October 26, 2012
ORF 467

Land Use Characteristics
Land use distribution
Map/Summary Tables
Demographics and Quality of Life
Demand for Transportation
Trip Generation
Table of Contents
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
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
3
7
7
11

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
6.7
4.49%
6.54%
7
2.4
2.3
3.2
6.84%
2.34%
2.25%
3.13%
2.5
5
7.6
8.4
9.4
2
16.6
15.2
4.9
2.2
2.4
1.95%
16.21%
14.84%
4.79%
2.15%
2.34%
2.44%
4.88%
7.42%
8.20%
9.18%
102.4
100.00%
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
Total land
Undeveloped Space
Developed Space
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.
20
21
22
23
16
17
18
19
10
11
12
13
14
15
24
25
26
27
28
29
30
31
32
5
6
7
8
9
3
4
1
2
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
1
14
42
15 43
16 17
13
2 3 18 19 40 41
44 46 45
20 21
4 61
5 6
7
8
23
62
22
24 25
26
27
38
37
39
36
35
52
50
51
47
46
49
48
53 54
55
34 57 56
29 28
9 10
11
30
30
31
30
33
58
59 60
32
12 59
59
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
20
21
22
23
16
17
18
19
10
11
12
13
14
15
24
25
26
27
28
29
30
31
32
5
6
7
8
9
3
4
1
2
168
152
32
22
25
24
20
67
70
24
21
49
50
76
84
94
46
1024
KEY
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

Demographics
Residential
Light residential
Medium residential
Large residential
Very large residential
Total
Employment
Commercial
Light Manufacturing
Heavy manufacturing
Agriculture
Public office
Recreational
Restaurants
Theme park
Educational
Hotels
Transportational center
Total
Residential Capacity
25000
58900
73500
94000
251400
6900
40200
63000
720
1150
1600
1000
12250
1760
1440
2500
132520
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.
Children under 5
Students (5 - 20 year olds)
Workers (21-66 year olds)
Elderly (66+ year olds) & unemployed
Total
20,000
60,000
132,520
37,480
250,000

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 Type
3 elementary + middle
16 high school (vocational)
22 elementary + middle
28 university
53 high school
Area (sq. mi.) % of Land
0.6
0.2
0.3
0.6
0.5
Total
0.59%
0.20%
0.29%
0.59%
0.49%
Enrollment
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.

Zone Summary Chart
Zone Type river
1 open space
2 recreational (movie theater)
3 educational (elementary & middle)
4 light residential
5 commercial (strip malls)
6 heavy manufacturing
7 agriculture
8 light manufacturing
9 medium residential
10 commercial (individual stores)
11 restaurant
12 open space
13 open space
14 heavy manufacturing
15 public
16 educational (vocational high school)
17 restaurant
18 commercial (individual stores)
19 medium residential
20 medium residential
21 recreational (sports std.,golf course,etc.)
22 educational (elementary & middle)
23 open space
24 commercial (mall)
25 heavy manufacturing
26 water
27 heavy manufacturing
28 educational (university)
29 public
30 large residential
31 commercial (strip malls)
32 very large residential
33 medium residential
34 light manufacturing
35 recreational (movie theater,stage plays,etc.)
36 hotel
37 restaurant
38 commercial (upscale stores)
39 theme park
40 commercial (theme park related / mall)
41 restaurant
42 light residential
43 open space
44 water
45 very large residential
46 large residential
47 open space
48 light manufacturing
49 commercial (outlets and big box stores)
50 public
51 transportation
52 commercial (mall)
53 educational (high school)
54 very large residential
55 water
56 open space
57 public
58 restaurant
59 large residential
60 open space
61 hotel
62 open space
30
32
7
30
24
10
4
2
49
4
2
6
4
24
6
39
25
12
8
15
20
3
16
28
9
6
8
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
4
6
20
4
4
24
25
3.0
0.4
0.6
2.0
0.4
0.4
2.4
2.5
2.93%
0.39%
0.59%
1.95%
0.39%
0.39%
2.34%
2.44%
3
1
4
3
1
3
3
3
3
7
12
10
13
13
17
23
0
0
15000
0
0
0
0
0
0
0
0
0
0.16
0.28
0
2.3
6
2
2
4
8
28
4
6
8
10
30
2.8
0.4
0.6
0.8
1.0
3.0
0.6
0.2
0.2
0.4
0.8
2.73%
0.39%
0.59%
0.78%
0.98%
2.93%
0.59%
0.20%
0.20%
0.39%
0.78%
3
5
5
6
22
15
11
10
11
9
12
29
31
29
31
6
3
3
5
5
7
6
0
0
0
0
0
0
0
6000
0
0
0
0
0.2
0.45
0
0
2.8
0
0
0.1
0.2
0
25
25
9
6
36
12
14
20
6
30
6
4
25
10
5
25
1.5
2.0
0.3
0.9
0.6
0.8
1.6
2.8
0.6
0.4
2.4
0.6
3.9
2.5
1.2
0.8
1.0
0.4
0.2
4.9
0.4
0.2
3.0
3.2
0.7
3.0
2.4
0.6
3.0
0.6
0.4
2.5
1.0
0.5
2.5
2.5
2.5
0.9
0.6
3.6
1.2
1.4
2.0
1.46%
1.95%
0.29%
0.88%
0.59%
0.78%
1.56%
2.73%
0.59%
0.39%
2.34%
0.59%
3.81%
2.44%
1.17%
0.78%
0.98%
0.39%
0.20%
4.79%
0.39%
0.20%
2.93%
3.13%
0.68%
2.93%
2.34%
0.59%
2.93%
0.59%
0.39%
2.44%
0.98%
0.49%
2.44%
2.44%
2.44%
0.88%
0.59%
3.52%
1.17%
1.37%
1.95%
9
12
12
10
12
14
15
13
13
10
13
16
18
20
18
18
20
16
16
20
17
19
21
28
24
30
26
26
30
26
23
24
20
27
30
30
25
21
23
27
31
15
11
11
10
13
15
15
14
18
22
25
25
28
25
31
27
22
18
15
15
13
11
6
7
3
2
11
8
8
13
13
15
15
19
19
19
19
24
24
23
28
29
29
9
18
0
0
9000
0
0
0
0
0
18000
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
12000
0
0
0
0
0
0
0
0
0
0
2.6
0.39
0
0
0.8
0
0
0
0
0
0.4
0
0
0
0
0
0.24
0.1
0
0.28
0.1
0
0
0
0
0
0.24
0
0
0.8
0
0
0
0
0
0.36
0.6
0
2.4
0
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.

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 commercial light Manufacturing heavy manufacturing agriculture public recreational restaurants theme park educational hotels transportation
Total
Total area (sq. miles) Population / Sq. mile Employment Capacity
4.6
1500 6900
6.7
7
6000
9000
40200
63000
2.4
2.3
3.2
300
500
500
720
1150
1600
2
4.9
2.2
2.4
2.5
500
2500
800
600
1000
1000
12250
1760
1440
2500
132520

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
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
58900
73500
1500
3000
4500
1200
1800
1800
900
1800
2700
3600
5400
5400
1200
2400
3600
94000 6000 1200 3600 3600 4800
Education Zoning:
Zone Type
3 elementary + middle
16 high school (vocational)
22 elementary + middle
28 university
53 high school
Area (sq. mi.)% of total land Enrollment
0.6
0.59% 15000
0.2
0.3
0.20%
0.29%
6000
9000
0.6
0.5
0.59%
0.49%
18000
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
6,000.00
9,000.00
300.00
500.00
500.00
500.00
2500
800
600
1000
6,900.00
40,200.00
63,000.00
720.00
1,150.00
1,600.00
1000
12250
1760
1440
2500
25.0
0.1
0.1
0.1
3.0
25.6
20.0
19.0
1.0
0.1
6.0

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
Outbound Homebased Work
(OHBW)
Outbound Homebased School
(OHBS)
Outbound Homebased
Shop/Recreate/Other
(OHBSDR)
60000
154260
Inbound Home-based
Work (IHBW)
Productions per Zone
132520
66260
Attractions per Zone
Comments
132520 Total # of jobs (or total # of workers)
60000
154260
66260
Total # of enrolled students
Assumed that the 37480 elderly and umemployed population would make approximately 4 trips on average per person
50% of Outbound home-based work
Links hw3_2.xls#OHBW_P_A_arrays hw3_2.xls#OHBS_P_A_arrays hw3_2.xls#OHBSDR_P_A_arrays hw3_2.xls#IHBW_P_A_arrays
42000 Inbound Home-based
School (IHBS)
42000
Inbound Home-based
Shop/Recreate/Other
(IHBSDR)
Work-based Nonhome (WBNH)
238520
66260
School-based Nonhome (SBNH)
18000
238520
66260
18000
70% of Outbound home-based school
IHBSDR = OHBSDR +
OHBW – IHBW + OHBS –
IHBS
50% of Outbound home-based school hw3_2.xls#IHBS_P_A_arrays hw3_2.xls#IHBSDR_P_A_arrays hw3_2.xls#WBNH_P_A_arrays
30% of Outbound home-based school hw3_2.xls#SBNH_P_A_arrays

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

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:
𝑇 𝑖𝑗
= 𝑃 𝑖
𝐴 𝑗
𝐹 𝑖𝑗
∗
∑ 𝑧𝑜𝑛𝑒𝑠
𝐴 𝑗
𝐹 𝑖𝑗
𝑤ℎ𝑒𝑟𝑒 𝐹 𝑖𝑗
=
1
𝐷 2 𝑖𝑗
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)
Outbound Home-based Shop/Recreate/Other
(OHBSDR)
Inbound Home-based Work (IHBW) hw3_2.xls#OHBS_TA hw3_2.xls#OHBSDR_TA 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)
School-based Non-home (SBNH)
Shop/Recreate/Other based Non-home (NHBSR) hw3_2.xls#WBNH_TA hw3_2.xls#SBNH_TA hw3_2.xls#NHBSR_TA

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
Trip Distance (Miles)
15.00
20.00
Home

School
Trips
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 2
OBHSt Trip Density
4 6 8
Distance (miles)
10 12 14
Home

Other

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
Trip Distance (Miles)
12.0
14.0
16.0
Work

Home
1.0
0.8
0.6
0.4
0.2
0.0
0.0
Cumulative Trip Density
5.0
10.0
Trip Distance (Miles)
15.0
Work

Other
20.0

1.00
0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
0.0
Cumulative Trip Density
5.0
10.0
Trip Distance (Miles)
15.0
School

Home
1.00
0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
0.0
School

Other
2.0
Cumulative Trip Density
4.0
6.0
8.0
Trip Distance (Miles)
10.0
12.0
14.0

1.00
0.80
0.60
0.40
0.20
0.00
0.00
Cumulative Trip Density
5.00
10.00
Trip Distance (Miles)
Other

Home
1.00
0.80
0.60
0.40
0.20
0.00
0.0
Cumulative Trip Density
5.0
10.0
Trip Distance (Miles)
15.0
Other

Other
15.00
20.0

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
Trip Distance (Miles)
10 15
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
Trip Distance (Miles)
10.0
12.0
14.0
16.0
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

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
Outbound
Homebased
School
Outbound
Home-based
Shop/recreat e/other
PT
M
0 0
1 704
2 15287
3 36088
4 20734
5 12206
6 9379
7 9484
8 8750
9 4487
10 2516
11 7013
12 302
13 1558
14 464
15
16
2
14
PT PT PT PTM PT
M
0 0
1 1162
2 5556
3 9242
4 2659
5 7002
6 5944
7 4792
8 3334
9 4395
10 2885
11 1491
12 2441
13 1301
9
10
11
12
13
14
15
16
5
6
7
8
3
4
0
1
2
6495
5538
1311
1551
638
1019
45
320
0
8211
25069
15963
15881
32973
15596
11776
10247
Inbound
Home-based
Work
PTM PT
0
352
7643
17599
9350
7469
4731
4509
4419
2311
1257
2779
871
792
232
1
7
9
10
11
12
6
7
8
3
4
5
0
1
2
13
14
15
16
Inbound
Home-based
School
PTM
10
11
8
9
12
13
6
7
4
5
2
3
0
1
PT
0
813
3889
3055
5275
4901
4160
3354
2325
3085
2019
1044
1709
911
Inbound
Home-based
Shop/recreate/ other
PTM
9
10
7
8
5
6
2
3
0
1
4
11
12
13
14
15
16
PT
0
12705
39383
24522
24804
51081
23981
18050
15697
9917
8515
2018
2374
948
1484
65
472
Non-homebased School
PTM
0
1
2 1873
3 1774
4
5 1680
6 1572
7
8 1498
9
10
11
12
13
PT
0
1100
5513
990
58
106
84
135
5
Non-homebased Work
PTM PT
0 0
1 3879
2 12746
3 17841
4 11551
5 8366
6 2255
7 3567
8 2051
9 716
10 1275
11
12
399
67
13
14
94
121
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:
Non-homebased
Shop/recreate/ other
PTM PT
10
11
8
9
12
13
14
0 0
1 48188
2 35606
3 26584
4 16489
5 3601
6 3046
7 17675
926
1178
324
389
239
7
15

Person Trip Length Distribution
40000
35000
30000
25000
20000
15000
10000
5000
0
-5000 0 5 10
Trip Distance (Miles)
15 20
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

Person Trip Length Distribution
10000
9000
8000
7000
6000
5000
4000
3000
2000
1000
0
0 2 4 6 8
Trip Distance (Miles)
10 12 14
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

Person Trip Length Distribution
35000
30000
25000
20000
15000
10000
5000
0
0 5 10
Trip Distance (Miles)
15 20
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

Person Trip Length Distribution
20000
18000
16000
14000
12000
10000
8000
6000
4000
2000
0
-2000 0 5 10
Trip Distance (Miles)
15 20
See notes on H->W distribution.
W->Other

Person Trip Length Distribution
20000
18000
16000
14000
12000
10000
8000
6000
4000
2000
0
0 5
Trip Distance (Miles)
10 15
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

Person Trip Length Distribution
6000
5000
4000
3000
2000
1000
0
0 2 4 6 8
Trip Distance (Miles)
10 12 14
See notes on H->S distribution.
S->Other

Person Trip Length Distribution
6000
5000
4000
3000
2000
1000
0
-1000
0 2 4 6 8
Trip Distance (Miles)
10 12 14
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

Person Trip Length Distribution
60000
50000
40000
30000
20000
10000
0
0 5 10
Trip Distance (Miles)
15 20
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

Person Trip Length Distribution
60000
50000
40000
30000
20000
10000
0
-10000
0 5
Trip Distance (Miles)
10 15
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.

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):
30000
Person Trip Length Distribution for
25000
20000
15000
10000
5000
0
-5000
0 5 10
Trip Distance (Miles)
15 20
1.00
0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
0.00
Cumulative Trip Density for 1/D
5.00
10.00
Trip Distance (Miles)
15.00
20.00
Re-running Home-Based Work Gravity Model by replacing the 1/D^2 with 1/sqrt(D):

0.6
0.5
0.4
0.3
0.2
0.1
1.0
0.9
0.8
0.7
0.0
0.0
Cumulative Trip Density for
1/sqrt(D)
5.0
10.0
Trip Distance (Miles)
15.0
20.0
18000.0
16000.0
14000.0
12000.0
10000.0
8000.0
6000.0
4000.0
2000.0
0.0
-2000.0
Person Trip Length Distribution for
0 5 10 15
Trip Distance (Miles)
20
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.

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.

40000.0
35000.0
30000.0
25000.0
20000.0
15000.0
10000.0
5000.0
0.0
-5000.0
0 2 4 6 8
Trip Distance (Miles)
10 12 14 16