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Analyzing Air Taxi Operations from a System-of-Systems perspective using Agent-based Modeling

Julian R. Archer1, Alden W. Black2, and Satadru Roy3 Purdue University, West Lafayette, IN, 47907

The purpose of this paper is to introduce air taxi operations as a system-of-systems type problem. Five primary traits, operational and managerial independence, geographical distribution, emergent behavior, networks, and trans-domain are highlighted since they call attention to a network-of-systems dynamic behavior focus as opposed to an individual system, static behavior focus. More specifically, this paper tries to extend work done by Mane and Crossley1 in an attempt to capture a more realistic air taxi operation via agent-based modeling using Matlab. Our interest is to understand which particular mixture of aircraft types, as selected for our preliminary analysis, are most viable for profitable air taxi operations between random city pairs given emergent business traveler demands. Mane and Crossley1 identified the Eclipse 500 and Cirrus SR-22 as two of the aircraft most promising for air taxi operations. However, our results revealed the Piper Meridian, Daher-Sacota TBM 850, and Pilatus PC-12/47 single engine turbo-props as the most efficacious aircraft.

I. Introduction he notion of air taxi operations isn’t new. In fact, the idea has been studied by numerous researchers at various research institutions, for instance: 1, 2, 3, 4, 5, 6, 7, and 8. The goal of air taxi operations in simple terms is to utilize

small aircraft (say single piston engine, twin piston engine, turboprop, or very light jets) to provide an on-demand “point-to-point” air travel service. The “point-to-point” service we referred to would be from a location (point) near the travelers’ origin to a location near their desired destination. The common agenda in understanding the dynamics that are involved in air taxi operations is the fact that it can serve as an alternative mode of transportation to the traditional commercial airline service, which requires passengers to: travel to a major airport via ground transportation to eventually board an aircraft; fly from that major airport to a hub where a connecting flight can be made; fly from the hub to a major airport within a reasonable radius of the passenger’s destination; utilized ground transportation once again to reach the desired destination. Air taxi operations are ideally an alternative that would reduce the travel time involved in moderate-to-long-distance ground (door-to-door) travel and reduce the hassle of using commercial airline services, for instance seemingly-inefficiently travel from the south of the US to the Midwest to “connect” before finally travelling to the northeast.

The air taxi idea at first seemed relatively straight forward. Unfortunately it is not, and there has been much debate on the marketability and viability of its operations, as cited by Mane and Crossley1: “On one side of the debate, several experienced airline executives and even a former director of an aircraft manufacturer have proposed and / or launched air taxi services. On the other side of the debate, aviation business analysts claim that air taxi service would not reach a sufficient share of the market to be successful”. To understand the debate we should realize various factors play a role in the determining whether the air taxi operation turns out to be a marketable and viable one, or fails. For instance, the service is not able to fly everywhere. Therefore, which airports and routes should be served? According to Boyd et al.3, the airports to be served would need to be nearby popular destinations and be easily accessible to ensure adequate passenger demand; also, the routes to be served between city pairs should not exceed 350 miles in point-to-point distance. Other questions of concern would be “What are acceptable passenger wait times if they show up?” and would like a flight immediately, and “Should passengers be flown within a certain window period (e.g. within 1-2 hours of arriving at the airport) or immediately on arrival?”

More interestingly is the issue of aircraft type. What types of aircraft and how many should we use and dispatch? We should realize that the dispatching method directly affects the number of deadhead flights during operations. 1 Graduate Student, School of Industrial Engineering, Email archerj@purdue.edu, and AIAA non-member 2 Graduate Student, School of Aeronautics and Astronautics, Email black36@purdue.edu, and AIAA non-member 3 Graduate Student, School of Aeronautics and Astronautics, Email roy10@purdue.edu, and AIAA non-member

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Deadhead simply means that the aircraft has to relocate and fly empty (without passenger) to an airport for continued operations. Should we use small-capacity ( 5 passenger seats) or large-capacity (5 but ≤ roughly 10 passenger seats) aircraft? Obviously there is going to be a tradeoff between the latter two aircraft options: a larger capacity aircraft can carry more passengers but at a usually higher cost and vice versa; and in low demand periods larger aircraft might not be the smartest option to have. Also, higher numbers of aircraft within a fleet may result in lower utilizations, which correlates to lower returns (overall profit).

Because of the interesting nature of the “aircraft type” problem previously mentioned, this paper will present work to investigate the costs and benefits of having certain types of aircraft within a given aircraft fleet when conducting air taxi operations. The work done by Mane and Crossley1 concluded that the Eclipse 500 very light jet and Cirrus SR-22 would be best suited (profitable) for air taxi operations, however we would like to challenge this outcome; we believe that it is only natural for a mixed-aircraft fleet to emerge as the most profitable. Our work tries to identify what this “ideal mixed-aircraft fleet” could possibly look like given several preliminary aircraft options. The aircraft types utilized in our research study will be compared based on trip time, trip cost, overall operating cost, and overall profit. The air taxi operation will be modeled using an agent-based modeling (ABM) approach via Matlab. Based on these comparisons mentioned earlier, observations regarding the most profitable aircraft fleet combination for air taxi operations between a randomized set of city pairs of different weights (probability of travelers going between one city pair versus another), will be presented. The target market of this study is assumed to be business travelers.

II. Problem Statement and SoS Definition Phase Congestion at major US hub airports and their surrounding airspace has paved the way for the use of air taxi

operations to relieve some of the congestion by shifting the passenger traffic to underutilized airports. Air taxi operations as introduced earlier are on-demand, regional, air transport services, utilizing aircraft with limited capacity (≤ roughly 10 passenger seats). The idea of air taxi operations is great in theory; however, there are many difficult logistical decisions that have to be made in order to ensure their marketability and viability, e.g. flight scheduling, fleet assignment, aircraft routing, crew scheduling, and crew roistering. Air taxi operations can be considered a sub-system of transportation under the national air transportation system, but at the same time, it is its own system-of systems (SoS), which exhibits the following traits: operational & managerial independence, geographic distribution, emergent behavior, networks, and trans-domain coverage. These traits make the optimization of such operations an extremely difficult problem to solve, where a closed form solution is not readily attainable.

A. Status Quo Our initial literature review indicates some

forays into this air taxi field. However, all of the papers examined thus far leaned towards a deterministic set of equations, with no guarantee of capturing the required emergent behavior. Day Jet, the failed Florida start-up famous for ordering thousands of Eclipse jets, sponsored much work devising an effective scheduling algorithm7 and 8. It remains to be seen whether some sort of overall scheduling system needs to be implemented to coordinated fleet movement (i.e. to produce a directed SoS) or whether the system will naturally fall into an optimized form. Researchers have examined the overall aggregate behavior of the air taxi network, without much thought towards capturing the dynamics3, 4, and 5. Mane and Crossley1 and 2, while considering specific aircraft operating characteristics and customer demand, also employed deterministic equations and left much undone in terms of capturing dynamic behavior and desired modeling fidelity.

With the latter being said, this study extends the efforts of Mane and Crossley1 to produce a more dynamic and faithful model of the air taxi system in an attempt to specifically identify which aircraft types are best suited for profitable air taxi operation.

Figure 1: (a) Trip composition for airline (orange), automobile(black) and air taxi (blue) travel modes [taken from Mane andCrossley1], and (b) Time-value cost vectors corresponding to thetravel modes which are color coded. Note, the longer the vector thegreater the travel cost based on time value, and vice versa.

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Learning from Mane and Crossley1 rather than attacking them, they considered the monetary cost of a trip when comparing potential travelers’ preference for air taxi services versus airline services; see Figure 1 (a). We agree with this approach because if you didn’t consider the latter, then airlines would always have the edge over air taxis, since they would provide the cheaper ticket option in most cases. Also, by only considering the door-to-door travel time, the airline service may not be an economical option for those business travelers with a concern for their time-value cost. Note that if we were the consider the perspective in Figure 1 (b) , we can realize that even though the travel cost may be lower for airlines than for the air taxi, the travel distance involved in airline travel is greater than that of air taxi, hence a traveler’s time-value cost is expected to be higher. The auto travel mode is a special case where a traveler’s time-vale cost varies based on whether ground delays are present along the duration of the trip, even though the door-to-door travel distance may be the shortest when compared to airline or air taxi travel. This variation is illustrated with the dashed black arrow in Figure 1 (b).

The part of the approach used by Mane and Crossley1 that we are not too comfortable with is the fact that they utilized Bureau of Transportation (BTS) data to evaluate the time-value cost to serve a city pair with a given aircraft. By trying to predetermine the market segment and size, they fail to account for the system dynamics that occur after the air taxi operation has been implemented. Our approach, as we will discuss later, will try to account for these dynamics by use ABM, with passengers and aircraft acting as agents.

Finally another point we would like to call to attention from the Mane and Crossley1 paper is that their study assumed each air taxi operations will have two passengers on board with a pilot to fly the aircraft. We think that this assumption deviates from reality as the air taxi is supposed to be an on demand service and the call for request is random during any given time of the day. Importantly, it is this flexibility feature of the air taxi operation that makes it a stand out competitor to the traditional commercial airline industry. Our work will attempt to capture this “flexibility” feature and account for the uncertain/random traveler market demand between city pairs.

B. SoS Traits, Categories and Levels The SoS model or perspective of understanding systems differs from traditional system models. This approach

has been applied to many complex large scale problems as noted in following references: 9, 10, 11,12, and 13. This approach of looking at complex systems benefits from the fact that it allows us as researchers to carefully pay attention to the system components as well as the whole (in our case, the individual aircraft and air taxi travel routes, and the aircraft fleet and entire air taxi network. Important SoS traits identified by Maier12 and DeLaurentis14 that apply to our air taxi operation under investigation are listed in table 1.

In the context of our air taxi operation under consideration, the functional levels of the structural SoS hierarchy, and the design/control variables are defined in Table 2. For the latter purpose, we adapted the categories from DeLaurentis14 for defining the goals and services (role, function) of each component in a SoS, as defined by the Greek symbols: alpha (), beta (), and gamma ().

Table 1: Distinguishing Traits/Features of our Air Taxi System-of-systems

SoS Trait/Feature Description

Operational and managerial independence

Arises from the nature of air taxi operations having multiple players (air taxi operators) with their own personal visions and goals. To accomplish these goals the operators independently manage a fleet/ fleets of aircraft operated by a resource pool of pilots working for the air taxi

Geographical distribution This is present from the spread of resources (aircraft, aircraft hubs, etc) that can exist in different locations

Emergent Behavior

This will particularly be evident in the traveler demand between city pairs, and in the aircraft type utilization based on the traveler demand, required travel time (based on the traveler’s time-value of money), and travel distance between city pairs.

Networks

The air taxi operation is essentially a network that consists of city pairs that travelers go to-and-from. Each city pair route has its own individual weight (probability) that a random customer at any given time will opt to travel via it.

Trans-domain

Understanding the air taxi operations requires unifying knowledge across different fields of study: aircraft operations; the economics behind traveler demand, population income, and the time-value cost; and policy behind safety requirements and operational regulations. Hence: Operations ∪ Economics ∪Policy

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Table 2: Use of Lexicon for Understanding Air Taxi System-of-systems

Levels Resources Operations Economics Policy

aircraft, travelers aircraft assignment, flight

scheduling, aircraft utilization

direct operating cost, ticket pricing

crew duty hours, aircraft safety, maintenance requirements, etc.

aircraft fleet, traveler

demand operations of an air taxi operator, fleet utilization

total operating cost, overhead and investment costs, revenue,

pricing strategy, etc., local supply/demand

air taxi operator safety, company regulations, FAA

regulations

overall market demand, company assets, regional air

transportation system

operations of all air taxi operators

industry operating costs and revenue, union salaries, market

sensitivity

government initiatives (incentives), government

regulations.

Problem Boundary: Our research scope is identified by the green highlighted section, and it goes up to the ( level. Specifically, we are going to focus on resources, operations, and economics. For resources, we are primarily concerned with the individual aircraft, aircraft fleet and traveler demand. For operations we are concerned with aircraft assignment, and flight scheduling. Finally, in terms of economics, we are concerned with total operating cost and profit, and ticket pricing.

Based on our problem boundary stated above, the -level and -level SoS components that are under consideration are put in perspective by defining them and identifying which SoS traits/features specifically apply to them.

The aircraft is the system mechanism via which travelers are transported from one city to another. Individual aircraft can be geographically distributed between different cities at any given moment during the air taxi operations.

The aircraft fleet, on the other hand, can consist of a mixture of aircraft types and therefore, depending on how the SoS reacts to factors such as the demand of potential travelers, emergent behavior is evident in the fact that the aircraft fleet configuration can change over time.

Traveler demand is basically a measure of the number of travelers wanting to go to a given city within the air taxi network at any given time. This would also exhibit an emergent behavior as passenger demand for a given city is expected to also change over time.

Aircraft assignment is the processing of assigning a particular type of aircraft to fly to a given travel route. This has a trans-domain feature since economic considerations need to be made in determining a practical aircraft type based on required operating characteristics, e.g. max range, operating cost, etc.

Flight scheduling refers to the decision making process of whether the travelers requesting to use the air taxi service are actually flown. Flight scheduling may be subject to emergent behavior as the demand of potential travelers fluctuates.

Total operating cost is simply the cost incurred for overall services rendered to travelers using the different aircraft types. These cost may primarily be associated with fuel and maintenance cost. Total profit is anything amount of monetary gain less total operating cost. Operating cost and profit may both have an emergent behavior feature since the aggregate cost and profit would fluctuate as a function of what aircraft types are utilized and how often they are utilized.

Ticket pricing refers to the price that will be established for a traveler to pay for a given flight. Ticket pricing also has emergent features as the price would adjust overtime during the air taxi operations as a function of traveler demand.

III. SoS Abstraction Phase

A. Resources, Stakeholders, Disruptors, and Drivers of the Air Taxi Operation The abstraction for our air taxi operations shown in Figure 2 builds from the levels and categoriss mentioned

earlier in section II part B. Two pair of entity descriptors are evident from the abstraction process: explicit-implicit and endogenous-exodgenous. The categories in this abstraction serves to organise the entities under consideration by their inherent nature. There are three entity categories for our air taxi operations (noting that we did not consider any disruptors such as adverse weather, delays, etc, hence we will ignore this category). Primary resources under consideration in our air taxi operation include time and money. The latter are explicit resources because they are physically experienced by the consumers, which for our purposes would be the customers/ business travelers.

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Furthermore, they are endogenous because they are under partial control by the customers and aircraft (note that partial control by the aircraft would be related to the fact that the various aircraft types can travel at different speeds).

The stakeholders (customers and air aircraft) of our air taxi operations are endogenous entities because they desire to exert forces on the architecture for their own interest. In the case of the aircraft, the personal interest is to maximize profit by transporting travelers; and in the case of the customers, their personal interest is to minimize their time-value cost by getting to their desired destination much faster for a reasonable cost. These behaviors by the stakeholders influence the demand and aircraft fleet configuration in the air taxi network. These stakeholders behave in an implicit manner because their actions aren’t clearly visible to the consumers. The air taxi environment contains exogenous entities outside the architect’s controllable domain. This entity class contains given assumptions and constraints about the air taxi environment. For instance, the drivers are concerned with economic and societal circumstances that influence the stakeholder network by implicit means. In our case, we account for: the population distribution, income distribution of the population, commercial airline network, and personal vehicle network. Note again that there were no disruptors considered in our air taxi operations.

B. Paper Model of the Air Taxi Operation To understand the general idea of how we considered the modeling of the air taxi operation, reference Figure 3

and let’s start on the passenger side of the paper model. The first thing to notice is that there are a few “bubbles” that are outlined in green; these green bubbles are our drivers, and they include (as mentioned earlier) income distributions, commercial airline cost, personal vehicle cost, and population distribution. These drivers feed into the customer agent’s beliefs, knowledge and information loop (BKI). Essentially, travelers are trying to get from, let’s say, point A and point B (two arbitrary points not depicted on the diagram above). These customers potentially have three means to get to their desired destination: via the commercial jet network, driving themselves in a personal vehicle, or flying in an air taxi. As a result, they look at and evaluate the cost of doing all three and they pick the option that is best suited to their income level. Considering that the customer has made this evaluation and has decided to choose the air taxi option, they are then seen by the air taxi system as demand, in the “Act” bubble still on the passenger side. It is this particular act that triggers the entire loop of trying to get them from point A to point B. This trigger is represented by the red arrow that crosses over to the air taxi side of the paper model. Once on the air taxi side of the operations, the aircraft are trying to increase their revenue; hence they also evaluate their own BKI. Initially, the idea was to tackle an entire fleet allocation and scheduling problem. However, the model became more of a lion and gazelle problem for practical computational purposes. The gazelles are the travelers and the lions are the aircraft, and essentially, the goal is to eat the travelers to get the most amount of money. Hence, what we are doing is letting the different types of aircraft compete against each other to see which aircraft types steer most profitably. As this is done over the long run, and because our demand is entirely stochastic, and because we keep making new networks, and run the Matlab model enough times, in the end we expect to end up with a good idea of which aircraft types are best for air taxi operations and to which parts of the population do they appeal to.

Figure 2: Entity-Centric Air Taxi Abstraction Model (adapted from DeLaurentis9)

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IV. SoS Implementation Phase

C. Methods/Data In order to further understand the air taxi operations beyond the paper model presented in section 3 Part B, an

agent-based modeling (ABM) approach was used. The platform used to simulate the agent behaviors was Mathlab. The code within our Matlab model utilizes a variety of unique design/ control variables, datasets and operational logic. Most of our data for generating the required distributions came from reference: 15

Any dataset or distribution plot used in or study will be presented in the Appendix due to the page limitation of this document.

D. Design/ Control Variables There were two primary design variables in this model, the aircraft type selection and stochastic distributions. Besides these

two general categories, the rest of the behavior followed simple rules of supply and demand, minimization of costs, crew duty days, etc.

1) Aircraft Type. Without providing the basic comforts of travel and ensuring a reliable service, the air taxi operations model becomes completely unsustainable. This is very true considering that the primary advantage of air taxi service remains its ability to save the potential travelers’ time while maintaining a service level comparable to commercial airlines. Unlike the traditional commercial airlines which suffer from delays and cancellations due to adverse weather, this behavior is unacceptable for air taxi operations. As a resut, the air taxi aircraft should possess all-weather capabilities (specifically, on-board weather radars and deicing equipment). Furthermore, to avoid encumbering the passenger with headsets and oxygen masks for high altitude operations, the air taxi aircraft should be turbine powered and pressurized.

In light of these considerations mentioned above, we decided to limit the air taxi operator to six possible aircraft, consisting of three single-engine turboprop aircraft, two very light jet aircraft, and a twin-engine turboprop aircraft with jet-like performance. The single-engine turboprop aircraft are: (1) the Piper Meridian, (2) the TBM 850, and (3) Pilatus PC-12/47E. The two very light jet aircraft are: (1) the Eclipse 500, and (2) the Phenom 300. The twin-engine turboprop aircraft with jet-like performance is the Piaggio Avanti II. A picture of each aircraft used in our study can be found in Figure 2 below. Note that it was important to understand the operating characteristics of each aircraft for modeling their operations realistically. Operating characteristics taken into consideration included: passenger capacity, aircraft speed, max range, and operating cost. The later data was obtained from the Aviation Week Business & Commercial Aviation Database via one of the authors’ subscriptions.

Figure 3: Paper Model of the Air Taxi Operations

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2) Stochastic Processes. Stochastic processes dominated much of the behavior in this model as explained in

subsequent sections. City locations, commercial airline network structure, population distribution, etc, all followed random distributions that could be altered to examine their effects on the air taxi operations. This enabled sensitivity studies such as examining the impact of the commercial airline network density on the air taxi average profit.

E. Operating Rules and Logic The ABM rules in this model are quite confusing at times. Consequently, the following section details the

semantics – including specific values – in a logical “information-flow” progression, after which a paper model attempts to give a pictorial representation of the model. The travel day lasts from 6:00am to 10:00pm. Outside of this time, no aircraft may fly and no passengers may travel. Each of the 20 cases runs for 7 days (a full week). The code tracks the individual movements of each customer and aircraft to yield a detailed time history with which to examine the results.

This model features 20 independent cases, each consisting of 8 cities distributed randomly across a 1000nm by 1000nm square area. Each case contains 100 individual customers, with income levels varying between $50,000 and $500,000 per year in proportions consistent with 2012 US Census Bureau data. These 100 persons were then distributed at random between the eight cities in proportion of the largest 500 cities in the US. Again, based upon US Census Bureau data, a person’s income determined the number of trips they made in a given year. Distributed across all the working week minutes in a year, this yields the probability at a given minute that a person decides to make a trip. While the resulting probability seems unreasonably low, over the course of a year a person will on average make a number of trips consistent with their income level. To determine the destination of a trip, each person possesses a probability to the other seven cities. This probability depends again on the income level as well as the distance between the origin and destination cities. The person also generates a randomly determined desired arrival time over the remaining time in the day.

These persons – the customers – are the first type of agent in the model. When a person decides to travel to a city, he or she chooses between three different modes of transportation: personal driving, commercial air transportation, and air taxi. They will evaluate the cost of each, including the cost of their own time (from their income level) and pick the lowest cost option. In all cases, the person also assumes a travel cost of $0.1998/minute, derived from the 2012 US average for per diem expense of $287.76. In other words, the total cost consists of the cost required to use a particular form of transportation and the time required to complete the trip multiplied by the sum of the per diem and income rate per minute.

For the air taxi, the passenger receives a quoted ticket price and quoted time if they decide to take an air taxi (explained in detail later). The commercial flight time (derived from the Aviation Week Database) mimics the performance of a 737/A320 series aircraft. If they elect to pick the commercial option, they pay a ticket price based upon route distance only (no scheduling or aircraft type concerns). Furthermore, they may only travel along the commercial network. The commercial network is randomly determined in each case based upon the distance between two cities and relatively population sizes. As one can see, the approach taken naturally leads to the creation

Figure 4: Air Taxi Aircraft

From top left-to-right and then from bottom left-to-right: Piper Meridian, TBM 850, Pilatus PC-12/47E, Eclipse 500, Phenom 300, and Piaggio Avanti II

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of hubs. Graphs supporting the latter are shown in the Appendix. In addition to the flight time, travel by commercial aircraft or air taxi requires additional time as detailed in table in the Appendix.

If traveling by personal vehicle, the 2012 AAA database provides an average cost per mile (including taxes, depreciation, finance charges, registration, insurance, license fees, gas oil, maintenance, and tires) for a mid-size sedan of $0.735 per mile. According to a recent study conducted by GPS manufacturer TomTom, the national US average highway speed is 67mph. This speed, in conjunction with the distance between any city pair, determines the travel time via personal vehicle. Furthermore, 15 minutes are added on to both “depart” and “arrive” the origin and destination cities respectively (adding 30 minutes to the total trip time) to account for time spent driving to and from the freeway. As expected, the air taxi logic generates the lion’s share of the complexity in the model

Scheduling and aircraft allocation is the heart of this simulation. Each aircraft here acts as an agent and has predefined rules that drive them. To start with, the approach identifies the demand for every given city pair in the network at any given instant of time. If the demand exists, all the aircraft available to the air taxi operator compete for it and the one that fetches the maximum profit wins it. Due to positioning of the aircraft it might be required to undergo dead flights to meet the demand and is accounted in the model. Once a demand is realized, a virtual schedule is created that determines the future flight path for that particular aircraft that offers least expense. This virtual schedule gets updated every minute until the departure time arrives. The dispatcher function keeps a track of the virtual schedule and the real time. When the real time equals the virtual departing time, the aircraft takes off from the city and its location is updated to the arriving city.

F. Uncertainty and Complexity Our air taxi SoS has many sources of uncertainty. Most of the uncertainty is statistical and scenario-based in

nature. The statistical uncertainty arises for the fact that nearly all the distribution utilized in our model for how we expect agents to behave are stochastic in nature and have probabilities attached to them. For instance, what is the chance that a person would be likely to travel between a certain city pair? Our distribution for passenger demand conditioned on the amount of income they potentially earn would give us a likelihood factor that the person chose a given city pair.

The scenario-based uncertainty that exists in our SoS model arises from the fact that we are trying to capture the types of aircraft that would be best suited for viable air taxi operations. Thinking about this carefully, we cannot attach a probability value of creating a certain mixture of aircraft types because this would be meaningless. In fact, it would be more realistic to have a sense for what possible overall outcomes may occur. For instance, if we are looking at a feedback parameter such as total operating cost and then we size that up with the utilization of different types of aircraft, we may realize that certain aircraft seem to be performing well in terms of overall profits made for the air taxi operation. In such a case we could reasonably assume with some uncertainty of the scenario that aircraft “x, z, and z” would probably be the resulting best choices for the aircraft fleet that generates the most profits for the air taxi operators, but this may not be the case that we may find in the end.

Overall, most of the uncertainty involved in our SoS model seems to be epistemic in nature and can potentially be reduced with a more in depth research on specific distributions on agent behavior, e.g. more current income distributions rather than historical ones, and passenger demand between city pairs via more refined distribution equations rather than “smoothing” the data.

In addition to uncertainty, our air taxi operation suffers from a high level of complexity, computational complexity and external complexity. In terms of computational complexity, the scheduling of aircraft and passengers is a very demanding task and utilized very long lines of Mathlab code. The logic involved in the latter issue considers a multiplicity of factors, and hence, each factor adds a string of equations that must be added to the Mathlab code.

In terms of external complexity, our SoS modeling approach of the air taxi operations considers multiple time scales for capturing agent (aircraft and passenger) behavior. On one end of the time scale you have the day-to-day operations of the air taxi service, and on the other end of the time scale you have the aggregate- long run operations of the air taxi service. Adding to this issue, it the fact that the future states are pretty uncertain (from the researcher’s perspective): We just don’t know what emergent behavior to expect from our air taxi SoS operations. We ran our Mathlab code through multiple scenarios and the results kept surprising us: sometimes our system is at a loss and sometimes we are at a profit.

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G. Verification and Validation Verification process started with a set of rules and paper model intended to mimic reality. As we programmed

however, we realized that the model as it stood was untenable – some of the rules and expected methods to model desired behavior were too hard to implement. Initial effort includes incorporating GAMS to maximize the network profit, but later, to reduce the computational complexity we laid down rules for the aircraft for capturing the demand. Effort has been made to keep the conceptual model and the computer model as consistent as possible. The proportion of trips made by a given income level remained fixed in proportion to data taken from the US Census Bureau. However, the overall scale of demand had to be artificially increased to yield even an appreciable amount of air taxi operations.

Once we had it running, we moved onto Operational validation – trying to make the computer model and “reality” as we knew it isomorphic. If we were able to achieve this, then we would be assured conceptual validation as well as it would safe to assume that our modeling and analysis “properly” captured reality (without being too constrictive to prevent emergent behavior of course). However to ensure that we have closely matched the reality, emphasized on the following points: Passengers making logical choices for transportation mode (lower income levels and shorter distances should

favor car) Making sure passengers not flying commercially where routes don’t exist Outlying cities should probably have a larger proportion of air taxi service Big air taxis used where demand is highest Air taxi’s not sitting idle Not all air taxi’s running at a profit These points being said, very little real world data exists for air taxi operations (besides the operating statistics of the aircraft themselves) with which to compare our results, leading to increased difficulty in the V&V stage.

V. Results From the average profit, Table 4 shows the three single engine turboprops – the Meridian, TBM 850, and PC-

12/47 – as the most efficacious. This owes primarily to their low operating costs, even though their speeds remain substantially lower than those of the other four aircraft. The average trip distance also seems to indicate that the Meridian, with the lowest seat capacity in the fleet, also tends to fly the longest routes amongst the single engine turboprops and also possesses the highest load factor as well. Besides these two points however, no other conclusions can be easily deduced from this table. Thus, one can answer the first question of the hypothesis – namely, which aircraft is best suited to air taxi operations – and conclude that single-engine turboprops function well in this environment.

Table 3: Aircraft Performance Matrix

Figure 5 depicts the ideal operating range of the air-taxi network. Although the proportion of profit to loss

generating flights remains sorely skewed in the wrong direction, the presence of the few profit generating flights and total number of air taxi flights indicate the ideal operating range over which air aircraft should operate, approximately 200-500nm. Any shorter than this and personal vehicular transportation proves more economical while travelling in excess of this range often proves prohibitively expensive compared to a commercial airline network.

Aircraft Type Meridian (1) TBM 850 (2) PC‐12/47(3) Eclipse 500 (4) Piaggio II (5) Phenom 300 (6)

Average Profit ‐317.91 ‐367.73 ‐340.62 ‐555.06 ‐569.47 ‐835.30

Average Air Taxi Trip Distance 365.56 322.04 254.50 408.79 304.52 355.90

Average Trips per Day 29.2 24.8 16.4 16 11.8 8.8

Average Flight Hours/Day 1.74 1.60 1.82 1.58 1.51 1.60

Average Passengers per Flight 1.59 1.27 1.55 1.18 1.61 1.38

Average Load Factor per Flight 39.73 25.32 22.13 29.38 23.00 17.22

Average Origin Population 14.26 10.43 14.27 9.86 10.66 15.42

Average Origin Links 3.37 3.49 3.45 3.16 3.37 3.38

Average Destination Population 14.08 10.81 13.68 9.33 10.59 14.76

Average Destination Links 3.31 3.62 3.62 3.38 3.53 3.60

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Figure 5: Number of trips vs range bracket

Figure 6: Number of Trips vs Passenger Income Bracket for the 3 modes of transportation

To answer the second part of the hypothesis – which segment of the population does the air taxi network serve –

one need only look at Figure 6 depicting the travel mode selection by the different income brackets. Obviously, the total number of trips is dependent upon the size of each of the income brackets, thus one must look at the relative composition of each income level. Note the substantially higher proportion of air taxi as the selected mode of transportation as the income level increases. As the individuals with higher income place higher value on their time, the advantages of air taxis become more appealing, resulting in higher utilization.

VI. Division of Labor Each member of our group assumed a role in line with his skills to maximize the efficiency of the group as a

hole. As the most experienced programmer, Satadru handled the lion’s share of the agent coding. Alden checked

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his work, created the aircraft specific functions, and troubleshot where necessary. Alden and Satadru also created the initial agent logic and overall structure, which later underwent refinement after discussion and numerous discussions with Julian. Given Julian’s unfamiliarity with Matlab, it fell on him to write the majority of the report (checked by his teammates of course). In doing so, it forced him to understand the logic, code, and implementation to create the model.

VII. Summary and Conclusions Although rushed, this air-taxi taxi modeling endeavor demonstrated the power of ABM. Although implementing

the logic requires inordinate amounts of time, the resulting ability to examine all aspects of the systems is unparalleled. Of course, one must always consider the necessity of pursuing such an approach, especially if the desired conclusions can be obtained via simpler means. In particular, one must always be careful to distinguish between true emergent behavior and simple exploitation of errors in the code, and determine effective metrics to measure the subsequent behavior. Even though this attempt fell into such a pitfall, enough data could be gleaned to hint at the viability of aircraft other than the Cirrus SR-22 and Eclipse 500 - in particular the Piper Meridian, TBM 850, and Pilatus PC-12/47 - as viable alternatives for aircraft for air taxi operations. Furthermore, air taxi operations seemed to only capture the high-end segment of the market, generally speaking those individuals with incomes in excess of $100,000 per year. Although the absolute values of the results generated in the study may fall far from truth, the insight into the system trends granted via the ABM demonstrates the power of this modeling approach. Further work with this method could yield additional useful insights.

References 1 Mane, M. & Crossley, W. Preliminary Cost Feasibility Study of Air Taxi Operations. in (American Institute of

Aeronautics and Astronautics, 2006). doi:10.2514/6.2006-7734 2 Mane, M. & Crossley, W. An Approach to Predict Impact of Demand Acceptance on Air Taxi Operations. in

(American Institute of Aeronautics and Astronautics, 2007). doi:10.2514/6.2007-7787 3 Boyd, J. A., Bass, E. J., Patek, S. D. & Lee, D. W. Investigation of future air taxi services using discrete-event

simulation. in Syst. Inf. Eng. Des. Symp. 2006 Ieee 25–30 (2006). at <http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4055107>

4 Cordeau, J.-F., Laporte, G., Potvin, J.-Y. & Savelsbergh, M. W. Transportation on demand. Transp. Handbooks Oper. Res. Manag. Sci. 14, 429–466 (2007).

5 Der Zwan, F. M. van, Wils, K. & Ghijs, S. S. A. in Aeronaut. Astronaut. (Mulder, M.) (InTech, 2011). at <http://www.intechopen.com/books/aeronautics-and-astronautics/development-of-an-aircraft-routing-system-for-an-air-taxi-operator>

6 Lee, D., Bass, E. & Patek, S. Characterizing the Aggregate Behavior of an Air Taxi Network. in (American Institute of Aeronautics and Astronautics, 2006). doi:10.2514/6.2006-7023

7 Espinoza, D., Garcia, R., Goycoolea, M., Nemhauser, G. L. & Savelsbergh, M. W. Per-seat, on-demand air transportation part I: Problem description and an integer multicommodity flow model. Transp. Sci. 42, 263–278 (2008).

8 Espinoza, D., Garcia, R., Goycoolea, M., Nemhauser, G. L. & Savelsbergh, M. W. Per-seat, on-demand air transportation part II: Parallel local search. Transp. Sci. 42, 279–291 (2008).

9 DeLaurentis, D. Understanding Transportation as System-of-Systems Design Problem. in (2005). 10 DeLaurentis, D. A. & Ayyalasomayajula, S. Exploring the synergy between industrial ecology and system of

systems to understand complexity. J. Ind. Ecol. 13, 247–263 (2009). 11 Phillis, Y. A. & Kouikoglou, V. S. System-of-Systems hierarchy of biodiversity conservation problems. Ecol.

Model. 235, 36–48 (2012). 12 Maier, M. W. Architecting principles for systems-of-systems. Syst. Eng. 1, 267–284 (1998). 13 Agusdinata, D. B. & Dittmar, L. Adaptive policy design to reduce carbon emissions: a system-of-systems

perspective. Syst. J. Ieee 3, 509–519 (2009). 14 DeLaurentis, D. & Callaway, R. K. A System-of-Systems Perspective for Public Policy Decisions. Rev. Policy

Res. 21, 829–837 (2004). 15 U.S. Census Bureau. "2010 United States Census Gazetteer for Places: January 1, 2010. (2010). at

<http://www.census.gov/geo/www/gazetteer/files/Gaz_places_national.txt>

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Appendix

Figure 7: One-Way Commercial Ticket Price Variation over Q1-Q3 2012. The figure on the right depicts the simple linear fit used to determine the ticket price.

Table 4: Time Requirements for Air Transportation

Segment Airline Air-Taxi Drive to Airport 30 15 Check-in 45 5

Board and Taxi-out 30 15 Flight variable variable Taxi-in and Unload 20 15 Drive to Destination 30 20

Note also that these values differ from those in the Mane & Crossley paper1.

Figure 7: # of trips (y-axis) against income level (x-axis)

0

100

200

300

400

500

0 1000 2000 3000

Average

 One‐W

ay Fare ($)

City Pair Distance (nm)

0

100

200

300

400

500

‐1000 1000 3000 5000

Average

 One‐W

ay Fare ($)

Average Daily Passegners on Route

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Figure 8: Frequency percentage travelled vs distance travelled as a function of income level

Figure 9: Population distribution across 715 cities in the US (x-axis is city index and y-axis is population)

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Figure 10: Passenger trips performed by air taxi and Average Air taxi mission length vs Income bracket

Figure 11: Average Profit per flight and Average trip length vs Commercial airline network density

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Figure 12: Average profit per flight and average trip length vs average city distance