October 26, 2012
ORF 467
Table of Contents
Land Use Characteristics
3
Land use distribution
Map/Summary Tables
Demographics and Quality of Life
Demand for Transportation
Trip Generation
7
7
Trip Productions and Attractions
Trips Type Purposes
Home-based Work
Home-based Education
Home-based Shop/Dine/Recreation/Other
Non-Home-based
Summary Trip Production and Attraction Tables
Trip Distribution
11
Trip Arrays Generation
Trip Arrays for Trip types
Summary of Trip demand
PersonTripLengthDistribution Analysis
Homebased Work Transportation Demand Implications
1/D Gravity Model
1/sqrt(D) Gravity Model
Person Trip Length Trip Length Distribution
2
Land Use Distribution and other Fundamental Characteristics
DD’s City of Delights is a square area of land totaling 102.4 square miles. It supports approximately 70% developed
space and 30% undeveloped space (i.e. water and open space). The developed space is then further divided into
areas of residential, commercial, recreational, educational and other types of land use. DD’s is characterized by mass
urban development: it supports many land zones used for manufacturing, transportation, and commericial purposes.
At its center is a large rectangular sized theme park, modeled after Disney’s theme park (thus the city’s name). The
table below summarizes the city’s total land use.
Land type
Commercial
Light Manufacturing
Heavy manufacturing
Agriculture
Public office
Recreational
Restaurants
Water
Open space
Theme park
Educational
Hotels
Transportational Center
Light residential
Medium residential
Large residential
Very large residential
Map Color
# Sq. Miles % of total land
4.6
4.49%
6.7
6.54%
7
6.84%
2.4
2.34%
2.3
2.25%
3.2
3.13%
2
1.95%
16.6
16.21%
15.2
14.84%
4.9
4.79%
2.2
2.15%
2.4
2.34%
2.5
2.44%
5
4.88%
7.6
7.42%
8.4
8.20%
9.4
9.18%
Total land
102.4
Undeveloped Space
Developed Space
Population/Sq. Miles
1,500
6,000
9,000
300
500
500
500
0
0
2,500
800
600
1,000
5,000
7,750
8,750
10,000
Land Use Capacity
6,900
40,200
63,000
720
1,150
1,600
1,000
0
0
12,250
1,760
1,440
2,500
25,000
58,900
73,500
94,000
100.00%
31.8
70.6
31.05%
68.95%
Below is the map of DD’s. The numbers on the zones correspond to their index in later production and attraction
arrays.
1
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
2
1
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
14
42
15
43
16 17
13
2
3
18
19
40 41
44
20
46
4
61
39
5
45
21
6
46
22
47
48
38
7
23
24 25
50
37
62
49
36
26
51
52
53 54
35
8
27
55
34
29
9
10
11
57
56
28
31
30
30
30
58
33
59
60
32
12
1
2
3
4
5
6
7
8
59
59
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
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
KEY
168
152
49
50
76
84
94
46
67
70
24
21
32
22
25
24
20
Water
Open space
Donald Duck Theme Park
Light Residential
Medium Residential
Large Residential
Very Large Residential
Commercial
Light Manufacturing/Industrial
Heavy Manufacturing/Industrial
Agriculture
Public Buildings
Other Recreational
Educational
Transportation Center
Hotels
Restaurants
1024
3
Demographics
Residential
Light residential
Medium residential
Large residential
Very large residential
Total
Employment
Commerc ial
Light Manufac turing
Heavy manufac turing
Agric ulture
Public offic e
Rec reational
Restaurants
Theme park
Educ ational
Hotels
Transportational c enter
Total
Residential Capac ity
25000
58900
73500
94000
251400
6900
40200
63000
720
1150
1600
1000
12250
1760
1440
2500
Light Residential: typically 1-2 people
per household; can hold a total 25000
people
Medium Residential: typically 2-3
people per household; can hold a
total of 58900 people
Large Residential: typically 4-5 people
per household; can hold a total of
73500 people
Very Large Residential: typically >5
people per household; can hold a
total of 94000 people
132520
In the above chart, each type of zone that employs workers is listed. Commercial zones, in
total, employ 6900 of the worker population, for example. Manufacturing employs the most
workers (with light manufacturing at 40200 and heavy manufacturing at 63000), while
agriculture employs the least (720). In total, there are 132520 employed workers in DD’s, and
the unemployment rate is at 9.72%. This implies that approximately 60% of the total
population is part of the labor force for the city. Though actual data for real cities vary, 60%
seems like a good rule of thumb for the labor force percentage.
There is a total population of 250000 people, whose population breakdown is given in the following chart.
Approximately 8% of the population is children under 5, 24% are students aging from 5 to 20 years old, 53% are
employed workers aging from 21 to 66 years old, 6% are unemployed workers aging from 21 to 66 years old, and
9% are the elderly (age 66 and over). These figures were modelled after the population statistics for Los Angeles in
the 1990’s.
Of the employed workers, 6626 are home workers, meaning that they work or telecommute in their homes rather
than travel to a workplace any given day. Children under 5 do not qualify as “trip-makers”, while the rest of the
population makes about 4 trips a day per person on average. In total, an average of 920000 trips are made on any
given day in DD’s.
Population Breakdown
Children under 5
Students (5 - 20 year olds)
Workers (21-66 year olds)
Elderly (66+ year olds) & unemployed
20,000
60,000
132,520
37,480
Total
250,000
4
There are 5 zones used for education purposes, whose types (including elementary school, middle school, high
school, and university) are given in the following chart. 40% of the enrolled students attend middle or elementary
school, 30% attend high school, and 30% attend university. A total of 2.16% of the total land area in the city is
devoted towards educational purposes.
Education Zoning:
Zone
3
16
22
28
53
Type
Area (sq. mi.) % of Land
elementary + middle
0.6
high school (vocational)
0.2
elementary + middle
0.3
university
0.6
high school
0.5
Total
Enrollment
0.59%
0.20%
0.29%
0.59%
0.49%
15000
6000
9000
18000
12000
60000
The city has a total of 62 zones, one of which is a major river that runs directly across the entire city while various
others are also open spaces that will not contribute toward the production or attraction of any trips for the city. This
river separates a narrow strip of the city from the rest, more bulkier part. Of note, most of the commercial,
recreational zones are located on the more bulkier part, to the right of the river. Also, residential areas tend to be
located on the sides of the city, while other zones that tend to be visited by more varied groups tend to be located in
the center of the city. The zones are all rectangular shaped.
Recreational areas and commercial areas have certain floor space amounts that can be converted into the number of
patrons such areas can support at a point in time. These were based off of estimates for the percentage of land in a
given commercial or recreational zone that may be used as support areas for the activities that go on there and are
not intend to be visited by any customers/patrons
Centroids are chosen as the point within the zone that has the most concentrated activity at an point in time; this is
obviously a generalized model of actual zone activities, but is the easiest representation that is still reliably
conceivable.
5
Zone Summary Chart
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
Type
river
open space
recreational (movie theater)
educational (elementary & middle)
light residential
commercial (strip malls)
heavy manufacturing
agriculture
light manufacturing
medium residential
commercial (individual stores)
restaurant
open space
open space
heavy manufacturing
public
educational (vocational high school)
restaurant
commercial (individual stores)
medium residential
medium residential
recreational (sports std.,golf course,etc.)
educational (elementary & middle)
open space
commercial (mall)
heavy manufacturing
water
heavy manufacturing
educational (university)
public
large residential
commercial (strip malls)
very large residential
medium residential
light manufacturing
recreational (movie theater,stage plays,etc.)
hotel
restaurant
commercial (upscale stores)
theme park
commercial (theme park related / mall)
restaurant
light residential
open space
water
very large residential
large residential
open space
light manufacturing
commercial (outlets and big box stores)
public
transportation
commercial (mall)
educational (high school)
very large residential
water
open space
public
restaurant
large residential
open space
hotel
open space
No. of pixels Area (sq miles) % of total land centroid (x-coor) centroid (y-coor) School Enrollment Floor Space (sq miles)
118
11.8
11.52% ---30
3.0
2.93%
3
3
0
0
4
0.4
0.39%
1
7
0
0
6
0.6
0.59%
4
12
15000
0
20
2.0
1.95%
3
10
0
0
4
0.4
0.39%
1
13
0
0.16
4
0.4
0.39%
3
13
0
0.28
24
2.4
2.34%
3
17
0
0
25
2.5
2.44%
3
23
0
2.3
28
2.8
2.73%
3
29
0
0
4
0.4
0.39%
5
31
0
0.2
6
0.6
0.59%
5
29
0
0.45
8
0.8
0.78%
6
31
0
0
10
1.0
0.98%
22
6
0
0
30
3.0
2.93%
15
3
0
2.8
6
0.6
0.59%
11
3
0
0
2
0.2
0.20%
10
5
6000
0
2
0.2
0.20%
11
5
0
0.1
4
0.4
0.39%
9
7
0
0.2
8
0.8
0.78%
12
6
0
0
15
1.5
1.46%
9
11
0
0
20
2.0
1.95%
12
10
0
0
3
0.3
0.29%
12
13
9000
0
9
0.9
0.88%
10
15
0
0
6
0.6
0.59%
12
15
0
0.36
8
0.8
0.78%
14
14
0
0.6
16
1.6
1.56%
15
18
0
0
28
2.8
2.73%
13
22
0
2.4
6
0.6
0.59%
13
25
18000
0
4
0.4
0.39%
10
25
0
0
24
2.4
2.34%
13
28
0
0
6
0.6
0.59%
16
25
0
0.24
39
3.9
3.81%
18
31
0
0
25
2.5
2.44%
20
27
0
0
12
1.2
1.17%
18
22
0
0.8
8
0.8
0.78%
18
18
0
0
10
1.0
0.98%
20
15
0
0
4
0.4
0.39%
16
15
0
0.24
2
0.2
0.20%
16
13
0
0.1
49
4.9
4.79%
20
11
0
0
4
0.4
0.39%
17
6
0
0.28
2
0.2
0.20%
19
7
0
0.1
30
3.0
2.93%
21
3
0
0
32
3.2
3.13%
28
2
0
0
7
0.7
0.68%
24
11
0
0
30
3.0
2.93%
30
8
0
0
24
2.4
2.34%
26
8
0
0
6
0.6
0.59%
26
13
0
0
30
3.0
2.93%
30
13
0
2.6
6
0.6
0.59%
26
15
0
0.39
4
0.4
0.39%
23
15
0
0
25
2.5
2.44%
24
19
0
0
10
1.0
0.98%
20
19
0
0.8
5
0.5
0.49%
27
19
12000
0
25
2.5
2.44%
30
19
0
0
25
2.5
2.44%
30
24
0
0
25
2.5
2.44%
25
24
0
0
9
0.9
0.88%
21
23
0
0
6
0.6
0.59%
23
28
0
0.4
36
3.6
3.52%
27
29
0
0
12
1.2
1.17%
31
29
0
0
14
1.4
1.37%
15
9
0
0
20
2.0
1.95%
11
18
0
0
1024
102.4
100%
60000
15.8
Note: The river running through the city is not indexed as a zone, and thus will not count towards any trip
productions or attractions since it is assumed that no activity goes on there.
6
Trip Generation
Process for Trip Production Generation: Each of the 9 production arrays for the different types of trips uses a
slightly different method for trip production generation. However, the main idea behind them is the same. We first
determine the number of trips that will be made for a certain type, and then proceed to break down the percentages
for the zones producing the trip. One zone might, for example, produce 5% of the trips for a certain type, while
another zone may produce 20% of the trips. More generally, for a certain trip type, a trip rate (trips per square mile)
is generated for each type of production zone (commercial type, recreational type, etc.). This trip rate is based off of
a trip generator number, which in essence is simply the number of people in a given type of zone that is likely to
generate production for the given trip type.
For example, for home-based school trips, it is given that the total trips in the trip production across all the zones
must equal 60000, since this is the number of enrolled students that attend some education zone on any given day.
For the production array, all zones except the residential zones will have a value of zero, and the values for the
residential zones must add up to 60000. Given this information, it is then just a matter of determining what
percentage of the total population in a given residential zone are aged 5 to 20. In general, the assumption was that
light residential zones would have a smaller student-aged population than very large (heavily populated) residential
zones, while medium residential zones and large residential zones would be somewhere in the middle.
Process for Trip Attraction Generation: Each of the 9 attraction arrays for the different types of trips uses a slightly
different method for trip attraction generation. However, the main idea behind them is the same. It is given that the
sum of the attraction numbers in the attraction array must necessarily equal the sum of the production array. Given
this, we can then proceed to break down this sum for the production array and determine what percentage of this
sum will correspond to an attraction zone type.
For example, for non-home-based school trip types, the attractions are all the zones excluding the residential zones
(and of course, the undeveloped open space/water zones). Commercial zones and recreational zones are assumed to
produce larger attraction values than manufacturing or public office zones. As such, 25% of the produced trips
correspond to commercial attractions, 25.6% correspond to recreational attractions, 19% correspond to the theme
park attraction (this is due to the fact that school aged children are likely to be attracted to such places), and only
0.1% correspond to zone types such as heavy or light manufacturing. A trip rate (trips per square mile) is deduced
based on these percentages, and the attraction value for a certain zone is simply the zone’s area (actual area or floor
space if it is a commercial/recreational zone) multiplied by the trip rate number.
Home-based Work: Home-based work includes inbound and outbound home-based work trip types. For this trip
type, the production arrays have non-zero elements for only the residential (home) zones and the attraction arrays
have non-zero values for only the zones that employ workers. In other words, these trips are “produced” at the home
zones, and attracted to the zones with employment capacity (which gives rise to the trip’s purpose). Since production
and attraction do not depend on direction, both inbound and outbound home-based work trips follow this logic.
Chart of attraction zone types for inbound and outbound home-based work trips:
Employment type
Total area (sq. miles) Population / Sq. mile Employment Capacity
commercial
4.6
1500
6900
light Manufacturing
6.7
6000
40200
heavy manufacturing
7
9000
63000
agriculture
2.4
300
720
public
2.3
500
1150
recreational
3.2
500
1600
restaurants
2
500
1000
theme park
4.9
2500
12250
educational
2.2
800
1760
hotels
2.4
600
1440
transportation
2.5
1000
2500
Total
132520
7
Home-based Education: Home-based education (school) includes inbound and outbound home-based education trip
types. For this trip type, the production arrays have non-zero elements for only the residential (home) zones and the
attraction arrays have non-zero values for only the zones that serve educational purposes. In other words, these trips
are “produced” at the home zones, and attracted to the zones that provide schooling for enrolled students (which
gives rise to the trip’s purpose). Since production and attraction do not depend on direction, both inbound and
outbound home-based work trips follow this logic.
The chart below summarizes the relationship between the residential zone types and the educational zones. For
example, light residential zones have a total of 1500 students enrolled in educational zone 3, which is a elementary
and middle school education zone.
Residential Type
light residential
medium residential
large residential
very large residential
Education Zoning:
Zone
3
16
22
28
53
Total Students Enrolled at each Educational Zone According to Residential Type
Residential Capacity Ed. Zone 3 Ed. Zone 16 Ed Zone. 22 Ed Zone. 28 Ed Zone. 53
25000
1500
1200
900
3600
1200
58900
3000
1800
1800
5400
2400
73500
4500
1800
2700
5400
3600
94000
6000
1200
3600
3600
4800
Type
Area (sq. mi.)% of total land Enrollment
elementary + middle
0.6
0.59%
15000
high school (vocational)
0.2
0.20%
6000
elementary + middle
0.3
0.29%
9000
university
0.6
0.59%
18000
high school
0.5
0.49%
12000
Total Enrollment
60000
Home-based Shop/Dine/Recreation/Other: Home-based shop/dine/recreation(SDR) includes inbound and outbound
home-based SDR trip types. For this trip type, the production arrays have non-zero elements for only the residential
(home) zones and the attraction arrays have non-zero values for only the zones that serve recreational, shopping,
dining, or similar purposes. In other words, these trips are “produced” at the home zones, and attracted to the zones
that provide services related to recreational, commercial, etc. (these services, or attractions, give rise to the trip’s
purpose). Since production and attraction do not depend on direction, both inbound and outbound home-based work
trips follow this logic.
The chart below summarizes which zone types are counted as shopping, dining, recreational, or similar attractions.
Commerical zones, recreational zones, dining/restaurant zones, as well as the theme park zone compose a high
percentage of the total attractions (25%, 25.6%, 20%, and 19% respectively). There is also a small percentage of
trips made with the transportation center or public office zones as the attraction. Finally, light manufacturing, heavy
manufacturing, agricultural, and educational zones are also included but given an extremely small percentage
(almost negligible) to account for any trips that may have these zone types as attractions. It would also have been
conceivable to simply not have any trips that use these zone types as attractions.
Land type
commercial
light Manufacturing
heavy manufacturing
agriculture
public offices
recreational
restaurants
theme park
educational
hotels
transportation center
Area
4.6
6.7
7
2.4
2.3
3.2
2
4.9
2.2
2.4
2.5
Population / SQ Mile Capacity % of total attractions
1,500.00
6,900.00
25.0
6,000.00
40,200.00
0.1
9,000.00
63,000.00
0.1
300.00
720.00
0.1
500.00
1,150.00
3.0
500.00
1,600.00
25.6
500.00
1000
20.0
2500
12250
19.0
800
1760
1.0
600
1440
0.1
1000
2500
6.0
8
Non-home-based: Non-home-based trips include non-home-based work trips (NHBW), non-home-based school trips
(NHBS), non-home-based other trips (NHBSR).
For NHBW trips, the production array includes non-zero elements only for the zones with employment capacity
(work zones), and the attraction array are the “other” options not including residential zones (the biggest players
would be commerical, recreational, etc. zones). The trips are “produced” at work zones (hence, non-home-based),
and “attracted” to the zones that provide “other” services such as commercial or recreational services (these services,
or attractions, give rise to the trip purpose).
For NHBS trips, the production array includes non-zero elements for the zones with student enrollment (educational
zones), and the attraction array are the “other” options not including residential zones (again, the biggest players
would be recreational, commercial, etc.). The trips are “produced” at school zones (hence, non-home-based), and
“attracted” to the zones that provide “other” services such as commercial or recreational services (these services, or
attractions, give rise to the trip purpose).
For NHBSR trips, the production and attraction arrays are exactly equal (with non-zero elements for the “other”
zones not including residential zones) as we assume that the total number of trips produced at and attracted to a
particular zone is the same. The trips are “produced” at zones that provide “other” services (hence, non-homebased), and “attracted” to the zones that provide “other” services (these services, or attractions, give rise to the trip
purpose).
The chart directly above gives a summary of the “other” zones for the non-home-based trip types. Namely, these
“other” zones are mainly used for commercial, recreational, or similar purposes.
Summary Trip Production and Attraction Tables:
Trip Type
Productions
per Zone
Attractions
per Zone
Comments
Links
Outbound Homebased Work
(OHBW)
Outbound Homebased School
(OHBS)
Outbound Homebased
Shop/Recreate/Other
(OHBSDR)
132520
132520
Total # of jobs (or total # of
workers)
hw3_2.xls#OHBW_P_A_arrays
60000
60000
Total # of enrolled students
hw3_2.xls#OHBS_P_A_arrays
154260
154260
hw3_2.xls#OHBSDR_P_A_arrays
Inbound Home-based
Work (IHBW)
66260
66260
Assumed that the 37480
elderly and umemployed
population would make
approximately 4 trips on
average per person
50% of Outbound home-based
work
Inbound Home-based
School (IHBS)
42000
42000
70% of Outbound home-based
school
hw3_2.xls#IHBS_P_A_arrays
Inbound Home-based
Shop/Recreate/Other
(IHBSDR)
Work-based Nonhome (WBNH)
238520
238520
hw3_2.xls#IHBSDR_P_A_arrays
66260
66260
IHBSDR = OHBSDR +
OHBW – IHBW + OHBS –
IHBS
50% of Outbound home-based
school
School-based Nonhome (SBNH)
18000
18000
30% of Outbound home-based
school
hw3_2.xls#SBNH_P_A_arrays
hw3_2.xls#IHBW_P_A_arrays
hw3_2.xls#WBNH_P_A_arrays
9
Shop/Recreate/Other
based Non-home
(NHBSR)
142180
142180
Assuming that each of the
230000 trips makers
(excluding children under 5)
make 4 trips on average, there
would be a total of 920000
trips on any average day. The
NHBSR production and
attraction numbers came from
this assumption.
hw3_2.xls#NHBSR_P_A_arrays
10
Trip Distribution:
Trip Arrays Generation Process:
After determining production and attraction vectors, we generated trip arrays according to the gravity model, using a
friction coefficient of one divided by the distance squared:
𝑇𝑖𝑗 = 𝑃𝑖 ∗
𝐴𝑗 𝐹𝑖𝑗
1
𝑤ℎ𝑒𝑟𝑒 𝐹𝑖𝑗 = 2
∑𝑧𝑜𝑛𝑒𝑠 𝐴𝑗 𝐹𝑖𝑗
𝐷𝑖𝑗
This gives us trip matrices in which the row sums produce the elements of the production vector, and the column
sums (ideally) produce the elements of the attraction vector, while trips are weighted by the inverse square of their
distance. We follow an iteratively convergent process to generate a “false” attraction vector input for the trip
matrix, such that it produces an output which has the column sums of the “true” attractions we are hoping to get.
This allows us to keep the trip distribution given by the gravity model while remaining consistent with the zonespecific attraction amounts.
Trip Array Links:
Trip Array Type
Links
Outbound Home-based Work (OHBW)
hw3_2.xls#OHBW_TA
Outbound Home-based School (OHBS)
hw3_2.xls#OHBS_TA
Outbound Home-based Shop/Recreate/Other
(OHBSDR)
hw3_2.xls#OHBSDR_TA
Inbound Home-based Work (IHBW)
hw3_2.xls#IHBW_TA
Inbound Home-based School (IHBS)
hw3_2.xls#IHBS_TA
Inbound Home-based Shop/Recreate/Other (IHBSDR)
hw3_2.xls#IHBSDR_TA
Work-based Non-home (WBNH)
hw3_2.xls#WBNH_TA
School-based Non-home (SBNH)
hw3_2.xls#SBNH_TA
Shop/Recreate/Other based Non-home (NHBSR)
hw3_2.xls#NHBSR_TA
11
Summary of Trip demand:
Cumulative Trip-Distance Charts:
Home  Work
Cumulative Trip Density
1.00
0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
0.00
5.00
10.00
15.00
20.00
Trip Distance (Miles)
Home  School
OBHSt Trip Density
1
0.9
0.8
0.7
0.6
Trips 0.5
0.4
0.3
0.2
0.1
0
0
2
4
6
8
10
12
14
Distance (miles)
Home  Other
12
Cumulative Trip Density
1.00
0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
Trip Distance (Miles)
Work  Home
Cumulative Trip Density
1.0
0.8
0.6
0.4
0.2
0.0
0.0
5.0
10.0
15.0
20.0
Trip Distance (Miles)
Work  Other
13
Cumulative Trip Density
1.00
0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
0.0
5.0
10.0
15.0
Trip Distance (Miles)
School  Home
Cumulative Trip Density
1.00
0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
Trip Distance (Miles)
School  Other
14
Cumulative Trip Density
1.00
0.80
0.60
0.40
0.20
0.00
0.00
5.00
10.00
15.00
Trip Distance (Miles)
Other  Home
Cumulative Trip Density
1.00
0.80
0.60
0.40
0.20
0.00
0.0
5.0
10.0
15.0
20.0
Trip Distance (Miles)
Other  Other
15
Cumulative Trip Density
1.00
0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
0
5
10
15
Trip Distance (Miles)
Cumulative Trip Density
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
Trip Distance (Miles)
Non-home-based Other
Non-home-based work
Non-home-based school
Inbound Home-based other
Outbound Home-based other
Outbound home-based work
Inbound home-based work
Inbound home-based school
Outbound home-based school
The trip density graphs varied from concave to S-curve shapes. The School  Home and Home  School
plots were concave and had the most linear appearance. Home  Other, Other  Home, and Other  Other
were clearly concave as well, with the sharpest increases on the left side f the graphs. Finally, Home  Work,
Work  Home, Work  Other, and School  Other were S-curve shaped, meaning the plot was first convex
16
and then concave. School  Other had the least consistent growth, as it appeared to have convex ridges. Most of
the plot appeared quite shaky before the 5-mile trip distance mark.
PTM = PersonTripMiles
PT = PersonTrips
Outbound
Homebased
Work
PT
PT
M
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
0
704
15287
36088
20734
12206
9379
9484
8750
4487
2516
7013
302
1558
464
2
14
Outbound
Homebased
School
PT
PT
M
0
1
2
3
4
5
6
7
8
9
10
11
12
13
0
1162
5556
9242
2659
7002
5944
4792
3334
4395
2885
1491
2441
1301
Outbound
Home-based
Shop/recreat
e/other
PTM PT
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
0
8211
25069
15963
15881
32973
15596
11776
10247
6495
5538
1311
1551
638
1019
45
320
Inbound
Home-based
Work
Inbound
Home-based
School
PTM
PTM
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
PT
0
352
7643
17599
9350
7469
4731
4509
4419
2311
1257
2779
871
792
232
1
7
0
1
2
3
4
5
6
7
8
9
10
11
12
13
PT
0
813
3889
3055
5275
4901
4160
3354
2325
3085
2019
1044
1709
911
Inbound
Home-based
Shop/recreate/
other
PTM
PT
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
0
12705
39383
24522
24804
51081
23981
18050
15697
9917
8515
2018
2374
948
1484
65
472
Non-homebased School
Non-homebased Work
PTM
PTM
0
1
2
3
4
5
6
7
8
9
10
11
12
13
PT
0
1100
1873
1774
5513
1680
1572
990
1498
58
106
84
135
5
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Non-homebased
Shop/recreate/
other
PTM
PT
PT
0
3879
12746
17841
11551
8366
2255
3567
2051
716
1275
399
67
94
121
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Person Trip Length Distribution Analysis:
Note: There are two plots for each trip type; the top graphs (number of trips at each trip distance) are simply
reference, while the bottom graphs (scatter plots for which each point is a value for one TAZ) are the actual graphs
that we are comparing and contrasting in turn.
H->W:
17
0
48188
35606
26584
16489
3601
3046
17675
926
1178
324
389
239
7
15
Number of Trips
Person Trip Length Distribution
40000
35000
30000
25000
20000
15000
10000
5000
0
-5000 0
5
10
15
20
Trip Distance (Miles)
For home-based work trips, we see a possible s curve effect. For the lower trip lengths, there are no places of work
near the home, while for the higher distances we see the effects of the gravity model. We see an almost linear
growth in number of trips in the middle of the graph (trip length 3-5 miles), which is likely due to the way our city
was zoned; areas with many jobs tend to be 3-5 miles from residential areas.
H->S
18
Number of Trips
Person Trip Length Distribution
10000
9000
8000
7000
6000
5000
4000
3000
2000
1000
0
0
2
4
6
8
10
12
14
Trip Distance (Miles)
For the home-based school trips, we see a relatively flat relationship between the trip length and the number of trips.
This is likely due to our city’s layout, where trip distances are increased if the origination and destination are on
different sides of the river. Through the gravity model, this keeps children heavily clustered at nearby schools, and
so this plot reflects the distance from homes to schools.
H->Other
19
Person Trip Length Distribution
35000
Number of Trips
30000
25000
20000
15000
10000
5000
0
0
5
10
15
20
Trip Distance (Miles)
Again, for home-based other trips we see an almost linear relationship between trip length and number of trips.
Noting the scale of the x axis, we see that there are very few long distance trips in this category, when compared to
other home-based categories. The linear effect again likely comes from the positioning of our zones in which the
largest attractions tend to be the farthest from residential areas.
W->H
20
Number of Trips
Person Trip Length Distribution
20000
18000
16000
14000
12000
10000
8000
6000
4000
2000
0
-2000 0
5
10
15
20
Trip Distance (Miles)
See notes on H->W distribution.
W->Other
21
Number of Trips
Person Trip Length Distribution
20000
18000
16000
14000
12000
10000
8000
6000
4000
2000
0
0
5
10
15
Trip Distance (Miles)
Work-based other trips provides one of the most interesting distributions, with a great deal more data points to
observe. We see many points with low numbers of trips, reflecting the many workplaces which employ small
numbers of workers. These trip lengths tend to be lower, and we do not see any of the linear relationships of other
plots. This seems logical, since post-work trips to shopping and recreation tend to be limited to small distances from
the workplace.
S->H
22
Person Trip Length Distribution
6000
Number of Trips
5000
4000
3000
2000
1000
0
0
2
4
6
8
10
12
14
Trip Distance (Miles)
See notes on H->S distribution.
S->Other
23
Person Trip Length Distribution
6000
Number of Trips
5000
4000
3000
2000
1000
0
-1000
0
2
4
6
8
10
12
14
Trip Distance (Miles)
For school-based other trips, we see a reappearance of the concave shape of the plot, which likely comes from the
gravity model. We have relatively few nonzero data points, since there are few schools in the city. Like the workbased other trips, we see very low trip lengths, as individuals tend to choose their destination based on distance.
Other->H
24
Person Trip Length Distribution
60000
Number of Trips
50000
40000
30000
20000
10000
0
0
5
10
15
20
Trip Distance (Miles)
For other-based home trips, we see the linear pattern again. This seems to be possibly related to the work-based
other and school-based other trips, which bring people further away from their houses. This has a steeper slope than
home-based other trips, which confirms that observation. Still, we see similar effects, likely because our largest
other attractions are far away from the residential areas.
Other->Other
25
Person Trip Length Distribution
60000
Number of Trips
50000
40000
30000
20000
10000
0
-10000
0
5
10
15
Trip Distance (Miles)
Other-based other trips show a great deal of noise, with a possible slight downward slope. These trips tend to be
very small (smaller than almost any other trips), with shorter trip distances generally favored over trips. Again, this
likely comes from the map layout, in which we cluster many of the shopping and recreation areas near each other.
This leads to very few long distance other-other trips being made.
26
Home-Based Work Transportation Demand Implications of Different Trip Distribution Behaviors :
Re-running Home-Based Work Gravity Model by replacing the 1/D^2 with 1/D (inverse distance):
Person Trip Length Distribution for
1/D
30000
Number of Trips
25000
20000
15000
10000
5000
0
-5000
0
5
10
15
20
Trip Distance (Miles)
Cumulative Trip Density for 1/D
1.00
0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
0.00
5.00
10.00
15.00
20.00
Trip Distance (Miles)
Re-running Home-Based Work Gravity Model by replacing the 1/D^2 with 1/sqrt(D):
27
Cumulative Trip Density for
1/sqrt(D)
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0
5.0
10.0
15.0
20.0
Trip Distance (Miles)
Number of Trips
Person Trip Length Distribution for
1/D
18000.0
16000.0
14000.0
12000.0
10000.0
8000.0
6000.0
4000.0
2000.0
0.0
-2000.0 0
5
10
15
20
Trip Distance (Miles)
Comparison with 1/D^2 Gravity Model:
Legend:
1/D^2
1/D
1/sqrt(D)
The overall shape of the Person Trip Length Distribution graphs for the 3 different trip distribution behaviors look
very similar. However, the trip distribution using the 1/D^2 relationship has comparatively higher values for the
total number of trips at a certain trip distance (in miles) than the trip distribution using the 1/D relationship.
28
Similarly, the trip distribution using the 1/D relationship has comparatively higher values for the total number of
trips at a certain trip distance (in miles) than the trip distribution using the 1/sqrt(D) relationship. However, this
analysis only remains true until the trip distance reaches approximately 4.5 miles. At this point, the relationships
invert. Now, the trip distribution using the 1/sqrt(D) relationship has comparatively higher values for the total
number of trips at a certain trip distance (in miles) than the trip distribution using the 1/D relationship. Similarly, the
trip distribution using the 1/D relationship has comparatively higher values for the total number of trips at a certain
trip distance (in miles) than the trip distribution using the 1/sqrt(D) relationship. Thus, something interesting
happens at the point when the trip distance reaches approximately 4.5 miles. Before 4.5 miles, the 1/D^2 trip
distribution model has a larger number of trips than the 1/D trip distribution model, and the 1/D trip distribution
model has a larger number of trips than the 1/sqrt(D) trip distribution model. After 4.5 miles, the relationships are
reversed.
This observation may be contributed to the friction factor F, which describes the amount of effort need to travel
from one location to another location. As the denominator of F increases(from sqrt(D) to D to D^2), F decreases in
magnitude as a result of its inverse relationship with distance. The observations made seem to show that as as the
denominator of F increases, people tend to make a less trips of smaller distance and more trips of longer distances.
Cumulative Trip Density for H->W Trip
1.0
0.9
0.8
Density
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
Trip Distance (Miles)
29
Person Trip Length Distribution for H->W Trip
40000.0
35000.0
30000.0
Number of Trips
25000.0
20000.0
15000.0
10000.0
5000.0
0.0
0
-5000.0
2
4
6
8
10
12
14
16
Trip Distance (Miles)
30