A National Disaggregate Transportation Demand Model for the Analysis of Autonomous Taxi Systems Alexander Penn Hill Wyrough Jr. May 8, 2014 Advised by Professor Alain L. Kornhauser

Designing Optimal Systems of Self-Driving Cars How do we use autonomously driven vehicles effectively? Autonomous Taxis (aTaxis) Modeling existing personal travel behavior Where do we want to go? When do we want to go there? Self-driving cars, or SmartCars as Professor K calls them, are quickly becoming a technological reality. With major car manufacturers joining Google, it is only a matter of years until autonomously driven vehicles are on the roads. However, a problem just as vexing as the technological solution is designing systems to effectively use these cars to increase personal mobility at a lower individual and societal cost. One possible idea is a network of aTaxi stands distributed around the U.S. or specific areas so that any personal trip could be serviced by aTaxis on demand, with the allowance of short walking distances. This alternative’s use of ridesharing is far more efficient and cheap, when compared to traditional personally-owned automobile use. To implement a network of aTaxi’s, one would need to know where to play aTaxi stands, how many aTaxi’s are needed in the fleet, where they should wait when empty, how long they should wait at an aTaxi stand for additional passengers, and many, many other crucial parameters. To begin answering these questions, likely personal demand and expected patterns of use of any such system must be known. To that end, modeling existing personal travel behavior is fundamental to the creation of self-driving automotive systems. For all the possible users of the system, you need to know the points of origin and destination and when they want to leave. This thesis creates a personal travel demand model for all the 300 million and more residents in the United States.

A National Disaggregate Personal Trip Synthesizer Objective: Create a daily trip tour for each resident in the U.S. for a typical work day with exact spatial and temporal attributes Modeling Methods Disaggregate or, Agent-Based, Modeling Activity-Based Modeling Home-Based Modeling Who you are and where you live can explain most of your predictable, routine, personal travel The practical objective of this thesis is to build all the personal trips undertaken throughout the U.S. on a typical work day. To accomplish this, the model sends all workers to an appropriate place of employment, all students to an appropriate place of schooling, and all residents on the other, recreational trips, that constitute a day’s activities such as to the supermarket, to the gym, to the bank, etc. This thesis uses several important modeling concepts for direction in its eventual use of analyzing autonomous taxi systems. This thesis concerns itself with disaggregate personal trip patterns, which is to say the trips taken by, and motivating factors for, a specific individual, rather than broad travel trends for the U.S. population. This focus is motivated by a singular objective: the full potential of an innovative transportation system relies on the manner and extent to which it can service the daily transportation needs and considerations of individuals. Secondly, it recognized travel as a derived demand, and the source of the real demand for travel is the desire to pursue activities throughout a day, such as attending school or going to work or going to see a movie. Assignment of those activities equates to assigning trips taken. Lastly, all daily trip tours, for simplicity, are considered to be home-based. That is they begin and end at home. This model rests on the belief that your personal identity can reasonably explain the activities your pursue through time and space. For rigid activities like work and school, this is an easy assumption. It is less clear for other recreational trips, but still possible. It is altogether not a realistic goal to model that I attend my actual, exact place of employment, but that on aggregate the trips taken by individuals comprise a dataset that reflects as closely as possible the true disaggregate travel behavior in the U.S.

Modeling Step 1: Population Synthesis The first step of the model builds the U.S. population exactly as it was in 2010, the last time the U.S. Census was collected. This thesis relies heavily on Census data at the block level. The Census block is the smallest geographical area in which 100% thorough data is collected. There are over 11 million Census blocks in the U.S. The first step of this thesis recreates each Census block, one by one. Using distributions of age and gender, household make-up, and household income, 308,745,538 residents are created to live within the system. The model assigns gender and age simultaneously by selecting from the distributions of that particular census block, with replacement. It then builds each household given its size and make-up, such as householder and familial relationships within households. Next, it assigns each household an income, and then distributes that income to individuals within the household if they qualify to earn an income, with the householder given preference. A commonly used figure to represent a population broadly is the age-sex pyramid which breaks down sex by age for a given population. Compared are the actual 2010 figures and the simulated results of the population synthesizer for females. Next we will look closer at the results at the state level.

South Carolina Simulated Population Recreate the U.S. Population Exactly Census Block Representations Assign Anchored Activities Work and School Assign ‘Other’ Activities Establish dataset for 308,745,538 residents taking 1,009,322,835 personal trips Shown here are the results of the population synthesis for South Carolina, as an aggregation of all of its census blocks. It is clear that using such a local level of data allows for a really accurate representation of the entire population as constituted by simulated individuals. This is at the heart of the disaggregate objectives of this model. Household income is the only slightly askew figure. This is because the U.S. census does not report household incomes about 200,000 dollars, and so the household income in the highest range distorts the distribution to skew left. It is important to note that each Census block is rebuilt in an identical fashion as all other census blocks. So the results for one state are indicative of the results for all other states. A underlying hypothesis of this thesis is that your gender, location, age, and income can reasonably explain your daily activities. Given these attributes, the next steps assign individuals to those activities such as work, school, and all other activities.

Modeling Step 2: Workplace Assignment Determining if he/she should work The Gravity Model of Attraction Selecting a county of work Selecting an industry of work Selecting a specific employer Sending a worker to work, so to speak, is a four step process. First, workers are filtered out from the general population, given their age, average employment rates, and other factors. The next three steps all involve selecting from a distribution created using a gravity model of attraction which computes a numeric weight of attraction given its popularity and varies inversely with distance squared. A worker is given a county in which to work using the Journey-to-Work Census so that the spatial distribution of commutes matches reality. Next, given his or her county of work, an industry of work is selected that matches the workers income. Finally, using a database of all the places of employment within the United States, a specific place of employment is selected where the attractiveness is the number of employees working there, and inverse to distance squared.

Shown here are the commuting trips for three random census blocks within Addison County in Vermont. One important feature of the model is that all residents of a census block are assumed to live at the center of that census block. It is easy to see that aggregation depicted here as all colored lines emanate from a specific point. However, also clear is the level of geographical specificity of commutes. The use of the Journey to Work Census, coupled with a gravity model, helps to make the length of the commute spatially accurate. To look more closely at those results, we will consider New York State.

New York State has a mean commute length of 12 New York State has a mean commute length of 12.1 miles and a median commute length of 7.94 miles, where just about 3% of trips are less than 1 mile and 1% of trips are over 60 miles. Given a rough translation of 2 minutes per mile, or 30 miles an hour drive, the simulated mean commute time of around 25 minutes is almost exactly the national average. Moreover, the distribution of median commute length throughout the state corresponds to the attributes of the state. Commutes are quite short around urban centers such as New York City, Albany, and Buffalo, and the commute length increases as you move away. The longest commutes are from East Long Island because there is not much work opportunity there, and most commute into NYC. This makes sense from a modeling standpoint and matches what you’d expect of true New York State behavior.

Modeling Step 3: School Assignment Determining if he/she should attend school Determining what county he/she attends school in Determining what type of school (private vs. public, 2 year college, 4 year college, trade school) The Gravity Model of Attraction Selecting a specific school Sending a student to school is very similar to sending a worker to work. Appropriate age filters are made, and the choice of an exact school is the result of narrowing decisions as to what county the student travels to and what type of school. Data from the Department of Education are used to assemble a comprehensive list of all the possible schools in the United States and their enrollments, as well as to define the rates of participation in different types of schools.

Shown here are examples of 4 public high schools in Mercer county, including Princeton high school. On the left are school commute filaments for each of the four high schools to show the spatial distribution of trips on a map. Note that the filaments do not accurately represent the density of trips. On the right are cumulative distributions of the trip length for these school commutes. As expected the vast majority of trips are less a couple of miles. The spatial distribution of school trips follow similar distributions throughout each state and match national averages for school commutes well.

Equally important though is that school enrollment matches actual data so that the right number of trips are going to each school. Above is a table of enrollment for mercer county public high schools compared to the enrollment data used. Note, two different scenarios were experimented with in the model, and the ‘without replacement’ scenario was ultimately used for obvious reasons. You can see fairly well that the enrollment in the simulation is extremely close to actual enrollment, where the only discrepancy is the result of preventing the weight of any one school in a distribution from going to zero.

Building the Trip Tour Assign Trip Tour Pattern Populate Other Trips Select from distinct set of 20 possible activity patterns throughout a given day Populate Other Trips Select Other trips using Gravity Model such that the place of patronage is within one county away Attractiveness of an Other trip equals that rate of patronage to that business Distribute Trips Throughout Time After the assignment of the two anchors of work and school, each resident is assigned a daily activity pattern which are combinatorial chains of H, W, S, and O nodes that begin and end at home and are made to mimic normal patterns such as commutes, work days with lunch breaks, errands after work, part-time jobs or school, etc. This is of course only a limited set, and the model only considers trip chains that involve 7 or less trips. The distributions of chains are made so that the expected number of trips taken per resident equals the national average of somewhere between 3 and 4, depending on the survey. After the chain is assigned, the places of patronage for other, recreational trips, are selected using similar methods as described earlier, where the attraction is a function of the rates of patronage. However, considering the nature of other trips as errands or convenience trips, other trips are confined to within one county of the point of origination. Lastly, the trips are distributed throughout time in a day. For work and school, there are start bell and end bell times and random arrival and departure times around that bell time that follow a Poisson process. For all activities, a duration is selected from a normal distribution according to the type of activity. In addition, all trips are considered to travel at 30 miles an hour throughout the day. In this way, each node of a trip chain is given an arrival time and departure time. This is the final layer of disaggregation that achieves a reasonably accurate temporal quality for the daily trip tour.

A sample output of Task 6 is shown for a worker in Mississippi's Grenada County. All times here are displayed in a 24-hour clock, but are actually stored as seconds from midnight. In addition, Node 7 and 8 data are not shown here because this trip tour ends for the day at Node 6. Note, his trip chain is H-W-O-H-O-H This sample output, chosen randomly, displays the complete day for a construction worker, who commutes roughly 30 minutes to work early in the morning, then goes to McDonald's after work ends around 5:00PM, before heading home for a brief period. He makes a quick errand to a Dollar General store before retiring for the night at around 9:30PM. Finally, all residents are given this same method treatment and we are left with trip files for each resident similar to this one.

The Resulting Data-Set 308,745,538 synthetic residents with personal attributes 1,009,322,835 personal trips taken that originate in the United States on a typical work day 3.27 trips per resident 3,143 county residency files Personal data for all 308,745,538 residents sorted by county of residents To analyze how residents of a region behave 3,143 oTrip files All 1,009,322,835 trips organized by county of trip origination To analyze the travel contained within a particular region The final output of this data set is an almost 100 gigabyte database of all the personal trips taken by the 2010 residents of the United States throughout a typical work day. This is a close, first approximation as to how individuals move throughout a day in time and space. Serving that travel demand is the goal of any new age transportation network, such as autonomous taxis. The work to be done besides fine tuning the model is transforming these trips to a contrived network and analyzing its pattern of use and results.