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The following set of parameters are defined in ADSM: the duration of one time step, the average number of departures in each sectors in corresponding time step, and the probabilities tha

Master’s Thesis

Building a Sector Flow Model for Air Traffic Demand Prediction

1710120 Tran Quang Khai

Supervisor Kunihiko Hiraishi Main Examiner Kunihiko Hiraishi Examiners Kazuhiro Ogata

Ryuhei Uehara Fumihiko Asano

Graduate School of Advanced Science and Technology Japan Advanced Institute of Science and Technology

(Information Science)

February 2019

In this paper, we propose a sector flow model for airspace traffic Inspired

by Cell-Transmission Model (CTM), which is initially adapted for land road traffic, the objective of this research is to form a CTM-based model for air traffic With that approach, the contribution of this research is as follows

We first refined the original CTM and its variations to form a deterministic model The purpose of this refinement process is to reduce the complexity

of determining the corresponding location of aircraft in the model After that, from the deterministic model, stochastic factors is considered by utiliz-ing Aggregate Dynamic Stochastic Model (ADSM) Final result is a discrete, Eulerian-based flow model that combines advantages of the original Cell-Transmission Model and its variations To validate the fidelity of the model,

we process and analyze CARATS (Collaborative Actions for Renovation of Air Traffic Systems) flight data provided by Japan Ministry of Land, Infras-tructure, Transport and Tourism (MLIT) and then make comparison with the output from the proposed model

The airspace is divided into several areas called sectors Sectors are the medium where aircraft travel In a simple concept, a sector is a polygon-shaped air area Each vertex of this polygon-polygon-shaped plane is defined by

a geographical coordinate pair (latitude, longitude) A formal definition of sector will be introduced later Aircraft, after taking off from airports and reaching certain altitude, will travel through various sectors to get to the destination airports In most commercial flights, pilots have to submit a document named flight plan to local Civil Aviation Authority Those flight plans include the intended flight paths of aircraft If no form of bad weather happens, aircraft are strictly expected to follow the flight paths filled in flight plans This distinguishes air traffic with land road traffic, where vehicles besides moving by plan, can also travel by habits of drivers Thus, it is reasonable to form a deterministic model of air traffic The impact of random events, such as bad kinds of weather, on flights should also be studied Due to the randomness of those events, a stochastic framework (Aggregate Dynamic Stochastic Model) will be used

As in fluid mechanics, there are two main approaches to model the flow

in traffic: the Lagrangian method and the Eulerian method In Lagrangian method, it takes into account trajectory of every individual vehicle, or in other words, Lagrangian method is suitable for modeling at microscopic scale

In contrast, Eulerian method represents the flow of traffic by volume Each volume has several properties such as flow rate, density, etc

Cell-Transmission Model is a discrete, Eulerian model It is first intro-duced by Carlos Daganzo to model the kinetic wave in highway traffic The idea behind CTM is to break a land road into several small, homogeneous parts called cells Now in each time step, vehicles will move from one to an-other cell Cell’s description such as density, flow rate, flow direction, will be defined Aggregate Dynamic Stochastic Model is a discrete, Eulerian-based flow model The idea of ADSM is to develop a Poisson process description to represent the flow of traffic between sectors The following set of parameters are defined in ADSM: the duration of one time step, the average number of departures in each sectors in corresponding time step, and the probabilities that aircraft moving between centers in corresponding time step

In our work, we refine existing CTM-based models for two goals The first goal is to reduce the computational complexity when determining a corresponding cell for each aircraft The second one is to make it easier to apply current stochastic frameworks In the airspace, there is no real road like land-road traffic Therefore to utilize CTM in air traffic, in each sector,

we define the term “route” A route is an imaginary road inside sector Aircraft will travel on a finite number of route to get to the destination A brief description of the process of forming a route is described as follows:

• Let A, B, and C be sectors

• If B and C are neighbors of A, then two routes connecting B and C will be created inside sector A: one route allows traffic from B to C and one route allows traffic from C to B Note that a route only allows traffic in one direction

• Aircraft that travel between sector B and C through sector A (and vice versa) are expected to travel on those routes In this research, we assume that the aircraft hold a constant speed for its entire journey

• The length of the route is determined by the average time that aircraft takes to travel from starting point to the end point of the route For example, aircraft take an average of 10 minutes to travel in one route, then the length of that route is 10 minutes This information can be extracted from CARATS Open Data

After clearly defining route, we define the core element of the model: cells As with original CTM, we divide a route into a fixed number of small, homogeneous elements called cells Each cell can contains a finite number

of aircraft Under typical operating conditions, all aircraft in one cell are expected to move to the next cell in the next time step The number of cells

2

in one route is the total number of time steps needed for aircraft to travel the entire route For example, the length of a route is 10 minutes and duration

of one time step is 2 minutes, that route has 5 cells

There are two possible cases for an aircraft to enter a route:

1 An aircraft has already departed in the middle of the airspace in a particular sector before the observation period, we need to put that aircraft into a corresponding route and cell

2 An aircraft starts the journey on the starting point of the route, thus that aircraft will be put on the first cell of the route

The problem of determining the corresponding cells in case 1 still persists

in previous studies To eliminate the need regarding particular details of departure schedules for aircraft, in this thesis, we assume that routes taken

by and the final airports of the departing aircraft are independent After defining all necessary terms, we mathematically describe the relationship of each cell in a route to form the model The output of the model is the sector count (total number of aircraft) in specific sectors at certain time steps

In our study, we perform the validation process of the model in Fukuoka Flight Information Region CARATS Open Data provided by MLIT are used in this process Raw data contain flight information such as latitude, longitude, altitude, etc However, it does not provide the information regard-ing sector Thus we need to analyze and extract necessary information for the validation process Four random-select sectors: Tohoku sector, Misawa West Sector, Chugoku High Sector, and Kanto East Sector are studied in this research

3

I would first like to show my sincerest thank to Professor Kunihiko Hiraishi,

my supervisor for the Major Research Project Without his unceasing sup-port in both finance and specialization, I would not be able to complete my master program I still remember the 2016’s summer, the time that changes

my life completely Professor Kunihiko Hiraishi welcomes me to his labo-ratory and encourages me to follow my research career He is the one who helps me fulfill the dream of studying in Japan His guidance is invaluable

to me

Secondly, I would like to thank Professor Hiroyuki Iida, my advisor for the Minor Research Project Three months working under his supervision is an amazing experience I have unique opportunities to learn a lot of interesting things to “blur the line between work and play” I would also like to thank Professor Kazuhiro Ogata, my second supervisor for his support in the last two years

I would like to acknowledge Professor Kazuhiro Ogata, Associate Pro-fessor Fumihiko Asano, and ProPro-fessor Ryuuhei Uehara for their comments and suggestions in my mid-term presentation and final defense Their expert advice helps me improve the quality of my thesis a lot

I would also like to thank all my friends Wherever you are in this world, you are always right behind me in this thrilling journey

Lastly, I would like to show my heartfelt gratitude to my parents Their unconditional love and support are the strength that raise me up in all the difficult time I have had

1.1 Background 1

1.2 Goals 4

1.3 Contribution 4

1.4 Thesis Outline 5

2 Related Works 6 2.1 The Cell-Transmission Model 6

2.1.1 The basic model 6

2.1.2 Extension in network traffic 8

2.1.3 Evaluation 9

2.2 Application of Cell-Transmission Model in modeling air traffic flow 9

2.2.1 The Modified Cell-Transmission Model 10

2.2.2 The Large-capacity Cell-Transmission Model 14

2.3 The Aggregate Dynamic Stochastic Model (ADSM) 17

3 Proposed Model 21 3.1 Flight Clustering and Route Determination 21

3.2 Route Connection 23

3.3 Model Descriptions 23

4 Experiment 28 4.1 CARATS Open Data 28

4.2 Numerical results and evaluation 30

5 Conclusion 42 5.1 Summary 42

5.2 Future Work 42

List of Figures

1.1 Fukuoka FIR (source: [1]) 2

2.1 A simple illustration of Cell-Transmission Model The black dots represent the current number of vehicles in cell 7

2.2 Merging and diverging traffic 9

2.3 A network with merging and diverging cells 9

2.4 1-D cell traffic flow 10

2.5 A sample airspace modeled using cells, diverge node, and merge node 13

2.6 A sample airspace modeled using nodes and links 14

3.1 Airspace in Original MCTM and Characterized MCTM 22

3.2 Route Connection 24

4.1 Sectors in Fukuoka FIR (Source: [2]) 29

4.2 Sector count for Tohoku sector (November 09, 2015) with dif-ferent time interval 31

4.3 Sector count for Chugoku Sector on different days 34

4.4 Sector count for Misawa West Sector on different days 35

4.5 Sector count for Tohoku Sector on different days 36

4.6 Sector count for Kanto East Sector on different days 37

4.7 Sector count error for Chugoku Sector on different days 38

4.8 Sector count error for Misawa West Sector on different days 39 4.9 Sector count error for Tohoku Sector on different days 40

4.10 Sector count error for Kanto East Sector on different days 41

List of Tables

1.1 Number of passengers carried by airlines (2008-2017) 3

4.1 Sample CARATS Open Data 29

4.2 Number of each type of routes in observed sectors 30

4.3 Some routes in Misawa West sector (S01) 32