NEW YORK CITY TAXICAB TRANSPORTATION DEMAND MODELING: EXPLORING THE POTENTIAL FOR RIDESHARING

Submitted to TRB August 1, 2015

AJ Swoboda (corresponding author) Department of Operations Research and Financial Engineering Princeton University 229 Sherrerd Hall (ORFE Building) Princeton, NJ 08544 T: +1 571 201 4415 Email: aj.t.swoboda@gmail.com

Alain Kornhauser, Ph.D. Professor, Department of Operations Research and Financial Engineering Princeton University 229 Sherrerd Hall (ORFE Building) Princeton, NJ 08544 T: +1 609 258 4657 F: +1 609 258 1563 Email: alaink@princeton.edu

ABSTRACT

Over the past decades, the automobile, its extensive infrastructure network, and their ability to together increase the capacity for personal rapid transportation have significantly contributed to the development of society. Yet the sustained dominance of today’s transportation system will continue on a path towards higher fuel costs, more foreign oil dependency, denser traffic congestion, and more. This paper acknowledges that, while others search for next-generation physical technologies to solve this modern transportation problem, an effective solution may already be possible with current technology on existing infrastructure – dynamic ridesharing. Using all recorded Taxi & Limousine Commission trips taken in Manhattan and the surrounding boroughs of New York City during 2013 as a proxy for transportation demand of NYC, this research examines characteristics of the current system and investigates how various ridesharing policies could perform if they were implemented as a replacement system. Three major findings resulted from analysis into the existing data. 1) Demand fluctuated daily (peaking twice around 6 AM and 7 PM), weekly (peaking on Fridays and shifting to later hours during the weekend), and annually (dropping during the summer months and the winter holiday). 2) NYC transportation demand did not appear to correlate with precipitation levels throughout the year. 3) Roughly 90% of NYC TLC taxicabs recorded at least one fare on an average day, however very rarely did half of the taxicab fleet generate revenue at any given moment in the week, with only 32% doing so on average. Ridesharing policies with varying levels of complexity and constraint were tested on the 2013 NYC TLC data. The most stringent of policies – one common destination with a 30-second time window and a 0.3-by-0.3 mile drop-off zone – reduced total annual vehicle miles by 0.3%. The most lenient of policies – up to five common destinations, with a 300-second time window and a 0.5-by-0.5 mile drop-off zone – reduced total annual vehicle miles driven by 23%.

INTRODUCTION The personal automobile has served to offer unparalleled mobility over the past decades and it's overwhelming superior service quality makes it the most popular transportation mode of choice throughout America and the rest of the world. In fact today, the automobile and its extensive network of roads indelibly defines transportation in the United States.

Unfortunately, the evolution of this type of personal mobility has inflicted substantial societal costs. Since many individuals use vehicles alone, a large number of the personal miles that are traveled (PMT) consume an equivalent amount of vehicle miles traveled (VMT). The societal costs associated with transportation – energy consumption, dependence on foreign oil, increased pollution, congestion, etc. – are more closely tied to the VMT metric than to PMT, so it is imperative that next generation transportation systems focus on minimizing VMT to diminish the negative externalities associated with transportation. Dynamic ridesharing, paired with internet enabled technologies and comprehensive algorithms, can provide such a solution without requiring a complete upheaval of the already-extensive transportation infrastructure.

In a sense, this is what conventional mass transit is about: serve a significantly higher number of PMTs without increasing the total VMT. However conventional mass transit does not work in enough places. The fundamental reason mass transit does not work more ubiquitously is not due to the public's aversion to travel with strangers, but rather due to either of the following facts: 1) that individual trips are not sufficiently correlated in both space and time enough to allow for the opportunity of traveling together; or 2) that even if that correlation does exist, there is no possibility for strangers to utilize the same vehicle. This conundrum results in people tending to travel alone or with closely related individuals, who likely are less convenient. Setting aside the question about people's willingness to travel with strangers, is PMT sufficiently correlated such that ridesharing could occur if a system was set in place to notify travelers of that possibility?

This is a very difficult question for many reasons, least of which is that there is not sufficiently detailed and comprehensive database of trips to empirically test such a propensity. However trips within a relatively closed system can be a different story. Trips taken by taxicab in NYC are essentially captive to cabs – they are usually too long to walk, their passengers do not have access to personal automobiles, and other motivations inclined the passengers to not use the bus or subway systems. In most cases there is not transportation mode choice, however they may be a dynamic ridesharing potential should the opportunity be made apparent.

The New York City Taxi and Limousine Commission (NYC TLC) released detailed logs of every taxicab trip taken during the 2013 calendar year [1]. The 2015 paper New York City Taxicab Transportation Demand Modeling for the Analysis of Ridesharing and Autonomous Taxi Systems by AJ Swoboda set out to empirically determine the relationship between trip correlation (the level of service offered) and ridesharing potential, hoping to address the extent to which there is rideshare potential amongst people who use cabs to satisfy their travel need. By exploring the nature and feasibility of a ridesharing model built off of actual real-life data – as opposed to

synthesized data – the research results could lead to a better understanding of the potential for a ridesharing framework throughout the United States.

A thorough discussion of the background, data processing, and activity of the NYC TLC is included in [2], as well as more detailed descriptions of the process and breakdown of the ridesharing algorithms used during simulation and its connections and implications related to national ridesharing. This specific paper focuses on the main highlights of taxicab activity and the important findings generated through automated ridesharing models.

TAXICAB PICKUP ACTIVITY ACROSS 2013 The demand for taxicabs in New York City can be best accurately represented by the distribution of taxicab pickups that occur. The day-by-day visualization of taxicab pickup frequency in Figure 1 provides a general understanding for the ebb and flow of taxicab demand over the course of an entire calendar year. Taxicab usage in 2013 was affected by seasonality – it experienced a drop during the warmer, summer months and the winter holiday – and it fluctuated more sharply day-by-day over the course of a week. Debunked more thoroughly on page 28 of [2], most of the overall trend’s irregularities exist due to lack of passenger demand during major holidays, while the sharpest decline in activity (in early August) resulted from a lack of drivers due to out-of-the-ordinary traffic closures.

FIGURE 1 NYC TLC Daily Demand and Manhattan Rainfall

No immediate correlation could be found between precipitation levels in this Northeastern city and taxicab demand. To account for the weekly trending patterns explained in Figure 1, this weather analysis was also conducted for each specific day of the week where, again, no significant relationship was found.

TAXICAB PICKUP ACTIVITY BY WEEK Perhaps a more enlightening insight is the examination of an average 24-hour day of NYC taxicab trips. However individuals’ routines differ based on the day of the week, so rather than inspecting an average day, the entire 2013 year was compressed into an average week to unveil characteristics of demand that would be indiscernible at a larger scale. Figure 2 explores the frequency of taxicab pickups, separated by NYC borough, during each minute of the week from 12:00 AM on Monday to 11:59 PM on Sunday.

Manhattan accounted for 90.3% of all taxicab originations over the course of 2013 and follows a logical pattern of demand as one traces through the week considering to- and from-work travel as well as nightlife and weekend activities. Queens’ almost-constant pickup demand from 6 AM through midnight of each day is heavily influenced by the presence of JFK and LGA airports, which together alone make up 3.5% of all NYC TLC 2013 taxicab pickups. The remaining 6.2% of all activity is broken down amongst the other four boroughs as the following: Brooklyn (3.1%); the rest of Queens (1.5%); the Bronx (0.9%); and Staten Island (0.8%). Further explanations begin on page 21 of [2].

FLEET ANALYSES Understanding how the existing fleet of taxicabs in New York City conducts business and serves inhabitants of allows for the discovery of inefficiencies within the transportation system. On an average day in 2013, 90.8% of the total taxicab fleet (12,480 medallions) recorded at least one trip, indicating that there is a cause for not all taxicabs to be able to serve customers each day. One possible explanation would be due to vehicles being serviced or repaired. The ebb and flow

FIGURE 2 Per-Minute Trip Demand during 2013 by Weekday

of Figure 3 can be compared to the oscillation in Figure 1 to understand whether a shortage in taxicab activity correlated more closely with a decrease in demand or in supply.

However perhaps a more insightful approach to understanding taxicab activity on a standard day is to consider how many taxicabs are generating revenue at a given moment during a day. For such an analysis a standard week with no extreme events was selected: Monday, March 4th through the end of Sunday, March 10th (as can be verified by observing this week-long span in Figures 1 and 3). For each minute in this selected week, every taxicab in the process of transporting a passenger from pickup to drop-off was tallied. Figure 4 displays the proportion of the taxicab fleet actively producing revenue at any given moment during the week. Although ridesharing solutions addressed in this paper do not specifically address manners in which taxicabs can be generating revenue more consistently, this figure is very telling of the

FIGURE 3 Per-Day Proportion of Taxicab Fleet that is Active

FIGURE 4 Proportion of Taxicab Fleet Generating Revenue

inefficiency of the current NYC TLC system. Very rarely in a standard week was half of the taxicab fleet generating revenue at a given minute, with only 32% of the fleet transporting a customer on average. It is infeasible to expect human drivers to complete constant back-to-back fares without taking personal breaks. Additionally, these independently-thinking drivers do not necessarily know the optimal repositioning location to find a new customer upon the termination of a taxicab fare. A connected network of vehicles has the potential to tell a different story.

PIXELIZATION OF NEW YORK CITY GEOGRAPHIC AREA

This paper discretized the 2013 NYC TLC data into a grid of 84,970 adjacent pixels in order to reduce the complexity of a ridesharing analysis. The original location components of the data involved specific latitude-longitude (lat-long) coordinates of each trip’s pickup and drop-off. The coordinate system’s accuracy is usually an asset, but due to its continuous nature it would have resulted in essentially an infinite number of lat-long combinations throughout the entire region of analysis covering the 850-square-mile area of land surrounding New York City’s five boroughs. Each pixel was measured to be 0.1-by-0.1 miles in size, a small enough assignment so as to not sacrifice the high level of detail included in the data. Further technical procedures for the dividing and tracking of the data can be found in Chapter 4 of [2].

Figure 5 depicts two 3D heat maps of the frequency of pickups (left hand side) and drop-offs (right hand side) by NYC taxis over the course of 2013. These 3D visualizations use the same scale and can appropriately be compared side by side. It is worth noting how the majority of NYC TLC pickups and drop-offs are concentrated in Manhattan, while the drop-offs over the year are more uniformly dispersed amongst the other boroughs. As mentioned earlier in this report, LaGuardia Airport and John F. Kennedy International Airport possessed high quantities of taxicab traffic relative to other non-Manhattan areas of New York City.

Although it may prove difficult to implement a broad-sweeping ridesharing system overnight, introducing the public to such a program at specific hot spots would be a feasible approach towards achieving an overarching goal of ubiquitous ridesharing. Airports, popular train stations, and city destinations would likely prove to be efficient starting points for such a next-generation transportation system. Table 1 comes from Chapter 5.4 of [2] and gives contextual information surrounding the most popular pickup and drop-off locations in NYC during 2013. A more detailed analysis revealed that the top-five pickup locations listed in Table 1 all possess an almost-constant flow of taxi demand throughout the course of an average 24-hour day.

It makes sense that the most popular locations in New York City for taxicab pick-ups consistently contain individuals looking for a ride, but this could not possibly be the case for every pixel

TABLE 1 Top Five Pickup and Drop-off Pixels

location in the city’s five boroughs. And for an effective ridesharing program to exist, it must focus on the locations with sufficient volume of demand in order to successfully match individuals together in dynamic rideshares. Upon further inspection of the almost 85,000 total pixels in the geographic area, it was found that 2,249 of the pixels make up 99 percent of all taxicab pickups over 2013 and that just 294 pixels accounted for 50 percent.

RIDESHARING: METHODOLOGY, POLICIES, AND RESULTS Dynamic ridesharing can provide a solution to today’s overwhelmed and inefficient transportation system, which struggles with issues of pollution, congestion, and more. As mentioned earlier, in order to quantify the degree to which a ridesharing transportation system can mitigate these negative byproducts, the single most complete metric to consider is vehicle miles traveled.

Ridesharing Methodology It will be valuable to first address some major conceptual assumptions and explanations of terms used throughout the remainder of this paper.

1) This ridesharing analysis is approached pixel-by-pixel, rather than using discrete lat-long coordinates, meaning each passenger’s departure is identified by a 0.1-by-0.1 mile square. When calculating distances the research assumes each departure occurs from the pixel’s centroid, and thus it may require an individual to walk a small distance to reach the pickup.

2) A ridesharing “policy” refers to an overarching, theoretical algorithm that determines how a rideshare match can be identified. Whereas a “framework” identifies the specific geographic-boundary and time-window combination of a given policy. Geographic boundaries refer to the relative sizes used when determining if individuals were heading to the same destination. A “superPixel” is a 9-pixel square and a “macroPixel” is a 25 pixel grid, translating to squares that are 0.3-by-0.3 and 0.5-by-0.5 miles in size. A time window refers to the amount

Drop-offsPickups

FIGURE 5 Proportion of Taxicab Fleet Generating Revenue

of time that a taxicab with one passenger would wait for another passenger to show up with a rideshare match before departing. For this research, the time window ranged from 30 seconds to 5 minutes. Eight distinct frameworks were chosen for analysis, and evaluated under each policy, but there is no limit to the number that could be studied.

3) Average departure occupancy (ADO), percent reduction in taxicab usage (%TaxiRed), and percent vehicle miles saved (%vMiles) are three important metrics to quantify the effectiveness of ridesharing implementations. ADO represents the number of passengers involved in an average taxicab departure. %TaxiRed refers to the percent fewer taxicabs summoned for trips over the course of the year, while still satisfying the entire demand for taxis. Most important, %vMiles represents the percent of vehicle miles that would not have been driven if the ridesharing policy had been implemented in NYC during 2013.

4) To prepare the trip files, the 2013 NYC TLC data was sorted chronologically by the trip origination date and time and each lat-long location was assigned the corresponding pixel identification. Once this preparation was complete, the simulation began with the following logic. An unobserved individual (rider-A) enters a taxicab and a timer begins, set to the length of whatever the pre-determined time window is. Any other individual who arrives at the same pixel within rider-A’s time window and who’s trip satisfies a ridesharing policy’s matching requirements is recorded as joining rider-A’s departure. Once the time window passes, rider-A and all of the other matching riders are logged as being in a single departure and set off towards their destination (or destinations). The methodology for determining whether a potential rideshare satisfies the ridesharing policy’s requirements will be explained later, but note that it varies based on the policy parameters. The top picture in Figure 6 gives a sample for how the algorithm’s logic searches and iterates through the dataset of taxicab trips – this sample framework consists of a megaPixel (MP) geographic boundary and a time window of 300 seconds. The bottom half of Figure 6 presents what would be the finalized departure list of the trip files from the top half.

FIGURE 6 Sample Execution of Rideshare Departure Creation

5) The term common destination (CD) refers to the number of destinations a ridesharing taxicab would be driving to before all passengers are dropped off. If CD = 1, then all trips within the rideshare departure are going to the same destination (determined by the geographic boundary size). For CD = x where x > 1, a departure would travel to x unique destinations. In order to take into account the potential inconvenience added to any member of a departure, an additional destination would only be added to the existing departure if it added no more than a specific percentage of distance to the existing total trip distance – this metric is referred to as “circuity” (CIR). An evolution of this CIR metric is another metric called directional circuity (dCIR), which eliminates the possibility of adding any other trip with a destination the opposite direction as the first destination by creating a dividing line that splits the geographical area into two sides. The orientation of this split is either North-South or East-West depending on the geographical relation between Origin and Destination #1. The process, including diagrams, is included in more detail in Chapter 6.4.1 (page 65) in [2].

6) To best understand the feasibility of a ridesharing implementation in NYC for taxicabs, there must be a well-defined scope of operation – the “service level” of the ridesharing program. A clear choice was to conduct analysis for a service level consisting of the 2,249 pixels that represented 99 percent of all taxicab activity in 2013. For other points of comparison, 50 pixels were hand selected, which represented all major entrance and exit points of major transportation hubs in NYC – Penn Station, NY Port Authority Bus Terminal, Grand Central Station, LGA, and JFK. A figure on page 53 of [2] gives the exact geographical location of each of the selected pixels overlaid onto a map. Lastly, service level considerations were made consisting of the pixels contained in the top-5, top-100, and top-1000 groupings once pixels were sorted by taxicab pickup activity in descending order. These were added to the analysis to give a snapshot as to how effective a given policy and framework may be as a ridesharing program would expand from initial implementation to more widespread usage throughout the city.

Ridesharing Policies and Results: (CD = 1) This subsection focuses on a (CD = 1) ridesharing policy and considers the benefits and effectiveness of implementing it over various service levels for eight frameworks – a superPixel or macroPixel geographic boundary combined with time window lasting 30, 60, 120, or 300 seconds. Python code included in Appendix B.5.1 of [2] shows how the ridesharing simulation was conducted, with the code in B.5.2 consisting of the subsequent analysis of the rideshare departure pairings.

As implied, this policy is concerned only with a single common destination between all passengers in the rideshare. Assuming that trips B and C fit within the specified time window of trip A, the left-hand side of Figure 7 gives a visual example of what a (CD = 1) departure assignment could consist of. A departure’s total length can be computed as the length of the longest trip in the departure list, since a vehicle would need to travel no further than that destination. So, the number of vehicle miles saved can be determined by subtracting the distance of the rideshare from the sum of the individual, original trips. With this example scenario, the number of vehicle miles “saved” is the sum of the trip A and trip C distances.

Table 2 shows the results of the analysis after running a simulation with the (CD = 1) ridesharing policy. When comparing the percentage values from the major transportation hubs and all NYC pixels, it is important to note that the transportation hub trips account for roughly 10% of all NYC trips. By comparing relative %vMiles and %TaxiRed metrics in the table, it can be concluded that implementing a (CD = 1) ridesharing program would be roughly two times as effective at just the major transportation hubs than if it were implemented throughout NYC.

The plots consisting of Figures 8(a) and 8(b) are cumulative percentage reduction plots, displaying the total reduction in vehicle miles as a percentage of original vehicle miles given an increasing number of pixels added to the overall ridesharing system. Furthermore, the addition of pixels along the x-axis is in descending order of individual-pixel vehicle mile reduction, meaning the first pixel on the x-axis is the most productive at reducing departure vehicle miles. So to repeat for clarity, one reads these plots by visualizing how the pixel-by-pixel increases in service level of the ridesharing policy corresponds to a decrease in %vMiles. The value at the tail end of each curve aligns with the associated value listed under “All NYC Pixels: %vMiles” in Table 2.

Figure 8(c) presents ridesharing system efficiency in a different manner by plotting effectiveness curves of differently-sized service levels. Each effectiveness curve displays the degree to which each individual rideshare framework reduced total vehicle miles. The x-axis of this plot is a discrete ordering of rideshare frameworks sorted by increasing inconvenience to the passenger – it was assumed that it is less convenient to wait longer before departing and that this is more

TABLE 2 (CD = 1) Ridesharing Policy at Two Service Levels

FIGURE 7 Example Logic of (CD = 1) and (CD = 3, dCIR) Ridesharing

severe of an inconvenience than being included in a destination consisting of a slightly larger geographic area. This figure highlights how the (CD = 1) policy places more value on the geographic size of a destination than on the time window, given by how the undulating effectiveness curves always dip when switching to a superPixel framework with the next-largest time window.

Ridesharing Policies and Results: Research Evolution The results presented in the previous section begin to shed light on the overall effectiveness of implementing a ridesharing program within the NYC TLC service. However they are difficult to appreciate without a comparison to other ridesharing policy results. [2] provides much further detail surrounding the evolution and progression of various ridesharing policies. To save time and space, only the major lessons learned will be mentioned here.

FIGURE 8 (CD = 1) Results

Increasing a ridesharing policy from (CD = 1) to (CD = 3, CIR = 0.2) brought forward a significant increase in effectiveness, particularly with shorter time windows. The 30-second time window frameworks witnessed a %vMiles increase by an average factor of 13, while the effectiveness of the 300-second time window frameworks increased by a factor of 8. This large jump makes sense, as the policy’s algorithm has more wiggle-room to find optimal rideshare combinations when more common destinations exist per departure.

Taking directionality into policy consideration – shifting from (CD = 3, CIR = 0.2) to (CD = 3, dCIR = 0.2) – improved %vMiles results, but only slightly. However this result is still promising, as the application of direction circuity would continue to enhance the overall ridesharing system effectiveness while also greatly pleasing passengers. A possible explanation for this increase could be that the previous algorithm would have added trips to a certain departure as long as the circuity constraint was not surpassed, even if a better assignment could have existed. Directional circuity logic helps ensure each trip addition is the “best” assignment.

Reducing the inconvenience level experienced by passengers – from (CD = 3, dCIR = 0.2) to (CD = 3, dCIR = 0.1) – resulted in a corresponding drop in performance. It makes sense that a more stringent policy experienced underperformance across all frameworks (especially the ones with less lenient parameters). Further research would need to be conducted to gain insight into the emotional difference for a rider experiencing dCIR = 0.1 as opposed to dCIR = 0.2; this would allow for a better understanding of the significance of the drop in policy effectiveness.

Lastly, the exploration of (CD = 5, dCIR = 0.1) and (CD = 5, dCIR = 0.2) produced interesting findings when compared with the results explained above. The addition of 2 more common destinations resulted in a jump in policy effectiveness while the greater dCIR constraint allowed for even greater performance. An intriguing difference between these policies and their CD = 3 counterparts was that the shorter time-windows experienced much smaller of an effectiveness increase. A likely reason being because, on average, there are simply not enough passengers to make a dramatic difference in filling all of the departure constraints if the time windows are small. It is also important to note that the performance of (CD = 5, dCIR = 0.1) exceeded that of (CD = 5, dCIR = 0.1), leading to the conclusion that a plausible best practice for NYC taxicabs could consist of a policy with a high number of common destinations and a low circuity ratio.

Ridesharing Policies and Results: (CD = 5, dCIR = 0.2) Although the previous subsection traced through the important findings from all of the result sections in [2], this subsection exists to give a quantitative and visual comparison between a basic ridesharing policy (CD = 1) and a complex ridesharing policy (CD = 5, dCIR = 0.2). Table 3 and Figure 9 show how the most inclusive framework in the “best” ridesharing policy would have witnessed a 23 percent reduction in vehicle miles for all taxicab trips over the course of 2013. Although any double digit reduction in %vMiles and %TaxiRed – when considering the total miles driven by all taxicabs over the course of the year – would be helpful in solving the issues presented earlier in this paper, it is an underwhelming result. It is particularly underwhelming when considering some of the assumptions made to reach it: all individuals

would share a ride if they could; all individuals would be willing to wait up to five minutes before departing; all individuals would be willing to potentially walk additional short distances to their destination.

TABLE 3 (CD = 5, dCIR = 0.2) Ridesharing Policy at Two Service Levels

FIGURE 9 (CD = 5, dCIR = 0.2) Results

CONCLUSION The United States is in desperate need of a reduction in vehicle miles traveled. Dynamic ridesharing appears to be a potential solution that effectively minimizes the amount of infrastructural and technological change required. Yet developing an effective ridesharing analysis across the United States to effectively test such a concept – be it from real or synthesized data – is a major undertaking. This research serves to provide a piece of analysis grounded in the real world in the hopes that it can answer questions about New York City and also be used as a basis of extrapolation to larger, national models. By applying ridesharing concepts to the 2013 NYC TLC data set, this research unveiled flaws in the traditional taxicab system and identified characteristics of a ridesharing program that could reduce the sheer quantity of vehicle miles driven in order for society to function.

With bold assumptions made during ridesharing simulations, the reductions in VMT (while leaving PMT unaffected) were not nearly promising enough to warrant the implementation of such a system, even in as dense of a city as New York City. These uninspired results still raise further questions when considering such a system for the city. If a cost-effective ridesharing system were implemented, would more inhabitants hail taxicabs and therefore increase the system’s ability to function? What would the success of a ridesharing program do to the other forms of public transportation in the city? How dense would a city need to become in order to allow for dynamic ridesharing to prove extremely effective at reducing total personal vehicle miles? Nevertheless, these underwhelming findings associated with the 2013 NYC TLC system prove to be troubling news for the future of any type of ridesharing network installed throughout the United States, where personal automobile travel becomes significantly more complex.

REFERENCES

[1] Chris Whong. FOILing NYC’s Taxi Trip Data. Mar. 2014. url: http://chriswhong.com/open-data/foil_nyc_taxi/.

[2] Swoboda, AJ. New York City Taxicab Transportation Demand Modeling for the Analysis of Ridesharing and Autonomous Taxi Systems. Princeton University, June 2015.