,861
1,894
2,160
2,272
2,592
1,136
1,296
2,272
2,592
379
432
1,515
1,728
379
432
2,272
2,592
13,056
14,890
14,756
16,829
1,632
1,861
125
153
8,160
9,306
9,223
10,518
5,400
6,618
3,000
3,677
30,675
34,096
13,834
15,777
16,601
18,932
8,704
9,927
15,232
17,372
5,440
6,204
8,704
9,927
2,160
2,647
30
37
3,000
3,677
1,200
1,471
8,704
9,927
3,030
3,455
3,409
3,887
-
-
-
-
122,120
Total One-Ways
21,708
21,708
212,500
212,500
242,351
242,351
Zone
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
Land Use
Area
Pop
light residential
0.9
4,010
airport
4.8
light residential
1.6
7,129
stadium/arena
2.5
light industrial
0.6
open space
4.2
medium commercial
2.1
light residential
0.8
3,564
open space
2.1
Recreation
1.4
medium residential
0.4
2,560
Restaurant
0.9
lake
0.6
light residential
0.2
891
light residential
0.6
2,673
medium residential
0.6
3,840
heavy commercial
1.2
medium residential
0.6
3,840
heavy residential
1.2 13,020
Education--High School
0.8
heavy residential
2.1 22,785
open space
1.8
lake
0.6
heavy industrial
1.5
medium residential
1.6 10,240
medium residential
0.3
1,920
medium residential
0.3
1,920
Recreation
0.3
medium residential
0.3
1,920
medium residential
0.3
1,920
light residential
0.5
2,228
Professional Office
0.8
light residential
0.6
2,673
light residential
0.3
1,337
light residential
0.6
2,673
open space
2.1
light residential
0.1
446
light residential
0.4
1,782
heavy industrial
0.4
light residential
0.1
446
open space
0.6
light residential
0.6
2,673
medium residential
2.4 15,360
heavy residential
1.6 17,360
medium residential
0.3
1,920
Town Hall
0.6
Professional Office
1.5
lake
2.5
medium residential
1.5
9,600
heavy residential
1.0 10,850
light commercial
0.9
Retail
2.0
Education--High School
1.2
stadium/arena
3.0
heavy residential
1.5 16,275
heavy residential
1.8 19,530
medium residential
1.6 10,240
medium residential
2.8 17,920
medium residential
1.0
6,400
medium residential
1.6 10,240
Restaurant
1.2
Public Buildings
0.8
lake
0.6
light industrial
1.4
light commercial
0.5
Retail
0.8
Education--Elementary
0.8
medium residential
1.6 10,240
light industrial
1.2
open space
3.2
light residential
0.8
3,564
light residential
0.9
4,010
Education--Elementary
0.6
Education--University
4.2
Education--Boarding/Day School
0.8
River
9.9
Total
102.4 250,000
Workers
1,440
1,000
5,100
18,900
140
270
18,000
320
30,000
30
2,400
8,000
120
4,500
2,700
600
480
1,200
360
160
11,900
1,500
240
320
10,200
240
1,680
320
School-based Other
P
A
383
1,446
64
41
2
2,295
520
9
26
3
138
77
549
782
55
1
77
31
957
1,085
1,855
462
-
Work-based Other
P
A
288
200
1,800
1,020
3,780
5,060
28
500
54
324
12
3,600
10,900
64
6
6,000
6
200
480
1,600
24
900
25
540
1,080
120
600
96
240
2,639
72
432
32
6
2,380
300
600
48
240
64
2,040
48
336
64
-
Other-based Other
P
A
3,956
3,956
7,033
7,033
3,517
3,517
2,526
2,526
879
879
2,637
2,637
3,788
3,788
3,788
3,788
12,845
12,845
22,479
22,479
10,102
10,102
1,894
1,894
1,894
1,894
1,894
1,894
1,894
1,894
2,198
2,198
2,637
2,637
1,319
1,319
2,637
2,637
440
440
1,758
1,758
440
440
2,637
2,637
15,154
15,154
17,127
17,127
1,894
1,894
9,471
9,471
10,704
10,704
16,056
16,056
19,268
19,268
10,102
10,102
17,679
17,679
6,314
6,314
10,102
10,102
10,101
10,101
3,517
3,517
3,956
3,956
-
-
122,120
Total One-Ways
5,427
5,427
24,424
24,424
246,639
246,639
R Script used to cycle out zeros in TripArray matrices for each of the nine different trip types
#HBW
#HBWTripArray.csv is a file containing only the 75x75 TripArray matrix
HBWTripArray<-read.csv("HBWTripArray.csv",header=FALSE);
HBWTripMiles<-read.csv("HBWTripMiles.csv",header=FALSE);
#finding indices of non-zero values
X<-which(HBWTripArray!=0,arr.ind=T);
#creating new matrix of non-zero [TripMiles, Trips]
HBW_PTMvsT<-matrix(0,length(X[,1]),2)
HBW_PTMvsT[,1]<-HBWTripMiles[X];
HBW_PTMvsT[,2]<-HBWTripArray[X];
HBW_PTMvsT<-round(HBW_PTMvsT,digits=4);
write.matrix(HBW_PTMvsT,file="HBW",sep=",")
The above script was used for all nine trip-types