alaink/Orf467F11/MyCityFinalRep… · Web viewThe gravity model also includes a “friction” factor that represents the disutility of travel; this friction factor is inversely proportional

H.M. Delgado-Medrano, N. Webb and T. Wenzlau

MyCity Project: Deliciousville10.25.11

The following document describes the MyCity traffic demand calculation project for the fictional city of Deliciousville. In sections one and two of this document we present information about the land use in Deliciousville and its demographic composition, respectively. In the third and fourth sections, we highlight the trip generation process and the trip distribution, along with some specific analyses of key transport statistics. Finally, the last section provides alternative scenarios where the friction factor is manipulated.

Deliciousville Land Use Characteristics

Deliciousville has a population of 250,000 and covers an area of 1024 square miles. Our population data is loosely based off of the population demographics for Plano, TX, a wealthy, thriving suburb of Dallas, Texas. Deliciousville is all this and more, adding a certain spark that cannot be found in the great lonely state of Texas, such as Deliciousville’s Center for the Arts and Opera House (not to mention our voluminous river!).

We divided our city into 70 rectangular TAZs, including water and undeveloped land. The bulk of our population (100,000) resides in mid-density housing on roughly 13% of the total land in Deliciousville. The largest single land use allocation (24.4% of total area) consists of low-density residential housing, dispersed mostly away from the center of the city, but conveniently served by educational centers and shopping/commercial districts. There are five large shopping districts dispersed throughout our city, each shopping district supporting shopping, dining and leisure activities. Other notable features of Delicousville are the three medical facilities, two government service centers (one conveniently located next to our financial district to ensure no foul play) and the College of Deliciousville (Go Yummies!!)!

Deliciousville is proud of the fact that roughly thirty percent of its land use is devoted to undeveloped space, protected bodies of water and spaces for parks and recreation. We find it important to maintain undeveloped land because it provides the opportunity for growth and also maintains a good balance with our natural surroundings. Also, having parks, a protected riverfront and lakes creates a nice contrast to the fully commercialized and energetic Downtown. Deliciousville is an attractive city, creating demand through its beautiful parks and lakes, but also through its bustling financial district, supported by various means of transportation, including our international airport. Financial and high-density residential areas occupy the desirable real estate along the central waterfront and the river also serves to support our heavy industries, which are on the outskirts of the city.

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Map of Deliciousville

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Deliciousville Demographics

The bulk of our population is between the ages 22-64. As mentioned earlier, the population percentages roughly follow the population percentages of Plano, Texas. Deliciousville mainly appeals to young, working adults with children in school. The demand for this working-age population is driven by the need to supply employees to the booming financial, trade and manufacturing industries that contribute to a large portion of the economy. As people get older and leave the workforce at age 65, they typically move away from Deliciousville (generally to warmer climes), which accounts for the relatively small percentage of people age 65 and older.

Population: % of PopulationUnder 5 4.40%Students 28.00%Workers 60.00%Non-working/Elderly 7.60%

We broke down the students into two categories, those in primary and secondary schools and those in the university. We assumed that the university does not provide housing for the students and that the students live in the residential areas. Thus, the total number of students is the sum of the population between ages 5 and 18, plus the population of college students. In Deliciousville, all residents are accounted for! Students are not allowed to play hooky and workers are not allowed to take vacations (luckily, nobody has any desire to leave Deliciousville)!

We further broke down employment into several categories. The largest sectors of the workforce are employed in professional and scientific careers and in educational, health and social services. This distribution of employment was created to most efficiently service the needs of Delicians. These percentages were computed over the entire workforce, 150,000 people.

Work: Employment share # employeesCommercial - Shopping & services 21.1% 31585Commercial - Restaurants 4.2% 6245Commercial - Leisure 1.2% 1784Commercial - Financial (CBD) 35.8% 53767Airport 2.7% 4099Medical facilities 4.3% 6510Light industries 4.3% 6389Heavy industries 13.8% 20766

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Working-Age: 169,000In workforce (75% of those over 16) 150000Not in workforce 19000


Government 1.8% 2773Arts Facilities - Opera House, etc. 0.3% 446Teachers 10.1% 15190Parks, recreation 0.3% 446Total: 100% 150,000

Trip Generation

We created production and attraction arrays that were later used to calculate trips between Traffic Assignment Zones (TAZs). The sum of the productions is equal to the sum of the attractions, which shows that all people are accounted for (all that leave home, eventually return that same day). In the assignment, we created production and attraction arrays for the following trip purpose categories:

1) Home Based – Work2) Home Based – School3) Home Based – Shop/Dine/Recreation/Other4) Non-Home Based

1) Home Based – Work

All of the productions are created in the residential areas and the attractions are located in all zones except for residential, undeveloped land and water TAZs. Thus, the productions from non-residential TAZs and the attractions in residential TAZs are both equal to zero in this trip purpose category. To create the number of productions originating from the residential TAZs, we calculated the area of each TAZ along with the respective population density. From this, we calculated the population of each residential TAZ. Once we had the population of the TAZs, we calculated the number of employees that live in each zone by assuming that 60% of residents are workers. In total, there are 150,000 workers. We then distributed the employees over the non-residential TAZs following the employment distribution seen above; the employees who go to the educational zones are teachers. The productions and attractions for students are accounted for in a separate array. The production and attraction arrays are equal to each other, which means that all workers are employed and make it to work.

2) Home Based – School

This production and attraction array takes into account all of the students going to school. All of the productions originate in residential TAZs and all of the attractions are located in educational TAZs; attractions in all other TAZs are equal to zero. We applied the demographic profile assumption that 28% of the population consists of students in order to calculate the number of students that live in each residential TAZ. In total, we have 68,850 students. We then distributed the students over the

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schools with respect to the size of each school. The production and attraction arrays each sum up to 68,850, showing that all students make it to class.

3) Home Based – Shop/Dine/Recreation/Other

This category takes into account all of the trips from home to the commercial districts. To create the productions array, we used the following formula: 1.5*(#21-64 non-workers + #0ver 64) + 0.3*School kids + 0.5* workers) from the population of each residential TAZ. We used the population demographics to come up with the number of workers, non-workers and residents over 64 years of age and students for each TAZ. To create the attractions array, we distributed the productions over the commercial, leisure, dining, recreation, shopping and park TAZs according to their relative draw (e.g. more people go shopping than to government offices) and the relative area of the zones.

4) Non-Home Based

We split Non-Home Based productions and attractions into three categories. The first category is “Work-based – Non-Home”, which consists of the trips taken by workers who go shopping or to recreational activities after work. We assumed that 50% of employees in each work TAZ make non-home trip after work. We distributed the number of workers who make these after-work trips over the shopping/leisure/parks and recreation TAZs in the attraction array based on the relative draw of the TAZs and their relative area. Secondly, we created production and attraction arrays for students who do not come home after school, but make a trip to go shopping, etc. We assumed that 40% of students make such a trip and the students are distributed over the shopping/dining/etc. TAZs based on TAZ draw and relative area. Lastly, we also created a production and attraction array for inhabitants that go shopping, etc. and then decide to go to another shopping/recreational venue. Most of us are likely guilty of partaking in such delightful trips, especially those who live in Deliciousville.

The Production and Attraction Vectors can be found in the attached file Deliciousville – Master.xlsx under the P&A Arrays tab.

Each of the above production and attraction arrays deals with outbound trips only. To account for inbound trips from work to home, we assumed that only 50% of employees return home after work. Thus, to find the number of work-to-home trips, we transposed the Home Based – Work trip matrix and multiplied it by a factor of 0.5. Similarly, to account for students coming home after school, we assumed that 60% of students came home directly and so transposed the Home Based - School trip matrix and multiplied it by 0.6. The calculation for people returning home from shopping takes into account the people that go shopping and return home, plus the people that go shopping after school and work.

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Trip Distribution

Overview

We used the gravity model in order to determine from what origins and to what destinations the residents of Deliciousville travel on an average day. The gravity model posits that the number of trips between any given origin and destination is proportional to the number of trips productions in the origin and the number of attractions in the destination relative to the total attractions in the city. The gravity model also includes a “friction” factor that represents the disutility of travel; this friction factor is inversely proportional to distance, so that the residents of Deliciousville are less attracted to destinations that are further away. Finally, there is an optional adjustment or “fudge” factor, K ij, that is used to take into account other characteristics of the TAZ’s that might affect trip distribution. In our analysis, we assume K ij=1. The model is summarized by the following equation:

T ij=PiA jF ijK ij

∑j=1

n

A jF ijK ij

Where:

T ij=¿ Number of actual trips between origin TAZ i and destination TAZ jPi=¿ Number of trip productions in origin TAZ iA j=¿ Number of trip attractions in destination TAZ jF ij=¿ Friction factor (travel disutility) between origin TAZ i and destination TAZ jK ij=¿ Optional adjustment factor between origin TAZ i and destination TAZ j

To carry out the distribution of trips for each trip purpose within the city, we separated the gravity model equation into its parts and created all of the matrices and vectors necessary to create the trip array matrix, T, for any given trip purpose. The components used for this purpose were: the production and attraction vectors for each TAZ, P and Ainput , the distance matrix, D, the friction factor matrix, F, the

vectors Sum and P/Sum, representing ∑j=1

n

A j Fij and P/∑j=1

n

A jF ij, respectively, and the

PA/Sum matrix, obtained by multiplying the P/Sum vector by the transpose of Ainput .

After having created the P and Ainput vectors for each trip purpose in the trip generation component of the exercise, we computed the distance matrix, D, which represents the distance between every origin TAZ i and destination TAZ j. To do this we calculated the centroid (X and Y coordinates) and area for each one of the TAZ’s. Because each pixel in our city has an area of 0.1 miles, in order to convert the coordinates from pixels to miles we multiplied all coordinates by the square root of 0.1. After computing and converting our centroids we calculated the Euclidean

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distance between the centroid of every TAZ pair and multiplied by a factor of 1.2, which has been shown to be a good estimate of circuity, thus accounting for the fact that people do not travel in straight lines always. For the distance traveled within TAZ’s we used half of the square root of the area of the TAZ after having converted area from pixels to miles by multiplying the pixels by 0.1. The D matrix employed for all trip purposes is the same, as the distance between any two points remains constant regardless of the trip purpose.

Second, we computed the friction factor F matrix, which represents the inverse of

the distance-squared between every origin TAZ i and destination TAZ j, (1D2

), for all

trip purposes, except for the “Other-Other” trip purpose category in which we used the inverse of the distance-cubed between every origin TAZ i and destination TAZ j,

(1D3

), in order to account for the lower utility of driving between two points within

the same TAZ; for instance, drivers are more reluctant to use their cars to travel from one store to another in the same shopping center than to drive from work to home.

Third, we computed the Sum vector by multiplying the F matrix by the Ainput vector and then created the P/Sum vector by dividing the P vector by the Sum vector.

Fourth, we multiplied the P/Sum vector by the transpose of the Ainput vector in order to create the PA/Sum matrix. Finally, we multiply the PA/Sum matrix by the F matrix in order to obtain our trip array matrix, T, for each trip purpose.

One major shortcoming of the gravity model is that when we sum the attractions within the trip array matrix across the rows, to obtain the Aoutput vector, the sums for each TAZ do not add up to the numbers estimated in the trip generation exercise, Ainput , which in this first iteration is equal to Ainput . In order to correct for this we multiply the vector Ainput by the adjustment factor of Adesired /Aoutput, where Aoutput is the incorrect A vector we obtain from the previous iteration, and obtain Anew . We then use Anew in a new iteration and repeat the process until the sum across the rows of the attractions for each TAZ are asymptotically close to the Adesired vector. Once we have arrived at those numbers, then we have finalized our outbound trip array.

We carried out this process six times to create six unique outbound trip arrays: Outbound Home-Based Work, Outbound Home-Based School, Outbound Home-Based Other (i.e. shopping/dining/recreation/services), Outbound Non-Home-Based Work-Other, Outbound Non-Home-Based School-Other, Outbound Non-Home-Based Other-Other. Rather than calculating the inbound trip arrays separately, for inbound trip array matrices we simply transposed the outbound trip array for a given trip purpose and multiplied by the appropriate factor. Specifically, for the Inbound Home-Based Work trip array we multiply the Outbound Home-Based Work trip array by a factor of 0.5; for the Inbound Home-Based School trip

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array we multiply the Outbound Home-Based School trip array by a factor of 0.6; and for the Inbound Home-Based Other trip array we multiply by a factor of 1.825, in order to take into account the people that go from Work and School to Other who must also eventually go back home.

Trip Arrays

All of the arrays can be found in the Excel spreadsheet titled “Deliciousville – Master.xlsx”:

- Outbound Home-Based Work: see “HB – Work – Outbound” tab- Outbound Home-Based School: see “HB – S – Outbound” tab- Outbound Home-Based Other: see “HB – Other – Outbound” tab- Outbound Non-Home-Based Work-Other: see “WB – Other” tab- Outbound Non-Home-Based School-Other: see “SB – Other” tab- Outbound Non-Home-Based Other-Other: see “Other-Other” tab- Inbound Home-Based Work: see “HB – Work – Inbound” tab- Inbound Home-Based School: see “HB – S – Inbound” tab- Inbound Home-Based Other: see “HB – Other – Inbound” tab

Trip Demand Summary

Total Trips

In total, there are 839,341 one-way trips in Deliciousville every day for a population of 250,000 individuals. Thus, on average, Delicians make 3.36 trips per day. The distribution of these trips by trip purpose is as follows:

- Outbound Home-Based Work – 150,000 trips- Outbound Home-Based School – 68,850 trips- Outbound Home-Based Other – 124,155 trips- Outbound Non-Home-Based Work-Other – 75,000 trips- Outbound Non-Home-Based School-Other – 27,540 trips- Outbound Non-Home-Based Other-Other – 50,904 trips- Inbound Home-Based Work – 75,000 trips- Inbound Home-Based School – 41,310 trips- Inbound Home-Based Other – 226,583 trips

Total Trip Miles

In total, Delicians travel 3,066,398 miles every day. On average, each Delician travels 12.27 miles per day. The distribution of these miles by trip purpose is:

- Outbound Home-Based Work – 542,187 mi- Outbound Home-Based School –278,548 mi - Outbound Home-Based Other – 506,585 mi

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- Outbound Non-Home-Based Work-Other – 234,119 mi- Outbound Non-Home-Based School-Other – 134,114 mi- Outbound Non-Home-Based Other-Other – 8,106 mi- Inbound Home-Based Work – 271,093 mi - Inbound Home-Based School – 167,129 mi- Inbound Home-Based Other – 924,517 mi

Mean Miles Per Trip

On average, each trip is 3.65 miles long. The average trip distance by trip purpose is:

- Outbound Home-Based Work – 3.61 mi- Outbound Home-Based School – 4.05 mi- Outbound Home-Based Other – 4.08 mi- Outbound Non-Home-Based Work-Other – 3.12 mi - Outbound Non-Home-Based School-Other – 4.87 mi- Outbound Non-Home-Based Other-Other – 0.16 mi- Inbound Home-Based Work – 3.61 mi- Inbound Home-Based School – 4.05 mi- Inbound Home-Based Other – 4.08 mi

PersonTrips and PersonTripMiles

Below is a table of PersonTripMiles (broken into appropriate buckets) and PersonTrips by trip purpose, as well as cumulative trip-distance charts for each trip array (number of trips on the Y axis vs. miles travelled on the X axis).

PTM: PT H->W:

PT W->H:

PT H->S:

PT S->H:

PT H->Other:

PT Other->H:

PT WB->Other:

PT SB->Other:

PT Other->Other:

Total:

0-1 1637 819 0 0 1202 2194 22221 0 50875 78,9481-2 26169 13085 13311 7987 16902 30847 11532 7567 15 127,4142-3 45678 22839 16473 9884 30772 56159 5999 2990 1 190,7943-4 23427 11714 9795 5877 20834 38022 7987 3283 6 120,9444-5 19618 9809 6654 3992 14142 25809 8500 3108 2 91,6345-6 16748 8374 6528 3917 19346 35306 11351 1497 1 103,0686-7 6606 3303 5649 3390 7984 14571 1618 1932 1 45,0547-8 3880 1940 6260 3756 4798 8756 1311 903 1 31,6038-9 2288 1144 2637 1582 3184 5812 1648 1858 0 20,1529-10 2097 1049 210 126 2177 3974 986 1221 0 11,84010-11 1042 521 1334 801 1961 3579 145 1941 0 11,32511-12 536 268 0 0 594 1084 0 323 0 2,80512-13 272 136 0 0 258 471 0 918 0 2,055Total: 150,00 75,000 68,850 41,310 124,155 226,583 73,297 27,540 50,904 837,639

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Cumulative Charts

In the following cumulative charts, we can see that with the steep initial rise in the graph for home to work and visa-versa, people tend to live close to work and so there is a high demand for short trips for this trip purpose type. There is a similar initial rise in home to school and back, though it appears that the trip distances are a bit further than the commute to work. Home to shopping/recreation and back also has a higher demand for shorter trip lengths. Trips from work to shopping and from one shopping/recreation venue to another start out with a very high demand for short trips, and there is a lower demand for longer trips.

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Person Trip Length Distribution Analysis

The following charts show the one-way person trip length distribution for each of the trip arrays. With regards to Outbound and Inbound Home-Based Work trips, we see that the length of the majority (63.5%) of person trips ranges between 1.0 and 4.0 miles, with a sharp drop thereafter; the peak in this distribution is between the 2.0 and 3.0-mile mark. This suggests that most people work relatively close to home, as would be expected since people either choose jobs close to home or relocate in order to be closer to home.

As for the Outbound and Inbound Home-Based School trips, we once again see a strong concentration of trip length between 1.0 and 4.0 miles, while the peak in this distribution is between the 2.0 and 3.0-mile mark. This suggests that most schoolchildren also live relatively close to the schools that they attend. Once again, this is to be expected as schoolchildren are generally sent to school at nearby institutions. We do not, however, see as sharp a drop in number of trips after the 4.0-mile mark than we do in the Home-Based Work trips distribution. This suggests that the proportion of schoolchildren that go to school beyond the 4.0-mile mark (42.5%) is greater than the proportion of adults who work beyond that threshold distance (35.4%). This may be due to the fact that the locus of jobs throughout the city is much more dispersed than are schools.

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The person trip length distribution for Outbound and Inbound Home-Based Other trips is almost entirely concentrated between 1.0 and 6.0 miles (82.2%), with two peaks, one between the 2.0 and 3.0-mile mark and a second smaller one between the 5.0 and 6.0-mile mark. This shows that most of the shopping, dining, recreation and services attractions are located within a range of 1.0 to 6.0 miles from residential areas. Regarding the second peak in particular, this concentration between the 5.0 and 6.0-mile mark may be due to some of the unique attractions such as the Arts Facility, Airport and Government Centers that draw people, but that due to their small number of facilities require some individuals to travel further than 5.0 miles.

Focusing on the trip length distribution of Non-Home-Based trips, we observe that the distributions are much more skewed towards shorter trips. In the case of Non-Home-Based Work-Other trips, we see that a large percentage (46%) of those trips are less than 2.0 miles in length. After the initial peak there is a strong drop and a second peak between the 5.0 and 6.0-mile mark. The concentration below the 2.0-mile mark suggests that individuals go shopping, dining, etc. not too far from work. Alternatively, the location of jobs and shopping and recreational opportunities are located relatively close. The second peak between the 5.0 and 6.0-mile mark also seems to point towards service-related activities that are located in unique locations, such as the Arts Facilities Opera House. Regarding Non-Home-Based School-Other trips, 61.5% of trips are between 1.0 and 5.0 miles long and we observe the largest peak between the 1.0 and 2.0-mile mark and no prominent secondary peak. This suggests that schools, which are fewer in number, are further, on average, from the recreational and service centers than are jobs.

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Finally, the person trip length distribution for Non-Home-Based Other-Other trips suggests that almost all (99.9%) of these trips are less than 1.0 mile. In fact, the average trip distance on this trip purpose segment is around 0.16 miles. This shows that most shopping, dining, recreation and services attractions are located relatively close to each other, so that, on average, the trip from one service or shopping center to another is short.

Friction Factor Tweaking

In the above calculations, we used a friction factor F equal to the inverse of the distance squared. If we change F’s relationship on distance, transportation demand is significantly impacted.

We reran the Gravity Model with F = 1/D and F = 1/√D for the Home Based – Work trip array. When we plot the Number of Trips vs. Trip Length with each variation of F superimposed on the same graph, we get the following results:

As F increases from 1/D^2 to 1/D to 1/√D, the Gravity Model gives a lower penalty on longer trips lengths. As we can see in the graph, when F = 1/D^2, there is a

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higher demand for shorter trips. As we progress to F = 1/√D, the distance does not matter as much and there is less demand (comparatively) for shorter trips, and increased comparative demand for medium-length trips. The same results can be seen in a cumulative graph below:

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alaink/Orf467F11/MyCityFinalRep… · Web viewThe gravity model also includes a “friction” factor that represents the disutility of travel; this friction factor is inversely proportional