Kristin Bergeson and Franklyn DarnisORF 46710/21/12

Final ReportWelcome to New Transportbury!

Land Use

The beautiful city of New Transportbury is divided into 67 Traffic Assignment Zones (TAZs). Nine of those zones are undeveloped: 11% of New Transportbury is comprised of rivers and lakes, while 30% is undeveloped land. These undeveloped areas keep the city looking idyllic, and also allow for the possibility of future expansion. Most of this undeveloped land is located on the outskirts of town, because the residential areas consume the prime real estate. New Transportbury’s unique features include a Costco, City Hall, a fire department, a performing arts centre, a zoo, a lush golf course, a multipurpose stadium, two hospitals, a widely-renowned public school system, and a conveniently located airport.

Roughly 30% of the city’s land is residential, including residential areas that cover a range of population densities. The least dense residential areas (“light residential”) are located on the outskirts of the city, and are mostly inhabited by elderly people and young families. Population density increases in the inner city, where the inhabitants of the residential TAZs are mostly workers, and where most of the city’s unemployed people live.

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Schools are located throughout the residential areas for easy commuting. The stadium is located in a high-population area for easy access and to increase demand. Office buildings and industry are located further from the central city, while recreation opportunities abound throughout New Transportbury. Three bridges connect the southern part of New Transportbury to the central city, reducing the cost of travel. Some commercial areas are very close to residential housing, while others are grouped in commercial blocks, making shopping convenient. Industry is located near water sources to provide hydroelectricity. The airport is located on the outskirts of town so that the airplane noise is not disruptive to any residents; its location near a bridge makes it reachable without difficulty.

Demographics

This first table displays the demographic breakdown of New Transportbury’sDid population. We break down the population between the six categories: Workers, Students, Home Workers, Elderly, Children, and Unemployed. These categories also translate roughly into age categories, as shown above. This is based on the assumption that all children between the ages of 6 and 17 attend school, and that all people that are at least 65 years old are retired. Since there is no university, all inhabitants enter the workforce after graduation (whether or not they can find a job is another question). The work capacity number is comprised of all those citizens who are of working age: 18-65. The ratio of males to females in New Transportbury is close to an even split: it is nearly 1:1 across all categories.

Above is New Transportbury’s student breakdown. Roughly half of the students are enrolled in public schools of some kind: each elementary school has a corresponding middle and high school. The remaining students attend private K-12 schools, which are heavily subsidized by City Hall. All of the schools in New Transportbury are of the highest caliber, so the choice

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between public and private schools is solely a matter of preference. Below is a more detailed summary of school enrolment and employment.

The table below shows the distribution of employment among different occupations.

The majority of workers are employed in professional offices, industry, and commercial settings. Workers in New Transportbury represent over 40% of the total population. The stadium, airport, hospitals, and schools are other major employers of New Transportbury residents. Other TAZs require few employees due to their smaller size and lower maintenance.

The table below specifies the

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employment breakdown for each TAZ. The chart above gives a detailed breakdown of the residential areas of New Transportbury. We display the square mileage of each TAZ, as well as the population density, which when multiplied yield the total population of each TAZ. We can see that the distinction between “light”, “medium”, “heavy”, and “super heavy” residential areas is given by their respective population densities. The elderly people of New Transportbury do not care for crowded areas, so they choose to live together in the light residential TAZs, with a few exceptions living with younger generations of their families in medium residential TAZs. Some unemployed people are stay-at-home parents, while others are seeking work or are between jobs. These residents tend to live in the more densely populated regions due to the lower costs of housing there. Families tend to live in the heavier residential areas, although there are some exceptions (unlike the unemployed residents).

Trip Generation

For our trip production-attraction generation process, we considered all of the comings and goings that occur in the course of a normal day for each of our 6 types of residents (listed above in “Demographics”). We took into account the need to go to work and school for certain residents, as well as the needs of all people to eat, shop, and recreate. 100% of workers and students are ‘produced’ from home and ‘attracted’ to work and school, respectively. After work and school, 80% of people come directly, while the remaining 20% go to other TAZs. Of the people who went home, 80% leave home again to do other activities, such as to buy groceries, golf, or attend a sporting event. 50% of people going to places other than work, school, or home, begin their trips at home; this same proportion then returns home. We also plan for people to make many “other-other” trips, in which the production and attraction vectors are identical. This is because people tend to run many errands once they are out and about. In every set of production and attraction vectors, we ensured that the sums were equal; everyone who goes to a place has to eventually leave that place.

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Home-Based Work Trips Everything in the production vector originated from residential TAZs. All of these trips are made up of all (and only) workers. The employment chart (bottom of page 3) details the TAZs that each worker is ‘attracted’ to for his or her job. Work-based home arrays are the opposite in that all of the production comes from employment TAZs and is attracted to residential TAZs. 80% of HBW trips become WBH trips.

Home-Based School Trips Everything in the production vector originated from residential TAZs. All of these trips are made up of all (and only) students. The student breakdown chart (top of page 3) details the TAZs that each student is ‘attracted’ to for school. School-based home arrays are the opposite in that all of the production comes from school TAZs and is attracted to residential TAZs. 80% of HBS trips become SBH trips.

Home-Based Other Trips Everything in the production vector originated from residential TAZs. These trips are made initially by non-workers and non-students, but also include 80% of those workers and students who make home-based other trips after work or school. All kinds of residents are eventually attracted to “other” destinations, whether those be recreational, commercial, etc.

Work-Based Other Trips Everything in the production vector originated from work-based TAZs. 20% of workers leave work to go to other destinations besides home. These are people who do not go home before running their after-work errands or recreating.

School-Based Other Trips Everything in the production vector originated from school-based TAZs. 20% of students leave school to go to other destinations besides home. These are students who do not go home before running their after-school errands or recreating.

Other-Based Other Trips Everything in the production vector originated and resulted in ‘other’ TAZs. These are people who go from errand to errand or recreation to recreation (or even recreation to errand!)

Our trip attractions-productions for each type of trip are summarized in the table below.

*the full P-A vectors are better seen on our googledoc under the tab “All Production and Attraction Vectors”

Trip Distribution

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The Gravity Model is the model we used to generate a trip array, using our production and attraction vectors. The model allows us to transform 2N-1 pieces of information into N2 pieces of information (no small feat!) In order to do this, we make use of a friction array of friction factors that represent people’s concepts of trip costs. We generate this using a distance array, which represents the distance between the centroid of each TAZ. We multiply the Cartesian distance by 1.2 to account for traffic, nonlinear paths, and other possible deterrents. To correct for intrazonal travel, we use the square root of the area of the TAZ as the distance between the TAZ and itself. We also use the correcting constant C (which we take in this case to be C=1). The friction of travel from TAZ i to TAZ j is then Fij = C / tij

n , where t is the distance between TAZs i and j and where we take n to be 2. This relationship suggest that the desire to travel between TAZs i and j is inversely proportional to the square of the distance between those TAZs. The Model also has an optional adjustment factor array; in our case, we take this to be the identity matrix (no adjustment). We now have all of the pieces of the puzzle and can generate the trip array using the data described above.

The last problem was that the rows summed to the production vector, but the columns don’t sum to the attraction vector. As a result, we need to put in an artificial attraction vector in order to generate columns that sum to the attraction vector. To generate this artificial attraction vector, we multiplied the desired attraction vector with the inputted attraction vector (initially, this is the desired attraction vector) and divided this by the vector that is the sum of the columns of the trip array (the output attraction vector). This generates a new output and a new input (the artificial attraction vector), which we then used to continue iterating and reducing the percent error, defined as (output attraction vector - desired attraction vector) * (100 / output attraction vector). We continued iterating until the maximum percent error for any component was less than 0.1%.

The PersonTrips are the total number of trips that are taken.

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We found this value for each of the trip types by summing either the production or the attraction vector’s components (they are equal to each other so it doesn’t matter which one). We also generated PersonTripMiles values, which are the average number of miles traveled by each person. The total number of miles was generated by multiplying each entry in the distance array by its corresponding entry in the trip array. Upon summing each of the individual miles for trips from one TAZ to another, we were left with the total number of miles. From here, we divided this value by the number of trips (because we are assuming that each trip consists of only one person) to generate the PersonTripMiles values for each trip type. The actual values are in the table below and can also be found in the tab (in our googledoc) titled “Summary Trip Demand.”

The greatest number of Person Trips are for Other-based-Other trips. We believe this is because many people take more than one Other trip. We think of these as people running errands, or spending time with friends by seeing a movie, or golfing, then going out for dinner, the possibilities are endless! The least number of Person Trips are for School-based-Other trips. This is because 80% of those who go to school come directly home, so this leaves 20% to go to Other right after school. The rest of the Person Trip values seem to gravitate around 100,000 or so, with Work-based-Other trips being small and Other-based-Home trips being large because everyone has to return home after doing other things.

The greatest number of PersonTripMiles is for Home-based-Work and Work-based-Home trips (15.15 miles per trip). We believe this is the case because, even if the distance is large between one’s home and one’s workplace, the distance must be travelled, so it is not a deterrent, whereas the distance between home and a restaurant might play a bigger role in deciding whether or not to take a trip to that restaurant. The smallest PersonTripMiles value is for Other-based-Other trips (1.8 miles per trip). This is because recreational and convenience (restaurants, malls, retail, etc.) tend to be close together, so the distance between them is usually small. Other large PersonTripMiles values occur for Home-based-Other trips. We stipulate that this is because once people are at other places, they will most likely travel to other places, which are a short distance away, so overall the distance per trip is not as much for the traveller and the decision to travel to the other TAZ is made. Aside from these extreme cases, most average trip lengths tend to fall between 5 miles and 10 miles.

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The above are six cumulative trip-distance charts, one for each trip array. A few of the charts are

easily analyzable, showing that, as the distance in miles from a TAZ tends to increase, the proportion of trips that are made at or less than at the distance tends to grow linearly without any big spikes or plateaus. Graphs that seem to follow this are the Work-Based-Home and Home-based-Work graphs. To a degree, the graphs for School-based-Other and Home-based-Other seem to follow this trend, however we can see that as the distance increases too much (around 30 miles for both), all the trips have been taken, so the earlier trend described applies, but not for all of the distances possible (only for distances between 0 and 30 miles or so). The last two graphs seem pretty similar to each other. The graphs for Other-based-Other and Home-based-School

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trips both have large peaks at the beginning and then plateau as the distances increase (moreso for Home-based-School trips than for Other-based-Other trips). This means that most people that make Other-based-Other trips or Home-based-School trips tend to decide to make the trip only if the distance is short. This makes sense for Other-based-Other trips because one would not decide to go eat at a restaurant and then see a baseball game 30 miles away from that restaurant. Similarly, Home-based-School trips being short makes sense. There are many schools in New Transportbury and this gives families the option to decide which school they want their children attending. If all schools in New Transportbury are the same educationally, what sets them apart is the distance from one’s home. The logical choice, then, is to have one’s children attend a school close to home. There are some exceptions to the graph for Other-based-Other trips because every now and then, someone might want to eat out at a fancy restaurant that happens to be far away from a gathering of friends at another place, but there are no exceptions for the Home-based-School graph because of the aforementioned logical choice of schools for families’ children to attend.

Generating the graphs proved too daunting a task to complete in our googledoc, so we generated the graphs in Excel. We have the basic set-up in the googledoc under the tab titled, “Trip / Distance Columns,” but we did not complete all the information, and instead did so in an Excel spreadsheet.

The 6 graphs on the previous page plot number of trips (on the Y-axis) against the trip length in miles

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(on the X-axis) with each point being the value for one TAZ. Most of them show what we would expect: that as the trip distance increases, the number of trips decreases because it becomes too unappealing to undertake longer journeys. We see this especially being true for Other-Based-Other trips, where there is a large peak in number of trips between 0 and approximately 3 miles of trip distance. This makes sense because if people are making long trips from other places, they are most likely going home and not somewhere else. This is also true of Home-Based-School trips, but for a slightly different reason. No child goes to a school that is far away; the furthest a school is away from an attending student is about 20 miles and, as a result, no Home-Based-School trips occur that are greater than 20 miles in length. The graph for Work-Based-Other trips is similar to these past two trips’ graphs in that there is a large peak at the beginning that levels off, but the difference is that there are a few exceptions here. There are about 1000 or so trips that occur for distances between 5 and 30 miles long. We can understand that one’s workplace might be far removed from a place that one enjoys going to, such as a restaurant, or golf course, or movie theatre. As a result, it makes sense that there are some exceptions in the graph for Work-Based-Other trips.

Three other graphs are pretty similar: Home-Based-Other, School-Based-Other, and Home-Based-Work. All three have an initial spike that peaks from 10-20 miles, depending on the graph, and slowly levels off until plateauing at 0 at around 35 miles or so. This makes sense because most trips are not bound to be 2 miles long and a 10 mile trip is not a burden because it only takes 15-20 minutes or so. As trips increase from there to the point that trips begin taking 30 or more minutes, people become more and more hesitant to make journeys and the number of trips decreases.

We then recalculated our Home-Based-Work Trip Array, using 1/D, the inverse of the distance, and then 1/sqrt(D), the inverse of the square root of the distance, to calculate the friction array. The results of recreating the scatterplots comparing trip length to the number of trips are shown in the graphs on the next page, with the original graph and the two modified graphs underneath.

These two changes have both decreased the denominator, thus increasing the friction. We expected (before producing the graphs) that the change in calculation for the friction array would decrease the maximum trip distance and narrow the graph. We were proved correct when we produced the graphs and saw that as the denominator gets smaller and smaller, the graph gets narrower and narrower (the 1/sqrt(D)-produced trip array’s graph is narrower than that of the 1/D-produce trip array’s graph, which is narrower than the original graph). The difference between 1/D and 1/D^2 is not huge, the left side of the graph slightly increases and the right side slightly decreases when compared to the original, however the 1/sqrt(D) graph has notable differences. The maximum decreases from around 40 miles to around 30 miles and there aren’t many trips undertaken past 20 miles in distance. The graphs are on the next page.

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