Air Traffic Control, Reliability Analysis and Cargo Operations - Imran A. Khan

8/16/2019 Air Traffic Control, Reliability Analysis and Cargo Operations - Imran A. Khan

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SYSEN 5200 Project ReportSpring 2016

Group Member: Joseph Kujawa [jdk277]

Imran Khan [iak26]

Stephen Lee [sjl345]

Bob(Kunhe) Chen [kc853]

Cornell University


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SYSEN 5200, Spring 2016

Table of Content

Executive Summary

1. Air Traffic Control

Section 1.1 - Problem Description

1.1.1 STATES AND EVENTS

1.1.2 SIMULATION MODEL

Section 1.2 - Result Discussion

Section 1.3 - Case Comparison

Case 1 – 10% Reduced Mean and SD Landing Time

Case 2 – 10% Reduced Mean and SD Recircle Time

Case 3 – 10% Reduced Mean and SD Queue Separation Distance

SUMMARY

2. Reliability Analysis

2.1 Problem Description

2.2 Analysis and Results

2.3 Summary

3. Cargo Operations

3.1 Optimization Model

3.1.1 Background

3.1.2 System Description

3.1.3 Optimization Objective

3.1.4 System Model

3.2 Simulation

3.2.1 Optimization

3.2.2 Solver

3.3 Analysis

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3.3.1 Results

3.3.2 System Analysis

4. Conclusion

Appendix A

Appendix B

Appendix C

Appendix D

Appendix E

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Executive SummaryThis report focusses on some of the challenges in the air transportation and the aircraft industry,

provides a detailed analysis of these challenges, and proposes solutions and recommendations.

Section 1 talks about air traffic control, focussing more on the landing queue system. Owing to

the safety measures of maintaining a certain separation distance in the queue, there are

challenges that the aircraft industry faces in terms of avoiding flight delays and better

management of air traffic. A discrete event simulation (DES) model is used and it is found that

the average queue length is between 2.48 and 3.13. This provides room for improvement since

it is desirable to have shorter queue lengths. A more detailed analysis found that about 17.4% to

23% of the time, the queue is clogged, which is defined as more than 5 planes in the queue. This is far from ideal because a clogged queue means flight delays and bad customer ratings.

Moreover, the total number of planes in a system for a given system requirement is

approximately 14 planes, which is again is far from ideal. The average number of planes in

recircles are also high. Thus, there is significant challenge in terms of reducing queue length,

reducing clogged queue time, number of planes in the system, number of planes in recircles,

and a variety of additional issues.

Following a static analysis, the report discusses the impact of a decrease in mean and spread of

landing times by 10%, which may be because of relaxation of stringent safety rules. It is found

that all the statistics improve to a great extent because of such a small change. Hence, it

becomes only advisable to research further on whether this 10% can be incorporated without

compromising on safety standards. Another static analysis was conducted to assess the impact

of a decrease in recircle distance by 10%. This analysis does not show a significant

improvement in the overall air traffic control system and hence can be reduced in priority. The

third static analysis was conducted to determine the impact of the change in plane separation

with a decrease of 10%. This results in a dramatic improvement to the amount of time the queue is clogged. Hence, this change should definitely be considered by the management with a high

priority. We believe that the first and the third change are highly feasible and should be

implemented following final safety tests. These recommendations can help to ensure effective

air traffic control.

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Section 2 focuses on the reliability analysis in the same setup of aircraft industry. Emotionally

driven customers give a lot of importance to safety. It is critical to understand the risks and how

those risks interact with one another and affect the system as a whole. The overall likelihood of

an accident is extremely small; however with increasing air traffic, this probability grows in

likelihood and becomes even more important to the industry. Giving pilots a new dynamic

control system, which will limit their response time in the event of an in-flight separation

violation, has the potential to reduce this overall risk. Thus, more errors can be absorbed by the

system. Section 1 discussed that the in-flight separation distance can be reduced for effective

air traffic control. However, if in-flight separation distance is reduced, then the new dynamic

control system has a demerit because it actually results in more accidents. Pilots think that there

is more room for error with this system, when analysis proves that it is not the case. The

benefits from the new dynamic control system are more than offset by the negatives of altering

the in-flight separation distance. It is recommended that these two options be considered in

disjunction in order to maintain high safety standards and from the reliability point of view.

Section 3 deviates from air traffic control and focusses on the cargo operations that take place

in an airport network. We built an optimization model to ensure smooth and cost-effective

management of cargo operations. There are often carrier capacities at each given airport, and

there is cost associated with transporting cargoes from one airport to the other. Having an

optimization model which minimizes cost for the aircraft company is always desirable because it

would mean more profit and insights into improving management. The analysis done shows the

complexity of such a problem, which can be seen from the fact the Excel fails to give a feasible

solution. With regards to the current system, the conclusion is that the current carrier capacity is

insufficient to achieve global optimum in a week. This is because of sudden peak influx of

cargoes at the airports which can be handled for only a short period of time. Not having enough

carriers increases the cost by 17%. In addition to purchase more carrier. The recommendation

is that weekly demand distribution be smoothened by keeping some extra cargos on the

weekends. If total carrier capacity is increased by 16%, global optimum can be achieved. It is

also recommended that the management charge the cargos not only on the distance but on the

origin-destination pair as well.

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1. Air Traffic Control

Section 1.1 ‐ Problem DescriptionThe landing queue at an airport is one of the most heavily controlled portions of the aircraft

industry, due to the dense distribution of planes within it. Each plane emits vortices behind it

which turn into a turbulent wake, which is a very dangerous phenomenon for a plane following

too closely. Additionally, if a following aircraft follows a landing plane too closely then the leader

will not have evacuated the landing zone by the time the follower has arrived. Thus, regulations

have been placed on separation distance to ensure adequate safety in the queue and landing

zone. The following is a study detailing the current regulations in detail, and comparing them to

a new set of potential regulations consisting of a lower separation mean with a tighter spread.

The following is a short summary of the landing queue system. First, a plane arrives at the

initial contact point, where the aircraft first contacts an air traffic controller. The plane then

proceeds to a landing queue, ensures a separation distance based on the current safety

regulations, and then flies through the queue until it reaches a threshold point. At this point, the

plane either circles back to the beginning of the queue if the landing zone is blocked, or the

plane proceeds to the landing zone and lands.

The Plane Queueing Problem is modeled using Discrete Event Simulation through the time of

two days, 172800 seconds, in each repetition. This approach is enabled using a few crucial but

reasonable assumptions. We first assume that no weather or emergency situations arise, which

could alter the necessary length between planes in queue or time taken at each stage. Thus,

the airport is considered to constantly be in a normal state of operation. In addition, pilot

behavior is assumed to be uniform, and every pilot adheres to a single distribution for each

phase of the Queueing problem. The airport is assumed to be empty at the beginning time (t=0)

of the simulation. The total simulation time is large enough that any bias effect on output statistics due to this assumption should not be significant. Within the simulation, a plane in the

landing phase is considered to be in the system, but not in the queue. Likewise, a plane that has

found the landing zone blocked and is circling back to the beginning of the queue is considered

in the system, but not in the queue. Finally, event times may never be negative – so if the

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simulation determines a negative interarrival time, it will simply continue finding random

numbers until it settles on a non-negative number.

1.1.1 STATES AND EVENTS As mentioned previously, this queueing problem will be modeled as a Discrete Event

Simulation. As with any DES, states and variables must be tracked at each time step. Within the

simulation the number of planes in the queue, the number of planes in the system, the status of

the landing zone (blocked or unblocked), and the Type of each plane in the system are states

tracked. In addition, the simulation also contains a statistic variable that is one when 5 or more

planes are in the queue and zero otherwise. A more detailed description of states tracked in the

DES system can be seen in Appendix A.

1.1.2 SIMULATION MODEL

In this DES, each point in the queueing problem previously described will be modeled as an

event. As there are four major points of change in the system, there are four major events. In an

initial contact event, a new queueing event is generated. If the arrival is new to the system (it

does not have a type yet), then the number of planes in system is increased, a type of plane is

generated, and a new initial contact event is created. In a queueing event, the number in the

queue is increased by one, the type of plane is added to a queue vector (which is used to

determine separation distances), and if the number in the queue is 5 or higher a tracking

variable is set to 1 – this is used to track proportion of time with a long queue. If there is only

one plane in the queue, set a threshold event at 40 seconds from now. Otherwise, the

separation between planes in the queue is set based on the type of plane that just arrived and

the one next in the queue vector. A threshold event is set up at that separation time plus the

event time for the next plane in the queue vector. In a threshold event the number of planes in

the queue decreases by one, and the long queue tracking variable is updated. If the landing

zone is blocked then the plane circles back, and a new initial contact event is generated. If the landing zone is open then a landed event is generated and the blocked LZ variable is set to one.

In both cases the plane is eliminated from the queue vector and all other entries are moved up a

spot. In a landed event the number of planes in the system is reduced by one and the LZ

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blocked variable is set to zero. A more detailed pseudocode of this DES system can be seen in

Appendix B, and the commented Matlab code itself can be seen in Appendix C.

Section 1.2 ‐ Result Discussion

The following result discussion provides confidence intervals for every statistic talked about.

After the confidence interval has been stated, further conversation will simply use the mean

value if needed in order to shorten the discussion. All confidence intervals were based upon 75

repetitions of the DES over a time span of 2 days, and are 98% confidence intervals –

corresponding to a z score of 2.325. The function used to generate the confidence intervals is

provided in Appendix D.

Intuition tells us that the length of the queue is a convenient way to quantitatively track the

performance of this system. A long queue indicates that there are too many planes in the

system and thus significant time is being wasted, likely during recircles. The 98% confidence

interval for average queue length is [2.48, 3.13]. This average queue length is completely

reasonable, but it shows plenty of room for improvement. A large queue contributes to a large

proportion of time that the landing zone is blocked, which leads to a high amount of recircling

and thus a large queue. Some of the largest factors in potentially decreasing the length of the

queue are the landing time distribution, the arrival rate of airplanes, the recircle time of an

aircraft, and shorter queue separation distance as discussed in the project description. The

arrival rate of airplanes is likely fixed, and cannot be changed here – thus no analysis will be

done. We expect the queue length to decrease with decreasing landing time, as the landing

zone will be open more often and thus recircles will decrease, leading to fewer entries to the

queue. The effect of reduced recircle time is more interesting, as a shorter recircle means

downtime will be spent more often in the queue, but also means that there will be more checks

on the landing zone to see whether a plane can land or not, decreasing the total number of

planes in the system. The change to separation distance is expected to decrease the average planes in the queue, as it results in more checks on the landing zone with no increase in

number of planes entering the queue. The results of these three changes are discussed in

Section 1.3 below.

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While the average length of the queue is important, a clogged queue is a significant time sink

and safety problem. We define a clogged queue as a queue with five or more planes in it. The

proportion of time that the queue is clogged is [17.4%, 23%], which is higher than ideal. We

expect to see the same changes in this as we do with average queue length.

The total number of planes in the system for the given system specifications is [13.39,14.19].

This number is far from ideal, and along with the proportion of time with five or more planes in

the queue are the two statistics that we wish to decrease. Decreasing the average number of

planes in the system would allow for an easier workload for air traffic controllers, and could

potentially lead to fewer controllers, saving the airport money. With our averages of number of

planes in queue and number of planes in system there are approximately 11 planes either

travelling to the queue, landing, or recircling to the beginning of the queue. Trimming down the

recircle time would have the greatest effect in decreasing this number, and we expect both

decreasing queue separation and decreased landing time to result in smaller decreases to total

planes in system.

Other significant statistics tracked are the percentage of time that the landing zone is blocked,

the average time that one plane spends in queue, the average time that one plane spends in the

system, and the average number of recircles by a plane. We expect the average time spent in

queue and system to trend the same way as the average length of queue or number of planes in system. We would like to have a low percent of time that the landing zone is blocked, such

that planes arriving at the threshold point have the opportunity to land more frequently. This

percentage is a driver to the number of planes in the queue and proportion of time that the

queue is clogged. The other major driver to reducing number of planes in the queue is the

average number of recircles by a plane. Implementing changes that affect these drivers allow us

to reduce the number of planes in the queue and system. All confidence intervals for these

statistics can be found in Figure 1.1 below. A larger, clearer version can be found in Appendix

E.

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Figure 1.1 Final Results from DES. A larger version is attached in the appendix.

Section 1.3 ‐ Case Comparison

***Note that all Confidence Intervals are shown above in Figure 1.1 . Approximate means are used below

for conciseness.

Case 1 – 10% Reduced Mean and SD Landing Time

In this case, we assume that either technology advances, airport policies, or less stringent

safety standards allow for the mean and spread of landing times to decrease by 10%. This

represents a decrease from 120s to 108s, which is not an unreasonable assumption. This

change leads to a decreased average planes in queue of around 1.2, which is over a 50%

improvement on the previous value. The reason for this decrease is that the percentage of time

that the landing zone is blocked is decreased from 65% to 59%. This allows planes at the

threshold point to proceed to the landing phase more frequently, leading to fewer planes in the

system and thus planes in the queue. Following from that, the average time spent in the queue

for a single plane decreases by half and the proportion of time with a clogged queue decreases

to 2%, which is a much more reasonable value than the original case. The average time spent

in the system by a plane also decreases significantly, due to a decrease in both the percentage

of time that the landing zone is blocked and the average number of recircles per plane. With this

change, planes recircle on average .72 times, whereas with the old standards planes had to

recircle nearly .93 times on average. Because planes that recircle have a wait time of 750s on

average and then reenter the queue (leading to more queue congestion), decreasing the

average number of recircles is a major driver to decreasing time in system for each plane. The

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team strongly recommends that this case be considered for further research due to the

disproportionate improvement in all major statistics for such a small improvement.

Case 2 – 10% Reduced Mean and SD Recircle Time

For this case we assume that pilots increase their recircle speed or the recircle distance is

decreased, such that average (and standard deviation of) travel time is decreased by 10%. This

corresponds to a decrease in mean recircle time of 75s, which seems a bit high but analysis will

continue to observe effects, and if this change is useful perhaps a smaller change could be

implemented for slightly reduced improvements. Upon implementing this change, we expected

that shorter recircle times would result in more checks of the landing queue at the threshold

point, and thus decrease time in the system. While time in the system does decrease, it only decreases by approximately the change in recircle time – in this case, about 80s. There is a

corresponding decrease in the average number of planes in the system at any given time, but

once again the change is very small, on the order of half a plane. Interestingly, we do not

observe the expected change in either average recircles per plane or percent of time that the

landing zone is blocked. The expected changes are likely offset by the mandatory separation of

planes in the queue currently instituted – an increased arrival rate to the system is not important

if the plane has to wait until the leading plane has adequate separation anyways. Thus, unless

there is some reason that a small decrease in average planes in the system or time in the system is needed, we would not recommend this change. The only improvements are small and

proportional to the percentage improvement, and even the 10% improvement used seems

better than is realistically manageable.

Case 3 – 10% Reduced Mean and SD Queue Separation Distance

This change is the change discussed in the project description, and corresponds to a reduced

required separation between planes in the queue and a tighter adherence to that separation.

The 10% decrease here corresponds to a mean change of anywhere from 6 to 13 seconds

depending on plane type, which is definitely reasonable. As expected, the average number of

planes in the queue decreases to 1.6, significantly better than the original value of 2.7 – and

correspondingly, the average time spent in queue decreases dramatically by around 40%. This

improvement comes from the fact that planes move through the queue quicker and thus

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proceed to either landing or recircling faster than in the original case. The fact that this does not

represent system-level improvement is reinforced by the unchanged proportion of time that the

landing zone is blocked and an increased average number of recircles for a single plane.

Because of how much of a time sink recircles are, decreasing the total number of recircles taken

would be the best way to decrease total time spent in system. While this may not be the best

method to decrease total system time, it does result in slight system time improvements of

approximately 2 minutes. In addition, the decreased average length of the queue leads to a

significantly improved proportion of time that the queue is clogged, now only around 6%. If the

airport is happy with slightly improved system level improvements and significant queue level

improvements, then this method is ideal. The changes have assumedly already been

researched from a safety and feasibility perspective, and allowing the pilots to follow a leader

quicker would be a popular change. Thus, the team recommends instituting this change.

SUMMARY

The current regulations for queue separation are lackluster and lead to long wait times both in

the system and in the queue itself. In addition, the high average number of planes in the queue

and high proportion of time that the queue is clogged are far too high and can lead to dangerous

situations. The suggested change to mandatory queue separation distance is a good change

that has been proven to be feasible and safe, and would allow for significantly decreased average length of queue, but does not have a significant effect on time spent in the system. The

team suggests a different change, one wherein the landing time is decreased. This leads to

significant changes in both queue time and system time, and is better across the board than the

same change applied to queue separation time. However, because the team came up with the

change recently, we do not know whether or not this change is possible – potential safety,

technology, or logistic issues could exist. Therefore, the team recommends that further research

be done into potential improvements to landing time and spread while the safer, proven change

to queue separation requirements are put into place immediately. While this queue separation

change does not have the same level or scope of improvements as the landing time change, we

know it is both safe and possible.

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2. Reliability Analysis2.1 Problem Description

As new technologies develop and standard operating procedures change, the primary thing all

organizations focus on is safety. This is especially true in the emotionally stressful and

customer driven market of air travel. There are several factors that can affect safety and the

public’s opinion as to the most reliable airports and airlines. These factors range anywhere from

weather delays, congestion back-ups, and most importantly serious accidents. In this section,

we will analyze the potential benefits associated with a new technology, as well as the existing

risks that exists within the landing sequence for arriving aircraft. Our analysis will provide an

assessment of the overall reliability of the system with regards to risk of incident and a recommendation as to the implantation of a new dynamic speed control system.

One of the biggest issues facing arriving aircraft and the corresponding air traffic controllers is

in-flight separation. The goal of any successful air traffic controller is to maximize the number of

aircraft that can flow through the airport in a given day. This will lead to more airlines providing

more flights in and out of the airport, which will correlate to more profit for the airport and

ultimately its employees. However, the Federal Aviation Administration (FAA) places specific

restrictions when it comes to the space that can exist between arriving aircraft because of the

increased likelihood for incidents as a result of what is known as wake vortex. Depending on

the size and payload of the leading aircraft, a wake vortex of varying significance is created.

The severity can be seen below.

Table 2.1: Probabilities of vortex creating dangerous situation.

These probabilities serve as a rough estimate for the likelihood an accident taking place;

however, they are not the only factor to consider when developing a method for approximating

the likelihood of an accident taking place. In order to accomplish that task, we developed a

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cause and effect diagram to assess, model, and generate an approximate solution for the

likelihood of an accident taking place.

2.2 Analysis and ResultsWe started off the process by defining the scope of an accident for this problem. Initially we

defined an accident as the unintended collision between two aircraft on the runway. This model

required that several assumptions be made that state an accident is the result of a violation of

the in-flight separation distance, this violation going undetected by the air traffic control unit, and

the previous plane still on the runway causing a simultaneous runway occupation. All of these

factors had to occur in order for an accident to take place. In terms of probability, we are

looking for the joint probability that these events take place. The equation we solved can be

seen below:

(accident ) (violation ) ( AT CU error ) ( simultaneous occupation ) P = P * P * P

This equation seems simple; however, these probabilities needed to be derived based on the

information provided after a series of air traffic studies conducted by the FAA. The table of

initial probabilities can be seen below:

Table 2.2: Summary of violations.

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After careful analysis, we determined that several of the given probabilities serve as conditional

probabilities. These probabilities are all in the terms of the probability of a violation occurring

given the occurrence of an isolated event. Understanding this property allows for the calculation

for the probability for a violation occurring given the following formula:

(violation ) (violation given mis ID of aircraft ) (mis id of aircraft ) (violation given landing retry ) (landing retry ) P = P * P + P * P

(violation given failure to communicate ) ( failure to communicate )+ P * P

This equation takes into account all the given information that could result in a violation

occurring. As you can see from the above table, all of these individual probabilities are

relatively small. This is due to the significant innovations made in aircraft and air traffic control

safety procedures over recent years. These innovations lead us to the conclusion that the . This provides us with the first aspect of our overall equation.(violation ) .43 E P = 1 − 5

(accident ) .43 E ( AT CU error ) ( simultaneous occupation ) P = 1 − 5 * P * P

The second component of this equation is significantly easy to calculate as the probability of the

air traffic control unit failing to detect the in-flight separation distance violation is given as

1.95E-3. This gives us the second component of our guiding equation.

(accident ) .43 E .95 E ( simultaneous occupation ) P = 1 − 5 * 1 − 3 * P

The last component of the guiding equation required careful analysis of the situations that could

result in a simultaneous occupation of the runway. We first defined a simultaneous occupation

as an instance where the lead aircraft is unable to vacate the runway for any reason. We were

provided the given probabilities for issues that could affect the ability of an aircraft. These

probabilities can be seen below

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Table 2.3: Simultaneous occupancy

After analysis of the situation, we made the assumption that similar to the probability of an

accident, multiple events had to occur for a simultaneous occupation to occur. However, this situation is significantly different. For an accident to occur, several event have to happen in

sequence, which leads us to calculate the joint probability for that event as the product of the

probabilities of the contributing events. Simultaneous occupation is the result of any one of the

given probabilities occurring, which leads us to calculate this as the sum of the individual

probabilities of the contributing events. This concept provided us with the following equation:

( simultaneous occupation ) (equipment failure ) (congestion ) P = P + P

(unable to execute go around ) (medical emergency )+ P + P

This equation provides us with . This completes our ( simultaneous occupation ) .38 E P = 2 − 3

guiding equation, which provides the overall probability for an accident as:

(accident ) .43 E .95 E .38 E P = 1 − 5 * 1 − 3 * 2 − 3

(accident ) .62 E 1 P = 6 − 1

Initially, this number seems extremely small, but let us think about what this number represents and put it into context. The National Safety Council estimates that an individual has a 1.02E-4

chance of serious injuries as a result of an airline accident. This probability increases

significantly when the accident is a known event. Using flight data from the National

Transportation and Safety Board from 1982-2009, there were 2924 aircraft fatalities out of 5454

individuals involved in an aircraft accident. This data provides an estimate of the probability of a

fatality given an accident as 54%. It is incumbent on the FAA and the air traffic controller to limit

the probability of an accident as much as possible.

Additionally, when the probability of an accident is considered with the overall number of flights

that operate daily, monthly, and yearly out of a particular airport this number again becomes

more and more relevant. For example, for the scope of this analysis we assumed that there

would be an average of 5000 aircraft landing at any particular airport hourly. We additionally

assumed that this would remain constant for at least 15 hours of every day. Using these

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numbers the following table shows the correlation with the number of flights and the

corresponding probability of an accident occurring.

Table 2.4: Flight statistics.

2.3 Summary

As the above table highlights, the likelihood of an accident increases as the number of flights

increases, resulting in a higher probability of an accident and serious injury occurring. The FAA

and air traffic controllers are making every necessary attempt to improve how accidents can be

avoided, including testing new dynamic speed control system.

The new dynamic speed control system will give pilots more control and limit the response time

required to execute a go around and reattempt the landing procedure if a violation occurs. What

this means for the pilots and air traffic controllers is that that they now have more room for error

in terms of preventing a simultaneous occupation. However, this new technology does have

some negatives associated with it. Even though the pilot now has more control over his speed, the probability that a go around cannot be initiated increases if reductions to the safe in-flight

separation distance are made. An analysis of these tradeoffs can be seen in the table below.

Table 2.5: New technology analysis.

This analysis highlights that although there may be a perceived benefit for the new system,

altering the safe in-flight separation distance negates any potential benefits and will actually

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increase the probability of an accident slightly. This new technology hopes to accomplish two

major objectives increased safety and allow more aircraft to move through the airport.

Unfortunately, you cannot have one without making concessions in aspects of the other. It is

our recommendation that the new technology be considered, but that the recommended in-flight

separation distance remain unchanged.

3. Cargo Operations3.1 Optimization Model

3.1.1 Background

An express package carrier transports cargos between three airports (A, B and C). The

inter-airport transportation cost and demand are fixed over a weekly cycle. The carrier will incur

a fixed amount of cost per weight to reposition itself, regardless of the amount of cargo it

carries, as long as its maximum capacity is not exceeded. The repositioning cost is summarized

in figure 3.1.

At the beginning of each day, the airport management can decide how many carriers fly from

origin i to destination j, as well as how much cargo the carriers have with them in the flight. The

amount of cargo on board must not exceed the carrying capacity, which is limited by how many

carriers stay at source i on the day before.

Figure 3.1: Fixed cost for inter-airport transportation of the carrier. The

cost is per kiloton (1,000 tons), measured carrying capacity.

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Everyday, there are cargos arriving at each airport waiting to be transported. Management may

choose not to move the cargos when they arrive, but rather to postpone the transportation when

they see fit. There is, however, a daily cost associated with holding the cargos on the ground.

Because the transportation cost and demand are known to the management beforehand, it is

reasonable to assume that an optimal weekly cycle exists. Furthermore, to simplify the model,

we assume that we have enough carriers and cargos to treat their transported quantities as

continuous. Secondly, flight time between every origin-destination pair is no more than a single

day; in other words, planes that arrive on day t can be immediately deployed on day t+1. Lastly,

the carriers must return to their start at the end of each week to complete the weekly cycle.

3.1.2 System DescriptionThe three-airport system will start on Sunday night with fixed amount of carriers distributed to

each one. Then everyday starting in the morning,

1. Cargos will arrive at each airport.

2. Carriers leave origin i for destination j. The carriers will have cargos with them (under the

limit). The amount of carriers is predetermined and has to be fewer than what stays in

the airport i the night before.

3. In the afternoon, the carriers will arrive at destination j and get recharged. Cargos that

haven’t been moved will incur charges based on their weight.

4. At night, the carriers are charged and ready to repeat till the end of the week (Friday).

Over the weekend, the carriers must redistribute themselves so that the system will be the same

as it started on the last Sunday.

The three assumptions we made to simplify the system make the model deterministic, lag-free

and periodic. The three properties make it suitable for us to optimize the weekly cycle using

linear programming.

3.1.3 Optimization Objective

To achieve an optimal cycle, we first specify the objective. For the airport management, the

objective is to minimize the overall cost throughout each week. There are three parts of the cost

involved in this system:

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● The transportation cost from origin i to destination j.

● The holding cost for cargos that are not moved on the same day of arrival.

● The penalty cost to reposition carriers at the end of each week.

The optimization objective is to minimize the total cost by the three parts.

3.1.4 System Model

To describe the system more analytically, we first define some state and control variables:

● is the transportation of cargo on day t from airport i to airport j, where 1 ≤ t ≤ 5 and i, jut ij

are in {A, B, C}.

● is the transportation of empty carrier on day t from airport i to airport j.vt ij

● is the cargo at the end of day t from airport i to airport j. In this case, 0 ≤ t ≤ 5. xt ij

Everyday, new cargo arrives at airport i before the shipment.bt ij

● is the carrier capacity at the end of day t at airport i. yt i

● is the cost to transport carriers from airport i to airport j.c ij

● is holding cost.d

The objective as described above is 1

( (u ) )min

∑5

t =1∑

i, jcij

t ij + v

t ij + d ∑

ij xt ij

A more involved discussion is needed to write out the constraints, but we sketch out the

motivation and results, while leaving the derivation details in the Appendix for review. The

following constraints are considered:

● On each day, the total cargo carried from airport i to airport j must not exceed the total

cargo:

ut ij ≤ xijt −1 + bt ij

● On each day, the total carrier leaving airport i must not exceed the total carriers

available:

1 The terminal cost is implicitly included using constraints.

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(u )∑

j

t ij + v

t ij ≤ yi

t −1

● The state variables change according to the transportation:

xijt +1 = xt ij + bij

t +1 − uijt +1

(u ) (u ) yit +1 = yt i − ∑

j ijt +1 + vij

t +1 + ∑

j jit +1 + u ji

t +1

● The total capacity of carriers in the system is 120 kilotons:

20∑

k yk

0 = 1

● To complete the weekly cycle, the following periodic condition is enforced:

x0ij = x

5ij = 0

yi0 = yi

5

By recognizing that the state variables can be condensed into an expression that is determined

by their initial conditions ( and ), we can simplify the constraints and write the system as x0ij yi0

linear programming problem:

( (u ) u )min

∑5

t =1∑

i, jcij

t ij + v

t ij − d ∑

ij∑t

τ=1

τij

Subject to

∑t

τ=1uτij ≤ ∑

t

τ=1 bτij

(u ) [ (u ) (u )]∑

j

t ij + v

t ij − ∑

t −1

τ=1∑

j

τ ji + v

τ ji − ∑

j

τij + v

τij ≤ yi

0

∑5

τ=1uτij = ∑

5

τ=1 bτij

[ (u ) (u )]∑5

τ=1∑

j

τ ji + v

τ ji − ∑

j

τij + v

τij = 0

,,ut ij vt ij ≥ 0 20∑

3

i=1 yi

0 = 1

Despite the complex form, this is in matrix form:

xmin

cT

Subject to

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x A ≤ b

x ≥ 0

3.2 Simulation3.2.1 Optimization

Given this model discussed in section 3.1.4, we can use the data given by figure 3.1 and table

3.2 to compute the optimal weekly cycle.

Table 3.2: Amount of cargos (in kilotons) between each

origin-destination pair on each day of the week.

The results will tell us how to best manage the transportation on each day in a weekly cycle. It

should also give us the global minimum of the total cost.

3.2.2 Solver

In the actual implementation of solver, the periodic condition is relaxed to guarantee a solution.

In other words, no longer holds. This is mainly because the system [ (u ) (u )]∑5

τ=1∑

j

τ ji + v

τ ji − ∑

j

τij + v

τij = 0

is incapable of satisfying the cargo transportation requirement and the periodic condition at the

same time, which we will later explain in more details. In its place, a penalty term is added to the

objective so that the solver will still try to get as close to the periodic condition as possible. In

reality, the penalty term is equivalent to moving the carriers over the weekend so that the same

carrier configuration will be available on Sunday.

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In addition to solving the given problem, we can also use the solver for various parameters and

gain insights into the system properties.

Figure 3.3: A screenshot of the Excel solver for our optimization model.

The control variables are highlighted on the left. The total cost consists of

holding cost, transportation cost and the penalty. The Excel solver isassigned to minimize the total cost under constraints, using GRG

Nonlinear solver.

3.3 Analysis

3.3.1 Results

There is no feasible solution from our solver. In this case, the solver is limited by the total

number of carriers available and cannot get a global minimum. This, however, does not indicate

that a “better” weekly schedule does not exist. The solver gives us a schedule that costs

3528.5=0+3254.2+274.3(hold, transport, penalty) to operate continuously.

The schedule fulfills some of the requirements we want from the system:

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● All the cargos are transported at latest on Friday. In this case, no cargo is stored. This

makes sense because holding is more expensive than transporting anywhere. If the

system has any carriers, it will send the cargo on the same day.

● The carriers configuration is restored over the weekend for a repeating start on Monday

morning.

However, it does not have enough carriers to send out from airport C. In this particular solution,

it needs 19 more carriers from airport C.

We can observe that in this system, a large number of cargos go into airport B from airport A

and C throughout the week, whereas a significantly smaller number comes out. This creates an

imbalance in the system that the management must address by moving empty carriers.

We traced the infeasibility to its root. On Thursday, there is a huge increase in the amount of

cargo from A to B (40 kton) and the system must use the carriers in airport A to move them.

However, on Friday, there is another peak showing up that the airport cannot handle, since

there are not enough carriers in airport A. Even when the management tries to move the empty

cargo on Thursday, it will not be able to find enough carriers in the system.

Figure 3.4: Two peaks show up on Thursday and Friday. The system is

incapable of handling the two demands in time.

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To see it more clearly, we increased the capacity to 140 and the system achieves its minimum

cost at 3480.0=0+3276.6+203.4. This value remains a constant as we further increase the

capacity. And 140 is roughly the minimum requirement for the system to complete the weekly

cycle.

Since we know the problem exists because of the uneven distribution of cargo going to airport

B, we can try to relax the situation by having the cargos staying over the weekend. We pay for

three day storage in exchange for a more even distribution of the cargo transportation demand.

We kept 10 cargos from airport A to B and 10 cargos from airport C to B. The minimum cost is

4080=600+3395.3+84.7. Note that this cost is 3480+600, and it is only 600(holding cost) more

than the minimum cost when there are enough carriers.

Figure 3.5: Optimization solver results from having cargos staying at the

airport over the weekend. The strategy allows us to have a more evenly

distributed cargo transport demand and therefore having an optimal

weekly cycle at low carrier capacity. We refer our reader to the attachedexcel file for further inspection of the above results.

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3.3.2 System Analysis

The system has an optimal weekly cycle when there are enough carriers to address the cargo

transportation demand. When the total carrier in the system is low, however, an shock peak in

the cargo arrival will make such optimal schedule infeasible.

The prominent effect of the shock peak is majorly a consequence of the uneven demand

distribution. More specifically, the demand is poorly distributed both spatially and temporally. In

space, cargos keep going into airport B without coming out, thus creating a vacuum in both A

and C. To counterbalance this effect, management has to move the empty carriers out of airport

B with a significant cost. The situation will be exacerbated if there are more cargos trying to

going into the airport C, because this system does not have enough carriers in it to address this

spatial asymmetry. On the other hand, if there are more cargos coming out of airport C, the

management could move them instead of empty carrier, which will bring in more profit.

In addition, there is the shock peak in time during a weekly cycle. As discussed in 3.3.1, the

system is incapable of handling the peaks and therefore must take measures to protect itself

against it. One solution we came up with is to have cargos stay at the airport over the weekend,

thus creating a more smooth distribution in time.

3.3.3 Managerial Recommendation

The current system suffers from an insufficiency in the total carrier capacity. This flaw is

revealed when a sudden peak influx of cargos arriving at the airports. The system can handle

such peak for one day, but not over a longer period of time. As a result, the airport has to have

cargos staying over the weekend and pay a premium for the storage. It is a 17% increase from

the optimal cost when there are enough carriers.

We recommend that the management actively seek opportunities to bring in new carriers into

the system. The situation can be improved when there are more carriers, and with a total number of 140, the system will be able to handle the weekly demand and achieve its optimum.

However, before purchasing the carrier, we recommend the management keep certain amount

of cargos at the airports over the weekend to smoothen the weekly demand distribution.

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Lastly, we recommend the management charge the cargo deliver based on origin-destination

pair instead of on distance alone. The goal is to create a price differential that can motivate

consumption and mitigate the spatial imbalance we discussed in 3.3.2.

4. ConclusionWe conclude that the air traffic control and cargo operation management are two of the most

important and complex challenges faced by the aircraft industry. There are multiple issues in

terms of queue clogging, delay in landing higher number of planes in recircles and in the

system, limits to carrier capacity.

Increased flights delay and compromise on safety standards result in loss in customers for any

airline because of customer dissatisfaction and discontentment. Thus, it is necessary for airlines

to make an effort, invest in research and development to come up with plausible solutions,

make the variables less stringent wherever it is possible, and at the same time ensure full safety

especially so that they don’t lose customers.

It is also profitable for the industry to reduce cost wherever it can. Cost reduction in cargo

operations is possible if it is managed effectively. Thus, time should be spent on devising better

management of cargo operations and increasing cargo capacities so that operations do not face

any problems and cost is also minimized.

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Appendix A

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Appendix B

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Appendix CNOTE: This is fully commented Matlab code of the DES. The actual Matlab

file will be submitted digitally.

function [Outputs] = PlaneQueue()

%%Runs a Discrete Event Simulation for Part 1 of Project

%Initialize our tracking (state) variables. Because we start at some very

%early time where the airport is empty, all of these tracking variables

%will be zero. NOTE - I could run for a short amount of time without

%tracking stats variables, then start after some time. Like the initial

%transient problem.

B=0; N=0; S=0; F=0; RCCount=0;

%Store the initial contact and time to queue stats

ICMu=180; ICSD=60;

QMu=600; QSD=150;

%Store the time from entering queue to threshold point in matrices. It is%the same format as Table 1 in the project documentation.

%Will find value of mu from ThreshMU(PlaneType2,PlaneType1) because the

%lead plane (1) determines the column of the matrix, the following plane(2)

%determines the row of the matrix.

ThreshMu=[64,64,64;108,86,64;130,130,64];

ThreshSD=[30,30,30;40,40,30;50,50,30];

%%Case 3 - Reduced Queue Separation - Comment out for original recipe

% ThreshMu=ThreshMu.*.9; ThreshSD=ThreshSD.*.9;

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%This will be used to find plane type - used as a cdf. So if U[0,1] less

%than .33, heavy. If less than .79 but bigger than .33, large. Else, small.

ThreshP=[.33,.79,1];%Store the time from threshold point to landing on ground and time from

%threshold point to initial contact point (recircle time)

LandMu=120; LandSD=30;

%%Case 1 - Reduced Landing Times. Comment out for original recipe

% LandMu=LandMu*.9; LandSD=LandSD*.9;

CircleMu=750; CircleSD=150;

%%Case 2 - Reduced Recircle Times. Comment out for original recipe

% CircleMu=CircleMu*.9; CircleSD=CircleSD*.9;

%Initialize the output vector of our discrete times stepped to

TimeOut=0;

%Now we create an interarrival time for an initial contact event, which

%will be the first event called since the airport is empty at time 0

%Remember that we only accept initial contact interarrival times of greater

%than zero. This code does that.

ICtime=0;

while ICtime


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[ICs,ICi]=Shortest(IC,E);

%This will tell us which event is soonest - an index returned of 1 is

%an IC event, index 2 is Queue event, 3 is Threshhold event, 4 is%Landed event. Basically, the previous four events found the soonest

%event in each individual event list, and this call of the function

%finds the soonest event total - the soonest of the soonest.

[Newt,NewEv]=Shortest([ICs,Qs,Ts,Ls],E);

%Here we make sure that if all events occur after E, no event is simulated.

if Newt>E

NewEv=0;

Newt=E;

end

%calculations of statistics variables. It follows the normal DES method

%of adding the time step multiplied by the given statistic variable

IntB=IntB+((Newt-t)*B);

IntQ=IntQ+((Newt-t)*N);

IntS=IntS+((Newt-t)*S);

IntF=IntF+((Newt-t)*F);

%Now we update the current time variable to the current event time.

t=Newt;

%This is the Initial Contact Event

if NewEv==1

%This checks whether or not the plane is new in the system - a new

%IC event has its third index as 0, a recircle plane has its third

%index of 1.

if IC(3,ICi)==0

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%A new plane increases the number of planes in the system and

%number of planes into the system by one

S=S+1;NumIn=NumIn+1;

%Generate new Initial Contact Event. Same procedure as the

%first IC event generated above to find interarrival time and

%plane type

ICtime=0;

while ICtime0

IC=[IC,[(Newt+ICtime);Type;0]];

else

IC=[Newt+ICtime;Type;0];

end

end

%Generate new Queueing event - this occurs in both the new plane

%and recircled plane case

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Qtime=0;

while Qtime0

Q=[Q,[(Newt+Qtime);IC(2,ICi)]];

else

Q=[(Newt+Qtime);IC(2,ICi)];

end

%Now we clear the IC event that we just ran through. This

%eliminated that event and moves all others up the event list.

IC(:,ICi)=[];

end

%Now comes the Queueing Event

if NewEv==2

%The number in the system increases by one, and the queue variable

%updates. The queue variable contains the time of each queue event

%and the type of each plane. This will be used to find the

%separation times for each plane in the queue.

N=N+1;

Queue(:,N)=Q(:,Qi);

%If the number of planes in the queue is one, then the time to the

%end of the queue is 40 seconds. We use that time step to set up

%the threshold event for this plane.

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if N==1

if length(T)>0

T=[T,[(t+40);Q(2,Qi)]];else

T=[(t+40);Q(2,Qi)];

end

else

%This is the hard part. We need to compare two types of planes

%clashing in the queue to see what the separation distance for

%threshold event is.

%We save the type of each plane in the queue to be compared

%here. Type1 is for the leader, Type2 is the follower

Type1=Queue(2,N-1); Type2=Queue(2,N);

%We get the mu and sigma from Table 1 in the project

%documentation using the plane types saved above

SepMu=ThreshMu(Type2,Type1);

SepSD=ThreshSD(Type2,Type1);

%The time stats we found are the separation distance - so on

%average the follower should arrive at the threshold at a given

%mu from the time the leader arrived at the threshold. Thus, we

%save the leaders arrival time here.

LeadArriveTime=T(1,N-1);

%This gives us a separation time based on Table 1.

Sept=0;

while Sept


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Sept=normrnd(SepMu,SepSD);

end

%Here we set up the new threshold event for the plane that just%arrived in the queue.

if length(T)>0

T=[T,[(LeadArriveTime+Sept);Q(2,Qi)]];

else

T=[(LeadArriveTime+Sept);Q(2,Qi)];

end

end

%If the queue is 5 planes or longer, then we trigger a tracking

%variable. This is used to track the proportion of time that we

%have a long queue.

if N>=5

F=1;

end

%Because the event has been completed, we delete it from the

%event list.

Q(:,Qi)=[];

end

%Now comes the threshold event

if NewEv==3

%There is one less plane in the queue (it will either proceed to

%landing or recircle)

N=N-1;

%When the LZ is currently blocked, we recircle to the beginning

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if B==1

%Here we generate an interarrival time for a recircle.

RCtime=0;while RCtime0

IC=[IC,[Newt+RCtime;T(2,Ti);1]];

else

IC=[Newt+RCtime;T(2,Ti);1];

end

%We add one to the counter of number of recircles

RCCount=RCCount+1;

%When the LZ is currently open, we proceed to land

else

%Here we generate a landing time, and use it to set up a landed

%event. At that time is when the LZ is declared clear.

Ltime=0;

while Ltime


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if length(L)>0

L=[L,[Newt+Ltime;T(2,Ti)]];

elseL=[Newt+Ltime;T(2,Ti)];

end

%Now the LZ is blocked, as a plane is landing... so blocked

%tracking variable is set to one.

B=1;

end

%Either way, the plane has left the queue, so we delete it from the

%queue variable.

Queue(:,1)=[];

%we recheck if the queue is long and update the tracking variable

%if that has changed.

if N


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%The LZ is no longer blocked, so change the tracking variable.

B=0;

%A plane has left the system, so the number of planes through the%system increases by one.

NumOut=NumOut+1;

%This event is complete, delete it from the event list.

L(:,Li)=[];

end

%We update the time output, which just tells us all of the times that

%the DES stepped to. Was used for testing and troubleshooting.

TimeOut=[TimeOut,t];

end

%%Do all ending calculations here, simulation is over

%This is the average length of the queue

AvgQueue=IntQ/E

%This is the average number of planes in the system

AvgSystem=IntS/E

%This is the proportion of time that the queue has 5 or more planes in it

PercentMoreFive=IntF/E

%This is the percent of time that the LZ is blocked

PercentBlocked=IntB/E

%This is the average time spent in the queue by a single plane

TimeInQ=IntQ/NumIn

%This is the average time spent in the system by a single plane

TimeInS=IntS/NumIn

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%This is the average number of recircles per plane

RCAvg=RCCount/NumIn

%This is the total number of planes through the systemNumOut

%This is the total number of planes into the system

NumIn

%Now we compile all outputs into a single vector for easier data handling

%in other programs.

Outputs=[AvgQueue,AvgSystem,PercentMoreFive,PercentBlocked,TimeInQ,TimeInS,RCAvg,N

umOut,NumIn];end

function [t]=PlaneType(p)

%%This function takes in the probability list of a plane being a given type

%%(heavy, large, small) and generates a plane type for the incoming plane.

%This generates a uniform random variable from 0 to 1.

type=rand;

%If that generated rv is less than the probability of being type 1, this

%plane is type 1. Else, if it is less than the probability of being type 2,

%it's type 2. Else, it is type three.

%NOTE: Remember that we use a cdf probability list here, so if the%percentages are say 30-30-40, then an rv between .3 and .6 is type 2 and

%between .6 and 1 is type 3.

if type


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elseif type0

[S2,Ind]=min(I(1,:));

else

%Some nonsense large number so it will never be the soonest event,

%because an event doesn't exist here

S2=E+100;

Ind=0;

end

end

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Appendix DNOTE: This is fully commented Matlab code used to generate Confidence

Intervals with DES inputs. The actual Matlab file will be submitted digitally.

function [CILow,CIHigh] = QueueReps()

%%This function runs N repetitions with Z score Z in order to create

%%Confidence Intervals of all of the important DES statistics. All formulas

%%used are the same as always in this course.

N=75;

Z=2.325;

AvgQ=zeros(1,N); AvgS=zeros(1,N); PM5=zeros(1,N);

PBL=zeros(1,N); TimeNQ=zeros(1,N); TimeNS=zeros(1,N);

RCAvg=zeros(1,N); NumOut=zeros(1,N); NumIn=zeros(1,N);

for i=1:N

[Out]=PlaneQueue(); AvgQ(i)=Out(1); AvgS(i)=Out(2); PM5(i)=Out(3);

PBL(i)=Out(4); TimeNQ(i)=Out(5); TimeNS(i)=Out(6);

RCAvg(i)=Out(7); NumOut(i)=Out(8); NumIn(i)=Out(9);

end

Mu=mean([AvgQ',AvgS',PM5',PBL',TimeNQ',TimeNS',RCAvg',NumOut',NumIn']);

SD=std([AvgQ',AvgS',PM5',PBL',TimeNQ',TimeNS',RCAvg',NumOut',NumIn']);

CILow=Mu-(Z.*((SD)./(N^.5)));

CIHigh=Mu+(Z.*((SD)./(N^.5)));

end

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Appendix E

Air Traffic Control, Reliability Analysis and Cargo Operations - Imran A. Khan

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