Adopt An Airport-Airport Capacity PDF

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Adopt and Airport Capacity Optimization using three different Mathemathical tools GHP, RBS & GDP and compare the efficiency and usuability of the tool for different scenarios....

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Airport Capacity: Representation, Estimation, Optimization

Krunal Ratan Badsiwal

Dani Cenador

Alvaro Quispe

[email protected]

[email protected]

[email protected]

Abstract: A major goal of air traffic management is to strategically control the flow of traffic so that the demand at an airport meets but does not exceed the operational capacity. This paper considers the major aspects of airport operational capacities relevant to the strategic management of air traffic as such as GHP, GDP and RBS. A representation of airport capacities that properly reflects an airport’s operational limits is discussed. A method is presented for estimating practical airport capacities under various operational conditions. A technique is proposed for optimizing the available airport capacity to best satisfy the expected traffic demand. The optimization is achieved by considering arrival and departure operations as interdependent processes and by strategically allocating the airport capacity between arrivals and departures. The underlying methods is explained in theory, but the heavy use of matlab is an abstraction to tackle the problem. Keywords: GDP, GHP, RBS and Linear Optimization(matlab)

I.

INTRODUCTION

The United States faces a real possibility of running out of airport capacity—not everywhere, but in particular at a number of the 35 most important airports in the national system. The problem is seldom lack of capacity in airport terminals Large airports are financially self-supporting and are generally able to finance terminal expansions. Rather, the problem is one of adding needed runway capacity. Without enough runway capacity, these airports will face increasingly serious problems of delay, which already plague the Philadelphia airport, and the problem doesn’t end here. The most critically important is that out airport is hemmed in by the expensive real estate. Adding a new runway of between one and two miles in length, requires a large amount of land due to security reasons and spacing of Air traffic and the most important constraint of adding a new runway is the cost. Thus we have to take a different approach to increase of capacity of the airport. Between all the capacities from different part of the airport, the most important ones are Runway Capacity and Air traffic. We will be performing our capacity analysis mainly focused on runways and air management.We will be beginning with the introduction of Slots allocation Mechanism

and continue widening our perspective with advanced optimization algorithms like GHP and GDP .[1] Implementing Ground Delay Program in a Flight Schedule Management purpose is to minimizing a delay in a severity of a weather or some other restriction. These restrictions are defined in the FSM as AAR or also known as Airport Acceptance Rate, and these AAR can change during various time-periods within the planning horizon and the set of flights that are included in the program (commonly known as the scope). When a GDP is implemented, these parameters are set based on the projected arrival demand and airport capacity. The difference between end and start times of the GDP,in our project also known as Hstart and Hend, typically coinciding with weather period of reduced arrival capacity. The AAR, which is defined as the number of flights allowed to land in an hour, is set based on the anticipated severity of weather. Based on the AARs, a set of landing slots are created, and each flight included in the program is assigned one such slot. The difference between the landing time is absorbed by delaying the flight at its origin airport. When a GDP is implemented, a subset of flights may be exempted from being assigned ground delays even if they are scheduled to arrive within the planning horizon. Typically, these are the flights that are either airborne at the time when GDP is implemented or that originate from airports located beyond certain distance from the destination airport. The primary motivation behind such distance-based exemptions is to prevent long-haul flights from facing unnecessary delays if weather Conditions improve earlier than anticipated. The subset of flights left is a groundbased ‘inventory’ of short-haul flights whose departure times can be revised. If weather improves earlier than anticipated, short-haul flights could be released with lower delays in order to utilize increased airport capacity. If the weather conditions worsen or persist longer, ground delays could be extended for those flights. Thus, distance-based exemptions not only prevent long-haul flights from facing unnecessary delays, but also provide additional

flexibility to respond to unexpected capacity changes by controlling the departure times of flights that have not yet departed. Following exemptions, the set of flights included in the program is assigned departure delays using the Ration-by-Schedule (RBS) algorithm, which is based on the first-scheduled-first-served principle. RBS is viewed as an equitable method of slot allocation. The next algorithm we will be studying to exempate the set of flights while minimizing the delay is GHP or also know as Ground Hold Program. II.

PREPARING

A. Nominal Capacity Taking a look at the Figure 2, we can have an basic idea of the Current Maximum Operations Capacity Range for each type of weather condition.

DATA

Analyzing our Airport Diagram, obtained from oficial FAA website. If we take a look, we see that there are 4 Runways available, with Runway number 27R/9L in a crossed configuration with runway 35/17 and Runway 27L in parallel with 9R and the Last runway 26, which is independent of the others. see Figure 1.

Figure 2 These weather conditions are determined on base of visuality, where Visual is defined for a Ceiling of at least 2300 feet and 4 miles visibility. While Marginal is defined for a Ceiling and visibility below visual approach minima but better than Instrument conditions. And Instrumental is defined for Ceiling and visibility below 1000 feet ceiling or 3 miles visibility. Now if we try to see the historical data for Visual Weather Condition Figure 3, the capacity is [60,60] (Departures, Arrivals). If we do the same for Marginal Weather Condition figure 4 we obtain [47,47] of capacity ,and for Instrumental Conditions the Capacities are [42,42]. As we can see the reduced capacity for the worst condition is of 42, but we wanted to push our knowledge and these algorithms to it’s boundaries, so thus we chose a PAAR of 20, which is almost half of our reduced Capacity, thus qualifying for our Analysis. If we can optimize our slots on such a low reduced PAAR, then we can also apply for our reduced PAAR defined in FAA document.

figure 3

figure 4

Figure 1: Philadelphia Airport Layout

figure 5

B. Generating demand data from real traffic

(PUJ)

The first step that has to be done is collect some traffic data which will be used during all project in order to obtain realistic results. The data was gathered in the web page Flight Radar [2], and we obtain the departures and arrivals of the airport PHL. This data is 6 consecutive hours, from 6 to 12 am, the 19th of February, and the useful data obtained about any flight of this time interval is the ID, ETA, airline, origin airport and aircraft. We also needed more information like the distance, the number of passengers, the number of connection passengers and if it is an international flight. With the origin airport we can get easily the distance and if the flight is international or no, flights with Canada are not considered international in the USA. And with the aircraft model we also can get a realistic number of passengers. Finally, the percent of connection passengers will be suggested by us knowing that PHL is a hub airport and which airline own the flight.

6:23 AA559

Charlotte American A332 (CLT) Airlines (N282AY)

6:28 UA6318

Washingt United on (IAD) Express

6:30 DL5023

Raleigh-D Delta urham Connectio CRJ2 (N927EV) (RDU) n

6:36 DL2036

Atlanta (ATL)

Delta Air Lines

6:38 AA196

Miami (MIA)

American B738 Airlines (N963AN)

6:40 AA870

A320 Oranjesta American (N104UW ) d (AUA) Airlines

6:40 AA4657

Toronto (YYZ)

American E75S Eagle (N119HQ)

6:41 AA1643

Dallas (DFW)

American A321 Airlines (N921US)

6:44 DL8937

Los Angeles (LAX)

Delta Air Lines

6:47 AA4899

Montreal (YUL)

American E145 Eagle (N672AE)

6:49 DL3498

Delta Cincinnati Connectio CRJ2 n (CVG) (N8783E)

6:57 AA5269

New Haven (HVN)

American CRJ2 Eagle (N218PS)

6:59 UA2399

Houston (IAH)

United Airlines

Table 1: Schedule of arrivals at PHL between 06.00 and 7.00, 19/2/18 (International flights marked in bold)

ETA

ID

origen

aerolinea Avion Southwes t Airlines (Coco B737 movie (N7816B) Livery)

6:00 WN5577

West Palm Beach (PBI)

6:00 1I779

WinstonSalem (INT)

Netjets

6:04 AA2114

Boston (BOS)

A321 American (N195UW Airlines )

6:05 WN1048

Dallas (DAL)

Southwes B737 t Airlines (N7865A)

6:10 AA729

London (LHR)

American A333 Airlines (N274AY)

6:15 WN578

Orlando (MCO)

Southwes B737 t Airlines (N7747C)

6:15 5X2084

Louisville (SDF) UPS

6:21 AA791

Punta Cana

CL35 (N779QS)

B752 (N415UP)

American A332 Airlines (N293AY)

CRJ7 (N504MJ)

MD88 (N919DL)

B752 (N654DL)

B737 (N24706)

C. Capacity during regulation The value for the AAR in our regulation will be the capacity in visual conditions (60), because, as it shows the figure 2, the visual configurations is the most used. About the value for the PAAR should be the capacity in instrument conditions (42), because the most common reason to reduce the capacity is weather, but to show the effects of RBS, GDP and GHP in a better way we decided to use a PAAR of 20. Higher capacity restrictions will show better the difference between this solutions.

III.

REGULATION DEFINITION AND RBS REFERENCE SOLUTION

The RBS solution is the simplest we will study. We will compute the number of slots we have in the regulated period and we will distribute it to the affected aircraft using as reference the ETA predefined before the regulation. The aircraft with the earlier ETA will fullfile his best slot and all the delay will be consumed in holding patterns.

This graphs show the amount of traffic each hour. Figure 6 is without a regulation and Figure 7 i s after the RBS is applied. We can compare them and see how the amount of arrivals at 7 am are reduced and distributed between the next ours without superation the reduced capacity.

Air Delay (min)

The values where we will apply the RBS are:

Total

7371

●

starting time: 7:00 am

Average

74.5

●

end time: 10:00 am

●

AAR=60; PAAR=20;

Maximum

240

●

size of the time slot: 1 min in AAR; 3 min in PAAR

Apply a RBS for this regulation and compute the corresponding delay for each flight and other interesting metrics (total delay, mean delay per flight, etc.). This will be a reference solution to which you will compare GDP and GHP.

IV.

GDP STUDY

The GDP is a solution to an imbalance between capacity and demand.The main difference with the RBS solution is that some aircraft will be controlled due his characteristics and will spend the delay caused by the regulation on the ground, before they take off. This aircrafts are the ones that their ETD is after the GDP is published, are inside the range of action of the GDP and are national flights. The ones excluded from the regulation will have to do air holding. As air holding is more expensive that ground holding, the excluded aircraft will be prioritized. D. Starting point -AAR=60; PAAR=20 -Regulated period from 7:00 am to 10:00 am -File time= 5:20 am

Figure 6

-Radius= 2000 km

Figure 8 Figure 7 With the computation of the traffic before (blue) and after (red) the regulation we get that the hour when the regulation

ends is 10:17 am, and the delay, the area between the two functions, is 3982 min. E. Results

Figure 11 Figure 9 Figure 9 show us how GDP modified the traffic to stabilize the capacity and the demand. Air delay (min)

Ground Delay (min)

Total

180

5859

Average

12

104.6

Maximum

150

240

F. Conclusion The GDP solution best point is that nearly all the delay is spend in ground holding, that is cheaper than air holding. Also the amount of delay is less than in the RBS solution. There is no doubt that GDP is a way better solution than RBS to apply in an airport during an imbalance between the capacity and the demand. Another important point is the time file and the radius. Selecting an small radius or an late time to publish de GDP will make the air delay bigger than ground delay. The optimal values are in the nearly constant region of the graphs (figure 10 and 11). V.

GHP STUDY

GHP is study used to predicate solely for giving ground holding for flights, and optimize them using a ILP, but we wanted to go one step further, so we mixed a GDP and GHP to come up with a better Algorithm, we separate the flights the same way that in GDP and we apply first the GHP algorithm on the excluded ones and then on the controlled ones. Thus may improve the efficiency of the algorithm to allocate flights in the Slots. G. Starting point

Figure 10 We also compute the effect of the file time and the radius. We can see how the distribution of the delay changes with his parameters, and we can select the optimal file time and radius to apply in the GDP.

As we are applying the same rules to GHP like we did in GDP, we would be repeating the process of aggregating the demand, and Computing Flight Status to Separate Excluded and Controlled flights for the analysis. [Figure 8] -AAR=60; PAAR=20 -Regulated period from 7:00 am to 10:00 am -File time= 5:20 am -Radius= 2000 km

Now formulating GHP, we know that in order to optimize our problem we will be using MILP (Mixed Integer Linear Programming). The deterministic GHP can be formulated as

Air delay (min)

Ground Delay (min)

Total

49

4017

Average

2.13

70.47

Maximum

28

174

Where the variables of these formula are Cft which corresponds to the cost associated to each flight

Optimal objective value

Xft represents each of our flights and it is a binary variable. e which is the earliest time interval at which flight f can arrive at the constrained airport,

Air

2288.260000

Ground

111847.460000

t which corresponds to time intervals 𝞮 which symbolizes the uncertainty of the demand, rf which is a coefficient allowing us to give higher costs to some flights. In this approach, 𝞮=0 that means simulating a ideal case and rf= connecting passenger + 1 or all flights which is equivalent to say that there isn’t any flight having zero cost. Reformulating the previous equation,

In order to solve the problem, some constraints are imposed. The first one is that each aircraft can only arrive once at the airport so it can only be allocated once and the second and last one is that the solution proposed can’t be negative, in these case it will be binary. In our cost function, if a flight arrive before an ETA, the cost of that flight will be very high,making impossible for the optimize function to take it. H. Results

I. Conclude on this part After glancing on the results, we can already see that the total delay is almost half from the results obtained from RBS. And continues to prove our point that, usually RBS is only used to have a basic idea of delay being added in the system by reduced capacity. Now if we compare our Mixed GHP with GDP, it seems that it is also great in reducing air and ground delay thus decreasing the total delay being added in the system. VI.

AIRPORT CAPACITY STUDY

J. Starting point To study the airport capacity of Philadelphia, we had to start by organizing the data we collected of arrivals and departures in slots of 15 minutes each list. Also, we need the capacity curves that we have already searched, but the capacity is hourly so we had to compute the capacity divided by 15 minutes instead of one hour. Our objective is to solve an integer linear problem, maximizing the following objective function.

Figure 15 .Objective function to maximize

Figure 12 [Figure 12] show us how GHP modified the traffic to stabilize the capacity and the demand.

Where N is the number of slots, i the number of iterations, alpha the weight coefficient that priorities arrivals when it’s close to 1, and prioritizes departures when it’s close to 0, and finally u is the arrival capacity and v is the departure capacity.

Also were focused on minimize any queue that is produced, so at the end this is a problem of commitments to find an equilibrium. Our constraints for this problem will be the demand from the slots we have filled with our data and the capacity lines adapted to our project that we have already searched previously. We study two scenarios of our airport, one with visual flight conditions and the other with instrumental flight conditions, or also as a consequence, nominal capacity at normal conditions and reduced capacity for bad weather respectively.

K. Results We solved our problem using Matlab and we obtained the following results. Both scenarios are very similar in our case, that’s why we will present only the case for instrumental conditions for alpha equal to 0, because with alpha equal to 1 we have the reversal results, all capacity points are located at y-axis and queues are inverted, being the departures one increasing unstable with time.

Figure 16.Capacity graph for alpha=0;

To find the optimal alpha value we had to try every alpha between 0.1 and 0.9 that has the equilibrium and distribution of accumulating queues and maximum cost. In our case, we found it at 0.1 with a cost of 1974 with equilibrated queues in both scenarios with equilibrated queues. These queues can be absorbed by adding more slots and delaying those flights. For our optimal alpha, in the case of nominal capacity we estimate that an addition of one slot can absorb the queue because our AAR is about 60 aircraft/hour that means 15 aircrafts/15 minutes and if we look at our plots the peaks for arrival and departure queues are at 4 and 6 respectively so we can absorb it a priori. We proceed with the same hypothesis for bad weather conditions where we used the proposed PAAR used previously and we deduce that we probably need 3 slots.

F  igure 17.Departure queue over time for alpha=0

Figure 18.Arrival queues over time for alpha=0

L. Conclusions First, we can say that maximize capacity for arrivals or departures ...