1

„]HE EFFECT OF SCHEDULINGON AIR TRAFFIC DELAV

byRandal R.,Crockett;

Thesis submitted to the Graduate Faculty of the

Virginia Polytechnic Institute and State University

in partial fulfillment of the requirements for the degree of

MASTER OF SCIENCE

in

Industrial Engineering and Operations Research

/”“Approved:

g J. w. Schmidt, Chairman

Q: G. K. Bennett ·•

R. Taylor

May 1974

Blacksburg, Virginia

*:.1

1L..@EEdeAES......................_........._______________________________________,,I

ACKNOWLEDGEMENTS

ii

E

TABLE OF CONTENTS

@92ACKNONLEDGEMENTS.......................... 11LIST OF FIGURES .......................... v

LIST OF TABLES........................... vii

DEFINITION OF TERMS ........................viiiChapter

l INTRODUCTION ....................... lCongestion and Capacity ................ 3

Proposed Research ................... 8

Literature Review ................... 92 DEVELOPMENT OF SIMULATOR ................. T4

Assumptions Concerning Aircraft ............ T4

Assumptions Concerning Terminals............ T6

Simulator Logic .................... T8

Extensions of Simulator ................ 223 INTRODUCTION TO SCHEDULING ................ 24

Scheduling Algorithms ................. 24C

Uniform Scheduling Algorithm ............ 25Simultaneous Uniform Scheduling Algorithm...... 26Peak Demand Uniform Scheduling Algorithm ...... 27Aircraft Tagging Method............... 29

Summary of Scheduling ................. 3l

4 VALIDATION AND RESULTS .................. 33

Analysis of Results .................. 37

5 SUMMARY AND RECOMMENDATIONS................ 54

iii

iv :

TABLE OF CONTENTS (continued)

EssBIBLIOGRAPHY............................ 57

Appendix A. DESCRIPTION OF COMPUTER PROGRAM............ 6O

Appendix B. SAMPLE OF INPUT FLIGHT DATA. .k............ 113

Appendix C. SAMPLE OUTPUT..................... 116

Appendix D. TABLES OF §A§_RESULTS................. 118

Appendix E. TERMINALS INCLUDED IN THE DISTANCE MATRIX....... 129

Appendix F. PROGRAM LISTING.................... 131

VITA................................ 232

I

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I

LIST OF FIGURES

Figure Page1.1 Re1ationship between Average De1ay and the Number of

Operations...................... 72.1 F1ow Chart of Simu1ator Logic.............. 19

4.1 Actua1 Data versus Data Obtained from Simu1ator..... 36

4.2 Average Departure De1ay per Aircraft for 1750 Aircraft . 44

4.3 Average Departure De1ay per Aircraft for 2250 Aircraft 45(Synthesized f1ights added in morning)........ 45

4.4 Average Departure De1ay per Aircraft for 2250 Aircraft(Synthesized f1ights added in afternoon)....... 46

4.5 Average Departure De1ay per Aircraft for 2750 Aircraft(Synthesized f1ights added in morning)........ 47

4.6 Average Departure De1ay per Aircraft for 2750 Aircraft(Synthesized f1ights added in afternoon)....... 48

4.7 Average Arriva1 De1ay per Aircraft for 1750 Aircraft . . 49

4.8 Average Arriva1 De1ay per Aircraft for 2250 Aircraft(Synthesized f1ights added in morning)........ 50

4.9 Average Arriva1 De1ay per Aircraft for 2250 Aircraft(Synthesized f1ights added in afternoon)....... 51

4.10 Average Arriva1 De1ay per Aircraft for 2750 Aircraft(Synthesized f1ights added in morning)........ 52

4.11 Average Arriva1 De1ay per Aircraft for 2750 Aircraft(Synthesized f1ights added in afternoon)....... 53

A.1 Macro F1ow Chart of Main Program ............ 76A.2 Macro F1ow Chart of Subroutine FLIGHT.......... 79

A.3 Macro F1ow Chart of Subroutine ADFLT .......... 80

A.4 Macro F1ow Chart of Subroutine UNIFM .......... 82A.5 Macro F1ow Chart of Subroutine PDUNIF.......... 84

v

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vi ZLIST 0F FIGURES (continued)

Eläüä @92.A.6 Macro Flow Chart of Subroutine TAGSCH.......... 86

A.7 Macro Flow Chart of Subroutine TERCAP.......... 87

A.8 Macro Flow Chart of Subroutine NEXT........... 88

A.9 Macro Flow Chart of Subroutine ACNEXT.......... 89

A.10 Macro Flow Chart of Subroutine TERNEX.......... 90

A.11 Macro Flow Chart of Subroutine AOPER .......... 91

A.l2 Macro Flow Chart of Subroutine ENROUT.......... 93

A.l3 Macro Flow Chart of Subroutine ERDEL .......... 94

A.l4 Macro Flow Chart of Function VECT............ 95

A.15 Macro Flow Chart of Subroutine SERDES.......... 96

A.l6 Macro Flow Chart of Subroutine UNSTAC.......... 97

A.l7 Macro Flow Chart of Subroutine DELAY .......... 99

A.l8 Macro Flow Chart of Subroutine FUTCAP.......... 100

A.l9 Macro Flow Chart of Subroutine OPWRIT.......... 102

A.20 Macro Flow Chart of Subroutine WRIDEL.......... 103

A.21 Macro Flow Chart of Subroutine TODEL .......... 105

A.22 Macro Flow Chart of Subroutine TNRIT .......... l07

A.23 Macro Flow Chart of Subroutine PUSHUP.......... 108

A.24 Macro Flow Chart of Subroutine NEXFLI.......... 109

A.25 Macro Flow Chart of Subroutine TCAPY .......... 110

A.26 Macro Flow Chart of Subroutine CHANG .......... lll

A.27 Macro Flow Chart of Function RAND............ 112

1I I __ _ _L

I

LIST OF TABLES

Table PageI Delay Time per Aircraft from Hartsfield Atlanta

International Airport ................. 34II Delay Time per Aircraft from Simulation.......... 35 _

III Results Dbtained from Simulation Concerning Average Delay. 38IV Three-way Analysis of Variance .............. 40

D.I Results of §A§_Three-way Analysis of Variance for l750Aircraft Based on Departure Delay ........... ll9

D.II Results of §A§_Three—way Analysis of Variance for 2250Aircraft Based on Departure Delay (Synthesized flightsadded in the morning) ................. l20

D.III Results of SA§_Three-way Analysis of Variance for 2250Aircraft Based on Departure Delay (Synthesized flightsadded in the afternoon) ................ l2l

D.IV Results of §A§_Three-way Analysis of Variance for 2750Aircraft Based on Departure Delay (Synthesized flightsadded in the morning) ................. l22

D.V Results of §A§_Three—way Analysis of Variance for 2750Aircraft Based on Departure Delay (Synthesized flightsadded in the afternoon) ............,... l23

D.VI Results of SAS Three—way Analysis of Variance for l750Aircraft Based on Arrival Delay ............ l24

D.VII Results of SA§_Three-way Analysis of Variance for 2250Aircraft Based on Arrival Delay (Synthesized flightsadded in the morning) ................. l25

D.VIII Results of SA§_Three-way Analysis of Variance for 2250Aircraft Based on Arrival Delay (Synthesized flightsadded in the afternoon) ................ l26

D.IX Results of §AS_Three—way Analysis of Variance for 2750Aircraft Based on Arrival Delay (Synthesized flightsadded in the morning) ................. T27

D.X Results of §A§_Three-way Analysis of Variance for 2750Aircraft Based on Arrival Delay (Synthesized flightsadded in the afternoon) ................ T28

vii

ILL._„_„..._„_...„_................_..._............................................„.L.-

DEFINITIONS OF TERMS

Airport: The building, runways, taxiways, and parkingfacilities which are the center of an airterminal.

Terminal area: The airspace enclosed by an imaginary circlecentered at the airport with radius of approxi-mately forty miles.

Actual terminal: A terminal which represents one major terminalarea in the United States.

"Catch—all" terminal: A terminal which represents several terminals.

Apron: The portion of the runway configuration which isused by waiting aircraft.

Gate: The area at an airport at which aircraft areserviced between flights and where passengersboard.

Independent runways: Runways at the same terminal which may be usedsimultaneously without any violation of FAAj regulations.

Taxi: The movement of the aircraft while it is on theground.

Departing: The status of an aircraft from the time it turnsonto the runway to the time it clears the runway.

Landing: The status of an aircraft between its entry to theglide path and its clearing the runway.

Glide path: The airspace which extends from a runway in whichan aircraft makes its approach to land.

Clearing the runway: The end of occupancy of the runway and itsassociated airspace by an aircraft, either ondeparture or arrival.

Taxiways: The paved portionscN°an airport which are usedonly by taxiing aircraft.

Turnoff: The paved portions of an airport which are used byaircraft which are clearing the runway on arrival.

Waiting stack: The aircraft which are waiting to depart or holdingto land.

viii

T.___ ---

ix 5

Saturation level: The largest number of aircraft which the terminalcan service during a given time interval. T

Movement rate of Speed at which aircraft operations can beaircraft: serviced.

Flow restrictions: The restrictions related to the flow of aircraftinto and out of a given terminal.

Flight leg: The components of a daily flight plan, specifyingdeparture terminal, destination, and time ofdeparture.

Peak demand periods: The periods in which the demands for service byaircraft are the greatest.

Operation: The departure or arrival of an aircraft.

Parameter: A variable which can be controlled by the analyst.

Scheduling algorithm: A method of controlling the departure times ofaircraft.

System: The air terminals and airspace which are understudy during a time period.

Class A aircraft: All jet aircraft requiring runway lengths exceeding6000 feet.

Class B aircraft: Piston and turboprop aircraft having a normalF loaded weight in excess of 36,000 pounds; jetaircraft not included in Class A but having normalloaded weight in excess of 25,000 pounds.

L

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Chapter 1

INTRODUCTION

At the present time, millions of dollars are being lost by major

airlines each year because of the inability of high density air terminals

to efficiently service all of the demands placed upon them during peak

periods of demand. Eventually, all of the demands will be serviced but

not without a vast amount of unscheduled delay which is not indicative

of an efficient system. Relative to the air transportation system and

high density air terminals, an efficient system would be one that could

service all aircraft at their scheduled times without delay. Unscheduled

delay is the delay encountered by a flight which causes it to miss its

regularly scheduled arrival or departure time. On the other hand,

scheduled delay is the delay which is "built in" to a particular flight

schedule and which is considered part of the normal flight time. This

delay may be due to weather conditions, long taxi times, or conflicts

with other aircraft under normal operating conditions. The following

statistics relate to unscheduled delay.

For the calendar year 1969 in which three airlines reported, there

were 2,239,144 operations of which 855,375 encountered unscheduled delay

[14]. This delay totaled 96,149.3 hours at a cost of $37,809,97l. This

includes the cost of fuel consumed in holding patterns or in departure

stacks, crew salaries, maintenance, and the cost of extra ticket agents.

Thus, approximately 39 percent of all the operations reported by the

three airlines were delayec, with an average delay of 2.58 minutes per

operation and an average cost of $6.55 per minute of delay. A study

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conducted by the Federal Aviation Administration [10] indicated that

domestic air carrier terminal delay at 240 airports served by FAA towers

totaled 19 million minutes in 1968 at a cost of approximately 118 million

dollars. The total delay encountered by all air carriers for the calendar

year 1969 was estimated to be 24 million minutes at a cost of 158 million

dollars [14]. A comparison between the estimate for 1969 and the

estimate for 1968 as reported by the FAA shows an increase in total delay

of approximately 26 percent. According to a joint DOT—NASA report [7],

the loss to major airlines could grow to about 600 million dollars by

1980 if attempts to reduce delay are not successful. This report also

estimates the cost of delay to the passengers involved, in addition to

the costs incurred by the airlines, to be approximately 100 million

dollars in 1969.

Eighty-nine percent of this delay and its related cost occurred at

35 high activity reports [10]. The top seven terminals, ranked by delay,

accounted for 56 percent of the total delay while only handling 27

percent of the total air carrier operations controlled by FAA. For

example, in 1967 at Los Angeles, 25 percent of all departures and 341 percent of all arrivals were delayed [16]. Also, 40 percent of all

departures and 45 percent of all arrivals were delayed at Atlanta in 1967.

These two airports were not considered to be operating at saturation

level at the time the study was conducted. Thus, a study which inves-

tigates procedures to reduce delay at high density terminals could

contribute significantly to alleviating much of the delay discussed in

these studies.

3

The problems concerning delay and its associated cost to airlinesand passengers mentioned in the studies above are still just as seriousat the present time as they were several years ago and probably more so.For example, consider the ecological effects stemming from the problem ofdelay. First, there is the effect of air and noise pollution caused byjet engines while aircraft are idling on the ground awaiting departure,or holding in the air waiting to land. In addition, the amounts of fuelconsumed by holding aircraft is of prime concern, especially since thereis a fuel shortage and a deficiency of fuel producing natural resources.Thus, the delay problem is a very critical one from several different

gtandpoints: the airlines, passengers, ecology and mankind in general.No solution to the problem will totally eliminate delay. However, attemptsmust be made to reduce delay if the future of air travel is to remainattractive.

Congestion and Capacity

The delay encountered by aircraft is primarily due to congestion atmajor air terminals, where an air terminal is considered to be theairspace enclosed by an imaginary circle centered at the airport withradius of approximately 40 miles. The causes of this congestion includerunway saturation, noise restrictions imposed by environmental regu-

lations, insufficient turnoffs from runways, lack of aprons and holdingareas, an insufficient number of gates, and inadequate access tofacilities and parking []6]. Relative to delay, inadequate access to

facilities and parking causes passengers to park in places which are

4

inconvenient and remote from the gate or ticket agent. Often remote

parking causes last minute passengers to arrive at the gate too close to

the scheduled departure time. Passenger and luggage checking takes time

and in turn causes delay. Similarly, the aircraft also have "parking"

problems. Many times there are an insufficient number of available gates

to handle the demands of arriving aircraft. when such a situation

occurs, aircraft are sent to remote areas of the airport causing longer

taxi times and subsequent delay. Over a period of time this delay,

although sometimes slight, adds up to an appreciable amount. The lack

of aprons and holding areas creates two situations which contribute to

delay. First, flights which are scheduled to depart are held at the

gate occupying positions which would ordinarily be assigned to arriving

aircraft. Thus, arriving aircraft end up going to remote areas of the

airport to wait for available gate space. Second, flights which have already

departed the gate occupy taxiways which could have been used by arriving

aircraft for quicker taxi in. Because of the insufficient number of turnoffs

from the runways, arriving aircraft occupy the runway for a longer

period of time and, in some cases, have farther to taxiin, both of

which contribute to delay. Noise restrictions dictate the runway on which

a particular type of aircraft may depart or land. This in turn could lead

to longer taxi times, holding times, and waiting times, all contributing

to excessive delay. Saturated runways, unable to service aircraft operations

expeditiously, cause aircraft demanding service to encounter ground

congestion and long waiting periods. Thus, it can be seen that the

congestion which causes delay is not only a function of the airport

é5

building design and runway configuration but also of parameters not

related to aircraft, such as parking facilities and access to airport.

In l969, the primary causes of congestion at Atlanta were lack of

simultaneous approach capability and an inadequate number of runways [2l].

At Chicago‘s 0‘Hare Airport, the important factors related to congestion

were inefficient layout of taxiways, saturated taxiways, and flow

restrictions into the air terminals in the New York area. These flow

restrictions are due mainly to the competition which airlines flying

between New York and Chicago have created. In l969, four airlines were

flying l8,000 seats per day between New York and Chicago of which only

8,500 were occupied [ll], The congestion at Los Angeles was caused not

only by saturated runways and the inefficient layout of taxiways, but

also by the insufficient number of aircraft gates and noise abatement

restrictions [2l].

Related to the concept of delay and congestion is the measure of

capacity for a given airport and runway configuration. Capacity is

usually defined relative to delay, implying that a given aircraft move-

ment rate produces a specific amount of delay [l]. After a maximum

acceptable level of delay has been chosen, the capacity is reached when

the movement rate results in the chosen level of delay. For example, if

the maximum acceptable level of delay were chosen to be four minutes per

aircraft, then the capacity of the airport would be reached when the average

delay per aircraft reaches four minutes. As with congestion, capacity

limitations are not always functions of airport parameters [9]. For

instance, man·made objects in the vicinity of the airport as well asnatural surroundings influence the capacity. Restricted airspace, caused

6

by several airports being located in the same area, affects the capacity

of a given airport. The New York area, containing John F. Kennedy, La

Guardia, and Newark Airports, is a good example of the restricted air-

space constraint.

The concept of capacity is actually a subjective one since it is

based on an acceptable delay level. Some sources use four minutes as the

acceptable level of delay. Thus, another measure of aircraft movement

rate, not involving subjective judgements and related to the demands of

aircraft within the terminal area would be more appropriate in a study

concerning delay and congestion at high density terminals. Acceptance

rate is such a measure.

Acceptance rate is defined to be the maximum number of operations,

arrivals and departures, that an airport can accommodate during a given

period of time [6]. Based on the above definition, acceptance rate is

greater than the capacity defined by an acceptable level of delay. The

reason for this difference is that acceptance rate is based on the maximum

technological "capacity" of the airport, including the surrounding

airspace [6]. The average delay related to the number of operations per

unit time may be given as in Figure l.l [6]. Referring to Figure l.l,

acceptance rate would be the number of operations at which the average

delay curve becomes vertical [6]. Because acceptance rates are independent

of delay, any study involving delay reduction would benefit from the use

of this measure of aircraft movement.

As mentioned previously, a study investigating the delay problems at

high density terminals would be most beneficial.. Considering the causesof congestion at major air terminals, there are not many alternatives

.

>~»fü'EC3Q)U')füLG)><

Number of Operations

Figure 1.1 Re1ationship between Average De1ay and theNumber of Operations

E8

from which to choose. For example, most major airports have beenengulfed by the cities which they serve. Thus, plans for additional

runways and building expansion at these airports are often infeasible.

In addition, noise abatement restrictions imposed by local, state, or

federal agencies pose still another constraint on such a study. One

approach that would be independent of the above constraints would involve

the manner in which aircraft are scheduled in a given system of terminals.

Up to the present time, studies involving congestion have been aimed

primarily at implementation of computerized techniques to aid the air

traffic controller during peak demand periods. However, some studies

have considered the use of advanced flow control procedures based on the

present schedule of flights, as given in the Official Airlines Guide,

but little effort has been expended in attempting to formulate a better

method of scheduling flights. By scheduling aircraft in a given system

in a different manner, delay could possibly be reduced at high density

terminals even more than it has been reduced by using advanced flow

control procedures. Thus, the approach which is to be taken in this

study involves testing different heuristic scheduling algorithms, based on

what has been done previously, to determine to what extent total system

delay can be reduced.

Proposed Research

As mentioned previously, the majority of the flights being flown

by commercial airlines today are encountering delay other than the planned

scheduled delay. Thus, the objective of this research is to test several

methods of scheduling aircraft, in a system of terminals, which are intended

to reduce the delay time encountered by flights in the system.

9 (

In effect, what will be done will be to determine methods which willreduce any delay which is not attributed to uncontrollable factors, suchas weather or mechanical breakdowns. The method of approach which will befollowed in studying the problem will be based on a simulator which modelsaircraft movement among N major terminals. Several different heuristicscheduling algorithms will be developed and the operations related to eachalgorithm will be simulated. For each algorithm, hourly statisticsrelated to the number of operations, average departure delay per aircraftand average arrival delay per aircraft will be calculated along with totalsystem delay times for arriving and departing aircraft. The resultsobtained from these algorithms will be analyzed and compared. Schedulingalgorithms which result in a reduction in delay time will be examined ingreater detail to determine whether or not such a schedule would actuallybe feasible and worthwhile. Thus, from this study methods of reducingdelay, based on previous studies, will be explored and the correspondingresults analyzed.

Literature Review

Centralized flow control procedures were intended to restrict the

number and flow of aircraft to levels which would be compatible with the

capacity of the air traffic control (ATC) system [20]. From the studies

concerning flow control procedures, advanced flow control proceduresemerged. Advanced Flow Control Procedures (AFCPs) were established under

FAA Order 7230.9A in late l968 to estimate delay and distribute it

equally among aircraft flying in the system during peak demand periods.

By equally distributing delay, no one aircraft would encounter an

excessive amount of delay at any time. Essentially, AFCPs are designed

l0l

to have aircraft absorb inherent system delay on the ground at points ofdeparture rather than in the air at points of destination. This isaccomplished by forecasting expected delay for each terminalperiodically. AFCPs also help to establish order within the system inan effort to aid the air traffic controller during peak demand periods.

Several sources have explored the delay problem and many beneficialresults have been obtained. However, the possibility of more efficientresults still remains. The Mitre Corporation [25] has carried outconsiderable research on the delay problem in conjunction with the FAA.

For example, one study by Ziegler, Simmons, and Dawson [25] developedcomputer program modules which determine allocations to terminals, total

delay expected, and maximum ground delay expected for any given flight

after implementation of AFCPs. These program modules, in effect, provideautomated assistance to the operation of AFCPs.

Another study conducted by Bellantoni, Coonan, and Medeiros [4]

evaluated the present AFCPs asudeveloped by the FAA in l968. This

evaluation was an attempt to determine the flow control procedures'

effectiveness as well as to explore possible modifications of the

procedures. Results from this study indicate that several impediments,

primarily related to the control of air delay at the destination, occur

when implementing AFCPs. For example, once the capacity for a terminalhas been estimated, there is no procedure to revise this estimate. The

authors point out that under the present implementation of AFCPs, air

delays are uncontrollable and to a certain degree unpredictable. They

suggest that by modifying AFCPs, these impediments could be alleviated.

ll

A study by Forys, Heffes, Holtzman, Horing, Messerli, Schwartz,

and Stiles [l2] develops a traffic flow model which generates the meansand variances of delay when arrivals to the terminal area are serviced

on a first-come-first—served (FCFS) basis. Kramer [l9] developed what he

called central flow control based on information obtained from airport

reservation offices (ARO) and AFCPs. Developed by FAA the methodology

assumes a FCFS service doctrine. It is also suggested that using another

service doctrine may lead to a reduction in total system delay. Eyster[:3] analyzed AFCPs from a systems viewpoint to determine the degree to

which air terminals interact in a closed loop network. He developed an

integer linear programming model for scheduling aircraft within the

system. while this model for scheduling aircraft produced beneficial

results, Eyster felt that a more efficient model could be obtained.

The methods used to schedule aircraft operations during peak periods

of demand i affect capacity and in turn the amount of delay an aircraft

will encounter [l]. Raisbeck, Koopman, Lister, and Kapadim [22] studied

the problem of delay from the standpoint of the passengers instead of the

aircraft. Consider the situation where delays are attributed to peak

demand periods and that to provide flights during these intervals leads

to delays in waiting queues. If a decision were made to spread the same

flight demands over a longer period of time each flight on the new

schedule may experience zero delay. However, the passengers would now

experience even more loss of time, due to later departure and arrival

times, on the average,than they did before the change in schedule.

Appleby, Blake and Newman [:2] developed procedures to produce a

timetable for a medium sized school using a digital computer. The

l2

solution procedures include the following concepts. A trial solution is

developed at random and then examined to determine the number of con-

straints which were violated. Once this has been done, pairwise inter-

change is performed to reduce the number of violations. Also, a heuristic

approach which begins with a blank timetable in which entries are

assigned according to various criteria, if any rules are broken the

entry may be rejected. These concepts may be extended to the scheduling

of aircraft waiting to enter the terminal area.

Howard and Eberhardt [l8], in a study concerning commercial airplane

markets, evaluated the economics of routing passenger travel demand.

The assumptions concerning the demand generating function were that l)

demand is uniformly distributed, 2) flights are uniformly spread throughout

period of scheduling, and 3) passenger demand is normally distributed

around a scheduled departure time. They proceeded to simulate various

aircraft characteristics to determine the optimum operating conditions.

Gacnon [T3] considered the flight schedules as defining a network over

which passengers flow from a point "A" to point "B." He assumes that

the passenger is influenced by the following when choosing a flight:

l) aircraft type, 2) number of stops, 3) frequency of service, 4) time

of day, 5) arrival times, and 6) competing airline schedules. Four

different models were developed based on the above factors. They were

the passenger allocation model, attractive path generator, trafficO

distribution estimator, and allocation process.

Glenn [15] views a flight schedule as a compromise among the

community, airport authorities, government, and customer. Communities

dislike airports because of noise and pollution, but they still want to

l3 [

be able to compete with other communities. Airport authorities strive

for smooth operations with no peaking of flights or passengers, while

the post office wants flights around pick up and delivery times. In the

end, the prime task of the scheduler is to meet the customer's desires.

Shaw [ZQ] developed a concept of scheduling which is concerned with

the "best schedule of flights." The basis of this concept is the estimation

of the proportion of prospective passengers who would be "attracted" to

use a flight from the given schedule. Shaw defined the "best schedule"

in two ways, the best day-pair schedule and the best weekly-leg schedule.

The best weekly-leg schedule is the set of departure times which would

attract the largest percentage of gross revenue from all the passengers

moving over the network during the week. whereas, the best day-pair

schedule is the set of departure times which would attract the largest

percentage of the gross revenue for a given day.

‘ II

Chapter 2

DEVELOPMENT OF THE SIMULATOR

The basis of comparison of scheduling algorithms·will be the

statistical results obtained from simulating the movement of aircraft for

a given scheduling algorithm. The simulator itself is programmed in

Fortran and is a next event simulator which will service aircraft demands

and periodically review the status of terminals to determine the point in

time at which acceptance rate changes for the terminal.

Assumptions Concerning Aircraft

The following assumptions are concerned not only with characteristics

of the aircraft, but also the movement of aircraft in the system.

l) Aircraft speeds for different types of aircraft are random

variables and are not dependent on weather conditions,

altitudes, and load factors.

This is an approximation to reality but under optimum operating conditions

pilots will fly at speeds which approach the best cruise speed of the

aircraft which they are flying.

2) Aircraft taxi times and runway occupancy times are equal for

all aircraft serviced during a given time period and terminal.

The aircraft which are being used in the system are either Class A or

Class B aircraft. Class A aircraft include all jet aircraft which require

runway lengths which exceed 6000 feet, whereas Class B includes jet

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aircraft not included in Class A‘ but having a normal loaded weight in

excess of 25,000 pounds [l]. The similarity between the different types

of aircraft included in the two classes is the basis for the above

assumption.

3) Once an aircraft has entered the waiting stack with the

intention of landing, it will remain in the stack until

it lands.

4) Similarly, an aircraft never reneges from either entering

the waiting stack or landing, no matter how large a stack

exists.

The probability of a flight leaving the waiting stack and going to its

secondary terminal is so small that it is unnecessary to consider it in

this model. Also, reneging, or wave offs, are so rare that they need

not be considered. This assumption is based on conversations with FAA

personnel at Atlanta.

5) The order in which aircraft enter and leave the waiting

stack is strictly on a first-come—first—served service

doctrine.

6) The length of time between flight legs is at least 30 minutes.

The basis for this assumption is the fact that servicing the aircraft,

unloading and loading bagqage, as well as passengers, requires certain

actions which are time consuming. A random sample (obtained from the OAG)

of the length of time between flight legs indicated that a period of at

‘l6

least 30 minutes duration existed between flight legs, with the average

being about 40 minutes.

Assumptions Concerning Terminals

The following assumptions relate to the terminal area as well as the

runways and taxiways.

l) Kennedy, Newark, and La Guardia compose one terminal, Chicago's

0'Hare and Midway a second, washington National and Dulles

International another, and Dallas-Fort Worth a fourth, with

Atlanta, Los Angeles and Denver completing the system.

The above groupings are in accordance with the previous definition of

terminal and is based on the conflicts which occur in the airspace around

each of the above airports. The system does not need to be composed of

the above terminals but may include others depending on the analyst's

desires.

2) The acceptance rate for each terminal is reviewed on a

. periodic basis.

This review is taken to determine the acceptance rate for the following

period. The acceptance rate may be increased or decreased depending on

weather conditions and the number of runways which will be operational.

3) Depending on the number of independent runways, more than

one aircraft operation can occur during the same time span.

1 7 I

At any terminal the number of simultaneous operations which may take

place is a parameter which is controlled by the analyst, thereby allowing

him flexibility in the use of the simulator.

4) The distances between terminals is taken from the air

distances given in the Official Airlines Guide.

These distances are base distances to which vectoring distances are added.

These vectoring distances are based on a normal distribution with a meanof 50 miles and a standard deviation of five miles. Several airlines

supplied the author with these estimates.

5) Runway occupancy times are based on the acceptance rate of

a given terminal.

Runway occupancy times are calculated by dividing the time period for

which the acceptance rate has been projected by the projected acceptance

rate for that period. For example, if the time period was 60 minutes

and the projected acceptance rate for that period was 30 operations, then

the runway occupancy time would be equal to two minutes.

6) The acceptance rate for a given terminal is an average plus

random error, all of which is based on collected data.

7) The system of terminals is composed of N actual terminals and

one "catch-all" terminal.

8) Any flight which originates at one of the N actual terminals

going to a terminal which is not one of the actual terminals

is sent to the "catch-all" terminal.

I

l8

9) The "catch-all" terminal has an infinite acceptance rate and

the ability to service an infinite number of simultaneous

operations.

Simulator Logic

As mentioned previously, the simulator is a Fortran next event

simulator which services aircraft operations in a given system of

terminals. The basic concept of a next event simulator was obtained

from Simulation and Analysis of Industrial Systems [23]. All the neces-

sary variable initialization is performed at the beginning of the

simulator and distances between terminals are read in at this time.

Referring to Figure 2.l which depicts the basic logic, it follows that

the initial acceptance rate for each terminal is defined and is the time

at which the first periodic review will take place. Next, all information

pertaining to the flights is read into the simulator. This includes the

following: name of airline represented by each aircraft, characteristics

of each aircraft (i.e., type and average cruise speed), flight number,

number of flight legs which each aircraft flies per day, departure

terminal, destination, and departure time for each flight leg. The flight

data will then be adapted according to the scheduling algorithm which

has been specified. The simulator will enter the process of determining

the type of next event which will occur and will continue in a cycle

until all aircraft are idle, an aircraft leaves a waiting stack after a

prescribed time, or the master clock is equal to 24 hours. The cycle

contains the following stages: determine next event type, operate onnext event, operate on events which are dependent on next event, return

II

19

INITIALIZEVARIABLES

DETERMINEACCEPTANCERATES AND

REVIEW TIMES

INITIALIZE. | D A

ASCHEDULING

ALGORITHM

DETERMINENEXT EVENT

AIRCR T“‘éVéHi'· M11?

0EcREAsE E E GL RINGACCEPTANCE ARRIVAL EÖNWAYA HOLD ENROUTE I

RATE äDEPARTUREFLIGHTCHECKcHEcK 1~siA~i STACK COMPLETION

STACKA CHECK

STACKINSTANT WAITNEW ‘ New FL16Hi ~•

TIME LEG IDLE

Figure 2.1 F1ow Chart of Simu1ator Logic

20

to determine the next event. For example, if the next event was an air-

craft clearing the runway, then the waiting stack would be checked to

determine whether or not an aircraft was waiting for a runway to become

available. If one was waiting, then it would be allowed to begin its

operation. In this example, the checking of the waiting stack and

servicing of any waiting aircraft would be the event which was dependent

on the next event, an aircraft clearing the runway.

Referring to Figure 2.l, two types of events may occur. The terminal

event is the periodic review of the acceptance rate for each of the N

terminals. This event may either be an increase or a decrease in the

acceptance rate. In both cases, the runway occupancy time will change

for the subsequent period. If the acceptance rate had been zero for any

terminal and an increase occurred, then the waiting stack would be

checked to determine if an aircraft was waiting for service. If so,

that aircraft will begin its operation. This check of the waiting stack

will be repeated until all independent runways are occupied or there are

no aircraft remaining in the waiting stack.

An aircraft event may be one of three types: departure, arrival,

or clearing the runway. First, if the event is a departure, then the

aircraft may begin departure service immediately or it may have to wait.

For the aircraft to begin immediate departure, three conditions must

prevail:

l) The acceptance rate at the departure terminal must not be zero.

2) A waiting stack must not exist at the departure terminal.

3) There must be at least one independent runway which is not

being occupied.

2l Ä

If any one of the above conditions is violated, then the aircraft must

be put into the waiting stack and wait until conditions allow it to begin

its departure. To clarify this concept, when an aircraft demands

departure service and finds all the runways occupied, it is put into the

waiting stack. It must then wait for a runway to become available

before it is allowed to depart. Thus, the two conditions that will

allow an aircraft to leave the stack are l) it is occupying the first

position in the waiting stack, and 2) an aircraft has just cleared the

runway. Along these same lines, if the event corresponds to an arrival,

the above three conditions must be prevalent at the aircraft's destination

if the arrival is to begin landing immediately. Otherwise, the aircraft

will be forced to hold until conditions permit it to begin its landing.

when the aircraft event corresponds to an aircraft clearing the runway,

one of two situations will occur, either the aircraft is clearing the

runway on take—off orit is clearing the runway after landing. If the

aircraft is clearing the runway on take-off, it will be put enroute to

its destination. Its next event time will be equal to the present time

plus the calculated flying time and random error. As indicated in the

example given previously, the waiting stack will be checked to determine

if any aircraft is waiting for an available runway. On the other hand,

if the aircraft is clearing the runway after landing a check will be made

as to the number of flight legs which that aircraft has completed. If

it has completed all of the required daily flight legs, then it will be

classified as an idle aircraft and will be removed from the system. If

it has not completed all of the required flight legs then that aircraft

will be assigned a new departure time and will remain in the system.

N

22

As before, the waiting stack will be checked to determine if any aircraft

is waiting for an available runway.

The above events are the primary events on which the simulator

operates. Any one event does not necessarily have to have a distinct

time associated with it. More than one event, either aircraft, terminal,

or both, may occur at the same instant in time with all being serviced

in the appropriate manner. Also, when any aircraft enters or leaves a

waiting stack the appropriate times are recorded and later used in

calculating the arrival and departure statistics concerning delay. In

addition, whenever a demand for departure service or a demand for arrival

service occurs, the appropriate values corresponding to the number of

departures or arrivals at a given terminal are incremented by one.

The following hourly statistics based on the results of the simulation

are calculated: the total number of aircraft departing each terminal,

the total number of aircraft which wait at each terminal, the total

number of aircraft landing at each terminal, the total number of air-

craft holding at each terminal, total waiting time, average waiting time

and standard deviation of waiting time, total holding time, average

holding time and standard deviation of holding time for each terminal.

Based on these statistics, a statistical test will be carried out to

determine whether or not a difference exists among the algorithms tested.

Extensions of the Simulator

The simulator may be extended with minor modifications to provide ~

the analyst with more than N actual terminals. Also, the N actual ter-

minals which were used in this research could be replaced by others.

{l

L23

The number of aircraft operations which are simulated can also be

increased. This increase would provide the analyst with a means of

determining the effect of more operations on both arrival and departure

delay in the system. Other possible areas of study include having a

terminal become inoperative, unable to service aircraft demands, and

having independent runways become unavailable for service to determine

the effect on system delay.

Chapter 3

INTRODUCTION TO SCHEDULING

As mentioned previously, millions of dollars are being lost bymajor airlines each year because of delay in and around the terminalarea. Efforts have been made to alleviate the problem of delay, every-thing from computer aided AFCPs to increasing airport capacity. Themethod to be used in this research will be based on the concept ofscheduling aircraft flying in the system in a different manner. Themethod assumes that air terminals could handle all demands placedthem up to the saturation level, after which delays will be encountered.with this in mind,algorithmsaimed at scheduling aircraft into a terminal

C

in such a way as to not exceed the saturation level at any time will beexamined.

CScheduling Algorithms

There are six basic scheduling algorithms which will be discussedin detail in this chapter. One of the six schedules is actually thepresent schedule of flights as given in the Official Airline Guide,North American Edition. This schedule was used for two reasonsz l) toaid in the validation of the simulator, and 2) to use as a basis ofcomparison for the developed algorithms. Thus, this schedule has the

departure time for each flight leg as the time given in the airlineguide.

y 24T

25 E

Unif0Pm—Scheduling Algorithm

0ne factor which must be considered in scheduling is that of meetingthe passengers' desires with respect to the time at which they wish to

travel. The trend at the present time is for the majority of the

passengers to travel between the hours of eight o'clock and ten o'clock

in the morning and five o'clock and eight o'clock in the evening. Thus,

if any change is made in the present schedule it should remain as

sensitive to the passengers' desires as possible. with this in mind,

the uniform scheduling algorithm is designed to schedule aircraft

departures from a major terminal during the same hour in which they are

presently departing.

The time between departure demands at a terminal using this method

of scheduling will be equal to the length of the period for which the

acceptance rate has been projected divided by the projected acceptance

rate for that terminal. For instance, if the acceptance rate is 60

operations per hour, then aircraft demanding departure service during

that hour would be spaced one minute apart. If a flight plan presently

has a scheduled departure time of 9:45 a.m. it is possible under this

algorithm for that flight to depart earlier depending on the number of

aircraft demanding departure service. In a later section, the consequences

of a flight departing earlier will be discussed. If nine aircraft had

demanded service before the one given above and the acceptance rate was

30, then the above aircraft would be scheduled to depart at 9:l8 a.m.

Flights which arrive during a given hour and which have another flightleg will be assigned a new departure time based on the number of flights

ll-..-

26

already scheduled for departure service at that terminal. Also, if the

number of demands exceeds the acceptance rate for a given hour, the

excess will be carried over into the next hour. The basic step—by-step

procedure is as follows:

l) Determine the number of departure demands during a given— time period.

2) Calculate time interval between departures (lgnggäluilgäjgg).acceptance rate

3) Assign departure times to aircraft on a first-come-first-

served basis.

This algorithm is based on the principle of having one aircraft occupying

one distinct time slot. The following algorithm is based on the concept

of having more than one aircraft occupying a distinct time slot.

Simultaneous Uniform Scheduling Algorithm3

Like the uniform scheduling algorithm, the simultaneous uniform

scheduling algorithm has the time between departures based on the

acceptance rate at a given terminal. As before the passengers' desires

were considered in the development of this algorithm and thus no flight

departs more than an hour from its presently scheduled time. Most major

terminals have more than one independent runway, which implies that more

than one aircraft may be serviced during a given time interval. with

this in mind, the simultaneous uniform algorithm schedules aircraft such

that two or more aircraft have the sane departure time. The number of

aircraft having the same departure time is based on the number of

independent operations a given terminal can service simultaneously. For

example, if a terminal has two independent runways then it can service

27

two aircraft simultaneously. Therefore, according to this algorithm,

two aircraft may have the same departure time.7‘ M

This scheduling algorithm is similar to the uniform scheduling

algorithm which uses the acceptance rate of each terminal to calculate

the time interval between departures. However, with this algorithm,

departure slots are established and then M aircraft are assigned to each

slot, with M representing the number of simultaneous operations which

may occur at a given terminal. The other conditions concerning arrivals

and excessive departure demands are processed in the same manner as

described in the uniform algorithm. The procedure used for this algorithm

may be given as:

l) Determine the number of demands for each time period.

2) Calculate the time interval between departure time slots.(length of period)

acceptance rate3) Determine the number of simultaneous operations, M, which

can be serviced at a given terminal.

4) Assign M aircraft to each departure slot.

Peak Demand Uniform Scheduling Algorithm

This algorithm resembles the previous two algorithms in that the

times for departures are based on the acceptance rate of each terminal.

Basically, this algorithm schedules flights uniformly throughout a

period of known peak demand while allowing flights not demanding service

during that period to depart according to the present Official Airline

Guide schedule. This algorithm will schedule flights during the peak

L _ _.

28 [

demand period either according to the uniform scheduling algorithm or

the simultaneous uniform scheduling algorithm, both of which have been

described in previous sections. Thus, with this algorithm flights may

be scheduled in one of two ways. They are

l) Peak demand uniform scheduling based on the acceptance rate

for each terminal.

2) Peak demand simultaneous uniform scheduling based on the

acceptance rate for each terminal.

These two algorithms are very similar to the algorithms described

previously. The only dissimilarity is that the algorithm is enforced

only during certain periods of the day. Hence, the step—by-step procedure

for each of the two methods are given below.

°Peak Demand Uniform Scheduling Based on Acceptance Rate

l) Based on present operations and passenger desires, establish

the peak demand periods of the day.

2) Calculate the time interval between departure demands.(length of period)acceptance rate

3) Assign departure times to the aircraft demanding departure

service during peak periods.

4) Schedule remaining aircraft according to the present schedule.

29 {l

Peak Demand Simultaneous Uniform Scheduling

Based on Acceptance Rate

l) Establish peak demand periods of the day.

2) Calculate the time interval between departure demand slots

for peak periods.

3) Determine the number of operations, M, which each terminal

can service simultaneously during peak periods.

4) Assign departure times to aircraft demanding departure service

during peak periods, with up to M aircraft assigned to each

departure slot during peak periods.

5) Remaining aircraft will be scheduled according to the present

schedule.

The advantage of the above procedures given is that it does not restrict

the present schedule for the entire day.

Aircraft Tagging Method

This method of scheduling aircraft is actually only a means for

controlling the present schedule. The basic concept is to calculate the

expected arrival time interval for each departing flight and then based

on this time interval and the projected number of flights previously

scheduled for service at a destination terminal during the time interval,

determine whether or not each flight should be allowed to depart at its

scheduled time. If the number of flights is less than the number which

that terminal can service, then the flight is allowed to depart. A more

I

30

concise step-by-step procedure will aid the reader in understanding theconcept on which the tagging algorithm is based.

l) Flight‘s departure time occurs.2) Expected time of arrival at destination is calculated for

that flight (present + enroute time + runway occupancy time).3) The expected time of arrival is used to compute the time

interval, T, in which the flight will arrive at its destination.4) Acceptance rate for time interval, T, is calculated, hourly

acceptance rate times T divided by 60.5) The number of flights already scheduled for service during that

time interval is compared to calculated acceptance rate.6) If the projected number of flights scheduled for service is

less than the acceptance rate, then the flight is allowed todepart as scheduled.

7) If the projected number of flights scheduled for service isgreater than the acceptance rate, the flight is not allowed todepart. The acceptance rate for successive T minute intervalsis reviewed to determine in which interval the flight could beserviced.

8) Once an interval has been found a new departure time will beassigned to the aircraft.

An example will aid in understanding the above procedure. Consider aflight which has 9:l0 a.m. as its departure time and an enroute time of45 minutes. Thus, the expected time of arrival would be 9:55 a.m. whichwould occur during the l5 minute time interval 9:45 a.m. to l0:0O a.m.

) si 'Assuming that the acceptance rate for that interval is I5, and l5 flightshave already been scheduled for service during that interval, then theflight under consideration would be delayed. Thus, the acceptance ratefor successive l5 minute intervals (lO:O0-lO:l5, l0:l5—l0:30, etc.) wouldbe compared with the corresponding number of scheduled flight servicesuntil an interval with an acceptance rate greater than the number offlights scheduled for service is found. Assuming that this situationoccurs for the interval l0:0O a.m. to l0:l5 a.m., then the above flightwould be delayed for l5 minutes. Hence, departure time would become9:25 a.m. and the expected time of arrival would become l0:l0 a.m. It ispossible that at 9:25 a.m. the flight may not be able to depart due tothe existence of a waiting stack, or weather conditions; however, byassigning the aircraft a special status, attempts are made to see thatit does.

Summary of Scheduling

In all of the above scheduling algorithms an effort was made to havethem sensitive to passenger desires since airlines wish to satisfy theirpassengers. However, in some cases a scheduling algorithm may have aflight departing at a time earlier than its present departure time.An example would be the uniform algorithm. This would require that thepassengers arrive at an earlier time in order to meet the flight.Initially, this would cause some inconvenience for the passengers;

A

however, as the new departure time was accepted by the public thisinconvenience would diminish. It should be pointed out that for theuniform algorithm departure times were never adjusted more than an hour

I _ _.

earlier or an hour later than the present schedule. Thus, the passengerswould not have to arrive at the airport more than an hour earlier. 0nthe other hand, a scheduling algorithm may cause a flight to depart laterthan its present departure time. An example would be the tagging algorithm.Later departure times could cause passengers to miss their connections;

however, delay encountered while holding in the air could also causepassengers to miss their connections. As far as the passengers are

concerned, a 20 minute departure delay is equal to a 20 minute arrivaldelay. From the airlines point of view, it is a lot more economical andsafer to have the aircraft waiting on the ground instead of holding inthe air. All of the steps of each scheduling algorithm are carried outwithin the simulator, based on the algorithm which is specified for a 2

particular simulation.

Chapter 4

VALIDATION AND RESULTS

Before any statistical tests can be performed and conclusions drawn,it is necessary to validate the simulation model. In order to validatethe simulation model, it is essential that it meet the objectives forwhich it is intended to achieve. The basic objective of the simulatorwas to simulate the operations of M aircraft in a system of N terminalsin a realistic manner so that various scheduling algorithms could becompared. In other words, the simulator was to allow aircraft to "fly"in a system of terminals according to various scheduling algorithms andhave the terminals service these aircraft. The simulator is able tosimulate various numbers of aircraft in the system using differentscheduling algorithms in an attempt to obtain a reduction of departuredelay and arrival delay. The simulator records the various delaystatistics needed for comparing the different scheduling algorithms.The sample output given in Appendix C gives an indication of the abilityof the simulator to simulate aircraft operations in the system. The mostsignificant validation step was in the comparison of actual data toresults from the simulator in order to determine whether or not thesimulator is realistic. Table I gives the delay time per aircraft foreach hour of the day during February l973 at Hartsfield Atlanta Inter-national Airport. Table II gives the delay time per aircraft for eachhour of the day obtained from the results of simulating the operations ofl750 aircraft scheduled according to the DAG. while Figure 4.l is a graphof the actual data points and the data points obtained from the simulator.

, 33T

( 34 ETable1DelayTime per Aircraft

from Hartsfield Atlanta International Airport

Hour 'Total Delay (hours, minutes) Delay/Aircraft

00 — 01 4 + 29 0.20301 - 02 + 32 0.03802 - 03 + 00 0.00003 — 04 + 00 0.00004 — 05 + 02 . 0.00605 - 06 5 + 17 0.26906 - 07 12 + 03 0.49607 — 08 + 44 0.07108 — 09 1 + 37 0.11109 — 10 12 + 54 0.47610 - 11 12 + 22 0.33511 - 12 11 + 06 0.29012 - 13 11 + 08 0.42013 - 14 + 47 0.04414 - 15 8 + 39 0.29415 - 16 6 + 64 0.21216 — 17 2 + 06 0.07417 - 18 16 + 32 0.47818 — 19 12 + 35 0.39619 — 20 23 + 24 0.64220 — 21 10 + 40 0.37421 - 22 2 + 25 0.10122 - 23 + 56 0.05223 — 24 9 + 53 0.371

1-aaaaa

35

Table IIDelay Time per Aircraft from Simulation

Hour Total Delay (hours, minutes) Delay/Aircraft

00 - O1 + 05 0.02801 - 02 + 01 0.004O2 - 03 + 00 0.00003 - 04 + OO 0.00004 - 05 + 01 0.00205 — 06 + 16 0.06406 — 07 + 56 0.34107 - 08 + 00 0.00008 - 09 + 09 0.07309 — 10 + 59 ‘ 0.19210 — 11 ’ 3 + 02 0.49511 - 12 2 + 540.53612

- 13 1 + 18 0.27413 — 14 + 22 0.13814 - 15 + 42 0.15415 - 16 2 + 47 0.53416 — 17 + 12 0.04517 - 18 . 1 + 15 0.29318 — 19 2 + 30 0.39919 — 20 + 19 4 0.077

(

20 - 21 2 + 47 0.48121 - 22 + 23 0.12022 — 23 + 11 0.09123 - 24 + 16 0.075

36

+ Actual data• Data obtained from simulator

+IIII30 q'IIIII

- II^ 25 IIW IE T I·3 II IF + Itn

'II II I I

: II II III IIZ II I I .+ II I-I-I 20 II II II IIII4- II I¤ I I I IS. II IU I I III I II I III I I III

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2 4 6 8 l0 l2 l4 l6 l8 20 22 24Hour of the Day

Figure 4.l Actual Data vs. Data Obtained from Simulator

y 37B

As can be seen, there appears to be a reasonable degree of similaritybetween the actual data and the data obtained from the simulator. Thus,

it was concluded that the simulator did indeed meet its objectives.

Analysis of Results

Once it had been determined that the simulator met its objectives,the operations of the various scheduling algorithms were simulated. Todetermine the effect on delay of an increase in the number of aircraft inthe system, the operations l750, 2250, and 2750 aircraft were simulatedfor each scheduling algorithm. Actual data was extracted from theOfficial Airlines Guide for l750 flights in the system, while theadditional flights were synthesized within the simulator. The departuredelay and arrival delay statistics were calculated for each combinationof the number of aircraft and scheduling algorithm. These statisticswere then analyzed and compared to determine which algorithms were ableto handle an increase in the number of daily operations with only aminimum increase in delay. The results obtained from simulating the

operations of l750, 2250, and 2750 aircraft scheduled by the airlinesguide served as a basis for comparing the results of the other algorithms.Table IIIgives the average departure delay per aircraft and the averagearrival delay per aircraft for each scheduling algorithm. It should bepointed out that the average departure delay per aircraft scheduled bythe tagging algorithm is somewhat higher than the other algorithms.However, this is in accordance with the basic concept of having aircraftabsorb delay at their departure terminals instead of their destination.Also, the complete results for three of the algorithms are not included

lT____-

‘I

38 I

Table IIIResults Obtained from Simulation Concerning Average Delay

Departure Arrival weightedSchedule Delay Delay Average

1750 21.29 8.71 15.402250 a.m. 42.84 38.26 40.67OAG 2250 p.m. 53.89 56.18 54.982750 a.m. 359.60 627.03 487.602750 p.m. 424.26 795.85 601.381750 1.81 4.32 2.972250 a.m. 22.90 32.70 27.54Uniform 2250 p.m. 30.68 43.45 36.732750 a.m. 413.24 611.53 508.212750 p.m. 388.43 623.51 501.031750 39.87 7.21 24.032250 a.m. 1429.03 12.72 758.48Tagging 2250 p.m. 1262.46 14.74 655.762750 a.m. 4683.04 48.72 2464.342750 p.m. 3870.87 107.52 2073.721750 13.11 8.04 10.75

P k D d 2250 a.m. - - -P? °'“a"2250 p.m. 37.84 45.95 41.68U"‘f°'“"‘ 2750 a.m. - - -2750 p.m. - — -1750 33.43 12.77 23.84Simultaneous 2250 a.m. — — —

Peak Demand 2250 p.m. - - —4 Uniform 2750 a.m. — - —2750 p.m. — - —

1750 50.81 13.24 29.50

Uniform 2750 aim: _ _ _2750 p.m. — — —

I_.

39in

the table due to the fact that each one resulted in an increase inunscheduled delay over the present method of scheduling l750 aircraft.The uniform peak demand algorithm did indicate a slight decrease inaverage delay; however, it was felt that it was insignificant. Thus, inan effort to minimize computation costs, this algorithm was not investi-gated in further detail. Hence it was decided to determine whether ornot there existed a difference among the remaining three algorithms.

The method used in comparing the three scheduling algorithms was athree-way analysis of variance which tested for the equality of meansamong the effects, schedule, terminal and hour of the day. The develop-ment of the three-way analysis of variance model is based on the modeldeveloped in Statistical Theory and Methodology in Science and Engineeringby Brownlee [ 5]. Let row index i correspond to the various schedulingalgorithms, column index j correspond to the terminals, and array index kcorrespond to the hour of the day. Thus, since there are three,r = 3,scheduling algorithms, seven,t = 7,terminals, and 24 hours, u = 24, therewill be 504 cells in the three-dimensional lattice. Now let 2 correspondto the index of the observation in each cell, where 2 = l, 2, 3. For themodel given above, all of the effects will be tested using the within-cell mean square. Table IVgives the source of variation, degrees offreedom, sum of squares, and the expected mean square for the model tobe used. In other words, the null hypothesis was

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42 l

where pi is the true mean for the ith schedule, vi is the true mean for

terminal i, and ak is the true mean for hour k. In effect, thisstatistical test was performed to determine whether or not a difference

in average delay among the three scheduling algorithms exists. Due to

the fact that there are such a large number of observations, the aid of a

computerized analysis of variance solution procedure, QAQ [3], was used.

The tables in Appendix D give the results obtained from §A§„ The main

effects which were tested for significance were the scheduling algorithms,

the terminal, and the hour of the day. As can be seen by referring to

Appendix D, all of the main effects proved to be significant when tested.

Thus, it was concluded that the mean delay associated with each of the

three scheduling algorithms was not equal. Even though there was a

significant difference in the mean delays, it was still not clear as to

which scheduling algorithm showed the greatest reduction in unscheduled

delay.

The uniform scheduling algorithm showed the greatest reduction over

the present schedule in departure delay and arrival delay. Uniform

scheduling implies that only one aircraft should be departing a given

terminal at any point in time. Thus, if a terminal can service N

simultaneous operations, then (n—l) runways would be available for arriving

aircraft to use. Hence, arriving aircraft would encounter little or no

delay, while departing aircraft would experience little or no delay

since there should always be, at worst,one runway which is not being

occupied by another aircraft. This algorithm would be quite effective

in reducing the total system delay. However, it would require a complete

change in the present schedule.

Based on the present schedule, the tagging algorithm showed areduction in unscheduled arrival delay but showed an increase in departuredelay. This is in accordance with the basic concept of having aircraftabsorb delay on the ground at their departure terminal instead of in theair at their destination. Nevertheless, from the standpoints of safety

and ecology, the tagging algorithm would be most effective in that theaircraft would not be consuming fuel holding in the air, but instead wouldbe on the ground conserving fuel. Also, no changes would need to be madein the present schedule. Figures 4.2 through 4.llare graphs of the Taverage hourly delay per aircraft for each hour of the day at the terminal

which corresponds to Atlanta for the three algorithms compared above.

One can conclude from the results given above that unscheduled »

delay can be reduced by scheduling aircraft in the system in a manner

different from the present schedule. To state which scheduling algorithm

is the best and most effective would be difficult without further study.

However, the objective of this research was to determine whether or not

unscheduled delay could be reduced by modifying, or changing, the presentscheduling procedure. Thus, the objective was accomplished.

l

. 1- I

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L 44

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Figure 4.2 Average Departure De1ay per Aircraft for 1750 Aircraft

I_T___ _ _ g

145—-—-

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Figure 4.3 Average Departure Delay per Aircraft for 2250 Aircraft(Synthesized flights added in morning)

1I I 46

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3 ——·-~- Tagging a1gorithm

t_?

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Figure 4.4 Average Departure De1ay per Aircraft for 2250 Aircraft(Synthesized f1ights added in afternoon)

1

Y 47 QF -————- DAG schedule

Uniform algorithm[ I -·-·—· Tagging algorithm

+0 . 1Q- •

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Figure 4.5 Average Departure Delay per Aircraft for 2750 Aircraft($ynthesized flights added in morning)

LN,

S48

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Hour of the Day

Figure 4.6 Average Departure De1ay per Aircraft for 2750 Aircraft(Synthesized f1ights added in afternoon)

1 49 1

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4-> 5,000*1-Q 4,000

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Figure 4.7 Average Arriva1 De1ay per Aircraft for 1750 Aircraft

I

50

0 -————- 0AG scheduleUniform algorithm

-·-·- Tagging algorithm5,000

2 4,000Eg 3,0002C) 2,000 ,m , .N/'\N Ui$--EC C 1000EE

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Figure 4.8 Average Arrival Delay per Aircraft for 2250 Aircraft(Synthesized flights added in morning)

I C _

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5l

———— OAG schedule]0’000 ——·-- Uniform algorithm4-S‘E -—··—·— Tagging algorithm

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Figure 4.9 Average Arrival Delay per Aircraft for 2250 Aircraft(Synthesized flights added in afternoon)

52F

·——-—- 0AG schedu1e10,000 --—— - Uniform a1g0rithm

—--·— Tagging a1gorithm

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Hour of the Day

Figure 4.10 Average Arriva1 De1ay per Aircraft for 2750 Aircraft(Synthesized f1ights added in morning)

1

I

1 53

—————— OAG schedu1e]Q,QQO -·— -- Uniform a1gorithm

—· —~·— Tagging a1gorithm

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2 4 6 8 10 12 14 16 18 20 22 24Hour of the Day

Figure 4.11 Average Arriva1 De1ay per Aircraft for 2750 Aircraft(Synthesized f1ights added in afternoon)

I

I

Chapter 5

y SUMMARY AND RECOMMENDATIONS

The purpose of this research was to determine the effect ofscheduling an air traffic delay. The airlines are losing millions ofdollars each year because of unscheduled delay which aircraft encounterat high density air terminals during peak periods of demand. Effortshave been made to reduce this unscheduled delay by attempting to controlthe flow of aircraft in the present system. For example, Advanced FlowControl Procedures developed by the FAA control the flow of aircraftin the system by having aircraft absorb delay at their departureterminals instead of their destination. It was felt that delay could

ibe reduced even more if other methods of scheduling were developed andstudied.

The scheduling algorithms developed are heuristic and were based onthe acceptance rates of the terminals in the system. It was assumed thatthere exists a given saturation level for an air terminal at which itcan service the demands without unscheduled delay. Based on thisassumption, the algorithms were designed to schedule aircraft in such away as to not exceed the saturation level at a given terminal. Eachalgorithm was intended to reduce delay and as seen in the previous chapter,several of the algorithms did indeed reduce the delay.

Although the research showed that delay could be reduced byscheduling aircraft in a different manner, the "optimum" schedulingpolicy was not developed as such. Thus, the need still existsfor54

55 ¤

further investigation in the area of flight scheduling. Possible

extensions of the research preferred in this study include:

l) Determining the effect on the scheduling algorithm andn delay of having the acceptance rate at a terminal become

zero.

2) Determining the effect of having the number of simultaneous

operations at that terminal be decreased during the

simulation.

3) Gathering and analyzing data on a consistent basis for all

major terminals.

4) Gathering and analyzing on a consistent basis data for

various flights throughout U. S.

5) Gathering and analyzing on a consistent basis data on

runway operation, maintenance, etc.

One of the major problems encountered in this research was the lack

of accurate data concerning runway availability. It was difficult to

obtain any information concerning runway maintenance and the percentage

of time runways are available. Thus, it was difficult to determine each

0ne's effect on terminal acceptance rate. The need exists for a more

accurate and consistent method of collecting and analyzing data

concerning the runways. There is also a need for more detailed and

consistent data concerning the various flights in the United States.

This data would be concerned with departure delay, enroute delay, arrival

delay, taxi out delay, and taxi in delay. It was most difficult to

56validatethe simulator due to the lack of this kind of data. Severalairlines did supply the author with some of this data, but it was notcomplete. Also, there was no information concerning the number offlights which actually reported that they encountered delay. Finally,there exists a need for major terminals to record data concerningacceptance rates, the effect of weather on aircraft operations and thedelay which aircraft encounter while in the terminal area. The lack ofthis kind of data also proved to be a factor in the validation of thesimulator. Atlanta does, however, record information concerning thetotal number of operations, the total delay encountered, and the hourlyacceptance rates which the author used in validating the simulator.Other major terminals need to record accurate information similar to thatobtained from Atlanta.

Also, combinations of the scheduling algorithms developed in thisresearch or other scheduling algorithms could be investigated to deter-mine the effect on unscheduled delay. For example, combine theOuniform algorithm and the tagging algorithm. Thus, the area of schedulingappears to be a lucrative one in terms of reducing unscheduled delay,one which should be investigated in more detail.

BIBLIOGRAPHY

1. Airborne Instruments Laboratory, "Airport Capacity Handbook,"Cut1er-Hammer, June 1969.

2. App1eby, J. S., B1ake, D. V. and Newman, C. A., "Techniques forProducing Timetab1es on a Computer and Their App1ications toOther Schedu1ing Prob1ems," The Computer Journa1, 3, Apri1-January 1960-1961, pp. 237-45.3. Barr, A. J. and Goodnight, J. H., Statistica1 Ana1ysis System,

Department of Statistics, North Caro1ina State University,August 1972.4. Be11antoni, J. F., Coonan, J. R. and Medeiros, M. F., Eva1uation ofthe FAA Advanced F1ow Contro1 Procedures, Report Number DOT-TSC-

FAA-72-8, January 1972.

5. Brown1ee, K. A., Statistica1 Theory and Methodo1ogy in Science andEngineering, New York: John wi1ey & Sons, 1960.

6. Car1in, A. and Park, R. E., "A Mode1 of Long De1ays at Busy Airports,"Rand Corporation, August 1969.7. Department of Transportation and Nationa1 Aeronautics and Space

Administration, Civi1 Aviation Research and Deve1opment Po1icyStudy, March 1971.

8. Eyster, J. w., "0ptima1 Se1f—Perpetuating F1ow in a C1osed-Loop AirTraffic Contro1 Netowkr," unpub1ished doctora1 dissertation,Department of Industria1 Engineering, The Ohio State University,1971.

9. "Factors to be Considered in Determining Termina1 Area Capacities andAcceptance Rates," FAA.

10. Federa1 Aviation Administration, The Nationa1 Aviation System P1an,1971-1980, March 1970.

11. F1ying, "The Airport Crisis," Staff Report, Ju1y 1969, pp. 59-76.12. Forys, L. J., Heffes, H., Ho1tzman, J. M., Horing, S., Messer1i, E. J.,

Schwartz, M. I. and Sti1es, J. A., "A Study of the Ana1ysis andContro1 of the F1ow of Air Traffic," February 1970.

13. Gacon, G., "A Mode1 for F1owing Passengers Over Air1ine Networks,"Transportation Science, Vo1ume I, August 1967, pp. 232-248.14. Ga1breath, A. and warfie1d, R. M., "Termina1 Area Air1ines De1ay

Data, 1964-1969," DOT—FAA, September 1970.

57

58 Q15. Glenn, C. H., "Factors to be Considered in Airline Schedu1ing,"

Canadian Aeronautics and Space Journal, June 1972.16. Heffter, M. S., wiley, E. and Crown, J., "Problems of Airport

Congestion by l975," Civil Aeronautics Board, September 1969.17. Hicks, C. R., Fundamental Concepts in the Design of Experiments,

Holt, Rinehart, andyyinston, New York, 1964.18. Howard, L. R. and Eberhardt, D. O., "Airline Simulation for Analysis

of Commercial Airplane Markets," Transportation Science, Volume I,August 1967, DD. 131-157.

19. Kramer, M. H., "An Overview of Central Flow Control," IBM TechnicalReport, FS6 72-6001, July 1971.

20. Martin, R. w., "Centralized Flow Control," FAA, May 1970.21. Million, L- N., Copeland, J. M., Hornsby, J. T. and Keepers, w. C.,

"A Suggested Action Program for the Relief of Airfield Congestionat Selected Airports," DOT-FAA, April 1969.

22. Raisbeck, G., Koopman, B., Lister, S. and Kapadia, A., "A Study ofAir Traffic Control System Capacity," Interim Report, September1969 - August 1970, Arthur D. Little, Inc., October 1970.

23. Schmidt, J. W. and Taylor, R. E., Simulation and Analysis ofIndustrial Systems, Richard D. Irwin, Homewood, Ill., 1970.

24. Shaw, G. C., "The Concept of the Best Schedule," 36th National‘ Meeting of the Operations Research Society of America, November1969.

25. Ziegler, E. w., Simmons, R. A., and Dawson, S. A., "Flow ControlSystem Description," Mitre Corporation Technical Report, Volume 6,No. 4109, August 14, 1971.

APPENDICES

59

II

_ Appendix A

DESCRIPTION OF COMPUTER PROGRAM

60

6l

Variable Definitions

NAl - the number of actual flights in the system.

NT - the number of terminals in the system.

NTIM - conversion factor converting minutes to seconds.

NSTOP - variable controlling the termination of the simulator.

INRIT — variable controlling the write statements in the simulator.= 0, written= l, not written

ISS T - variable controlling which scheduling algorithm will beused.

= 0, OAG= l, uniform= 2, simultaneous uniform= 3, peak demand uniform= 4, tagging

NREPS - the number of days to be simulated. ‘

IADD - the number of synthesized flights in the system.

IADl — the variable controlling the time interval when thesynthesized flights will be added.

= 0, morning;_D, afternoon

ENDEL - total enroute delay.

_ SENDEL — the sum of squares for enroute delay.

NEN — the number of aircraft which actually go enroute.

NDAY — the present day being simulated.

NA — the total number of aircraft in the system.

ISZ — variable related to tagging algorithm which indicateswhether or not an aircraft gets tagged when its initialdemand for departure occurs.

= 0, tagged= l, allowed to depart

ISU - variable controlling when the number of aircraft that mustwait is incremented in subroutine FUTCAP.

= 0, increment number by one= l, do not increment

62

IX — seed for random number generator.MSTOP — variable controlling the termination of the simulator,associated with NSTOP.MBEGPD — variable controlling beginning of peak demand period inthe morning.MENDPD — variable controlling the ending of the peak demand periodin the morning.NBEGPD — variable controlling the peak demand period in theevening.NENDPD - variable controlling the end of the peak demand periodin the afternoon.

ITHDEL — total arriving delay for aircraft in the system.ITNDEL — total departing delay for aircraft in the system.DIST(I,J) — distance between terminal I and terminal J.KFA - variable used in controlling which algorithm will be used inin conjunction with the peak demand uniform algorithm.= l, uniform

= 2, simultaneous uniformNAI — counter used in determining the number of idle aircraft inthe system.

NAM(I,J) — array containing the airlines corresponding to aircraft I.CHAR(I,J) — array containing the characteristics of aircraft I.J = l, type

· J = 2, cruise speed

NFN(I) - flight number corresponding to aircraft I.NDF(I) - number of flight legs which aircraft I has each day.NADFl(I,J) - departure terminal for Jth flight leg of aircraft I.NADF2(I,J) - destination terminal for Jth flight leg of aircraft I.NADF3(I,J) — departure time for Jth flight leg of aircraft I.CSA - random error associated with cruise speed.NDDF(I) - current flight leg of aircraft I.NTAG(I) - variable controlling whether or not aircraft I has beentagged.

= O, has not been tagged= l, has been tagged.

63 QZ

NACFT(I,J) - array storing present information concerning aircraft I,used as a "working" array which changes with time.

J = l, departure terminalJ = 2, destination terminalJ = 3, status of aircraft .

NACTM(I) - array storing next event time of aircraft I.

NTER — terminal under consideration at any given time.

NUST(L,K) - stores the number of departure demands already scheduledat terminal L during Kth hour.

NHAC(L,K) - stores the acceptance rate for terminal L during Kth hour.

NST - time between departure time slots.

NSOP(L) - the number of simultaneous operations which can occur atterminal L.

NFCAP(L,M) — the number of aircraft scheduled for service at terminal Lduring the Mth fifteen minute interval of the day.

TNEXT — next event time.

NCCAP — time interval between periodic reviews of terminal.

NDT(L,K) — number of departures from terminal L during Kth hour.

NAT(L,K) — number of arrivals at terminal L during Kth hour.

NHT(L,K) - number of arrivals which hold at terminal L during Kth hour.

NwT(L,K) - number of departures which wait at terminal L during Kthhour.

IwDEL(L,K) — total departure delay at terminal L during Kth hour.

IHDEL(L,K) - total arrival delay at terminal L during Kth hour.

SSQUD(L,K) - sum of squares of delay time for departures at terminal Lduring Kth hour.

SSQUA(L,K) - sum of squares of delay time for arrivals at terminal Lduring Kth hour.

NACAP(L) - number of aircraft actually occupying runways at terminal Lat any given time.

NWS(L) - number of aircraft in waiting stack at terminal L.

T"'“"“Ü""'““"""“"""———‘—""‘"—————————————'—"‘iittt—————————————————————————————II

64

NCHCAP(L) — time of next periodic review at terminal L.

INEXT(J) - array storing smallest time associated with terminals andaircraft.

J = l, aircraftJ = 2, terminalJ = 3, end of simulation

NUEV(J) — variable corresponding to whether or not an aircraft andterminal event occurred simultaneously.

J = l, either type occurredJ = 2, both types occurredJ = 3, end of day's operation

NV — number of aircraft having the same next event time.

NFFP(N) - array storing aircraft number associated with the Nthaircraft having the present next event time.

NIAT - number of terminals having the same next event time.

IDMT(N) - array storing terminal number associated with the Nth terminalhaving the same next event time.

NKN - aircraft number associated with Nth event.

NCAPTR(L) — present acceptance rate for terminal L.”

EDIS - random error associated with distances between any twoterminals.

ENRT — enroute time.

EX - random error added to enroute time.

DISTAN — distance presently being considered.

NCSAV(L) - variable used to indicate whether or not the acceptance rateat terminal L has increased from zero.

NCE - random error associated with the acceptance rate of a giventerminal.

NEARTM — expected arrival time used in tagging algorithm.

NFMAC - acceptance rate associated with the expected time ofarrival and the l5 minute interval in which it occurs.

NwSO(M,L) - aircraft number corresponding to Mth position in waitingstack at terminal L.

65 iT

NDEL(I) - time at which aircraft I demanded service.

NDUM(M,L) - dummy array used in moving aircraft up in the waiting stackonce an aircraft leaves the stack.

AWT - average waiting time.

SDNT — standard deviation of waiting time.

AHT - average holding time.

SDATS

- standard deviation of holding time.

RAND — uniformly distributed random number.

NTT — the number of terminals in system minus one.

IKEY - variable controlling when the number of aircraft that mustwait, or hold, is incremented.

= 0, increment by one= l, do not increment

LF — departure terminal.

LT - destination.NEN - number of aircraft which actually go enroute.

XLAM - mean of normal distribution.

SIG - standard deviation of normal distribution.

NXTD - total number of aircraft that depart.

NXTA - total number of aircraft that land.

XNTT - total holding time for arriving aircraft.

XNTT - total waiting time for departing aircraft.

wTT(L) - total waiting time at terminal L.

NTDT(L) - total number of departures at terminal L.

NTwT(L) - total number of aircraft that must wait at terminal L.

NTAT(L) — total number of arrivals at terminal L.

NTHT(L) - total number of aircraft that must hold at terminal L.

66

SDSQ(L) - sum of squares for total departure delay at terminal L.

SHSQ(L) - sum of squares for total arrival delay at terminal L.

XWTT - total system departure delay.

XHTT - total system arrival delay.

AEND - average enroute delay.

AXWTT - average departure delay per aircraft in system.

AXHTT - average arrival delay per aircraft in system.

67

Main Program

The purpose of this portion of the simulator is to control the basic

operations of the simulator. From it the subroutine to read in the

flight plan data, the subroutine to initialize variables associated with

the terminals, the subroutine to determine the next event, and the sub-

routine to calculate the statistics concerning delay are called. Also,

the matrix containing the distances between terminals, variables associated

with the different scheduling algorithms and variables related to the

termination of the simulator are initialized. In the cycle of determining

the next event, the main program acts as the beginning and the end of the

process which determines and services the next event. In other words,

the subroutine that determines the number of idle aircraft in the system

is reviewed. If all aircraft are idle then the simulator terminates and

the hourly delay statistics are calculated. Otherwise, the minimum next

event time is found and is operated upon, until the day's operations have

been simulated. At this time the hourly delay statistics are accumulated.

(For flow chart see Figure A.l.)

Subroutine FLIGHT

The purpose of this subroutine is to read into the simulator the

daily flight plans for each aircraft in the system. The following

parameters are given for each aircraft in the system:

l) Airline associated with each flight

2) Aircraft characteristics

a) Type (i.e., 707, 727, 747, DC8)b) Best cruise speed

l__

I

68

3) Flight number

4) Number of daily flight legs

5) Departure terminal, destination terminal, and departure time

for each flight leg.

After all the parameters given above are read into the simulator for any

given aircraft, the ones associated with the initial flight of the day

are stored in the corresponding arrays which will be used in determining

the next event. Thus, the original data is not used in determining the

next event but instead "working" arrays which are continuously changing

are used. (See Figure A.2 for flow chart.)

Subroutine ADFLT

This subroutine will synthesize N additional flights during a given

time interval during the day. This includes departure terminal,

destination, and departure time for each flight synthesized. These

flights are synthesized to determine the effect of more aircraft in the

system on the various scheduling algorithms. (For flow chart see Figure

A.3.)

I Subroutine UNIFM

This subroutine is used to schedule aircraft either according to the

uniform scheduling algorithm or the simultaneous uniform scheduling

algorithm. The method used is based on the following concept. First,

determine the departure terminal of the aircraft under consideration.

Second, determine in which hour of the day that aircraft demands

69

departure service. Third, calculate the time interval between departuretime slots using the acceptance rate of the departure terminal for thehour calculated above. Finally, based on the hour of the day and the

number of aircraft previously scheduled at the departure terminal underconsideration, assign the aircraft being considered a departure time.

(For flow chart see Figure A.4.)

Subroutine PDUNIF

Subroutine PDUNIF schedules aircraft either according to the uniform

algorithm or the simultaneous uniform algorithm during the peak demandperiods of the day. The basic procedure is given below. First, determine ifthe aircraft under consideration has a departure time for its first flightleg during one of the peak demand periods. Second, determine the depar-

ture terminal for the aircraft being considered. Third, calculate the

hour of the day in which the departure demand occurs. Finally, assign

a departure time to the aircraft based on the number of aircraft

previously scheduled at the same terminal and the terminal's acceptance

rate. (For flow chart see Figure A.5.)

Subroutine TAGSCH

Subroutine TAGSCH is used in conjunction with the tagging scheduling

algorithm. At the beginning of the simulation it calculates the

projected number of flights departing each terminal during any given

time interval. This is only done for the initial flight leg of the day

for each aircraft. when an aircraft completes its first flight leg and

has remaining flight legs, the projected number of flights departing a

I

70

terminal is incremented during the appropriate time interval, which isbased on the new departure time. (For flow chart see Figure A.6.)

Subroutine TERCAP

This subroutine will read in the time interval between periodicreviews at each terminal, the number of simultaneous operations each

terminal can service, and the average hourly acceptance rate for each hour

of the day. Also, it initializes all variables associated with the I

terminals concerning the number of departures, the number of arrivals,

the number of aircraft that must wait, and delay time. (For flow chartsee Figure A.7.)

Subroutine NEXT

This subroutine controls the steps for determining the next eventtime. The steps involved are finding the smallest next event time amongall aircraft, finding the smallest time among periodic review times forthe terminals, setting the end of simulation time and choosing the

minimum time among the above times. 0nce this has been done theappropriate subroutine, which will operate on the next event, will becalled. (For flow chart see Figure A.8.)

Subroutine ACNEXT

Subroutine ACNEXT determines the minimum next event time among allthe aircraft in the system. It is called from subroutine NEXT and returnsINEXT (l) to subroutine NEXT. (For flow chart see Figure A.9.)

I

7l fSubroutine TERNEX

Subroutine TERNEX determines the minimum next event time among theterminals in the system, where the event would be a periodic review ofthe acceptance rate. This subroutine is called from subroutine NEXT andreturns the value of INEXT (2) to subroutine NEXT. (For flow chart seeFigure A.l0.)

Subroutine AOPER

Subroutine AOPER services the aircraft next events according to thestatus of a given flight. Depending on the status of the flight underconsideration, the aircraft will either be allowed to occupy a runway,either departing or arriving, will clear the runway and start its

)enroute portion of the flight, or become idle, or be put into the

waiting stack to wait for conditions to permit its service. (For flowchart see Figure A.ll.)

Subroutine ENROUT

This subroutine calculates the enroute time for any given flightbased on the distance to be travelled, vectoring distance, and best

cruise speed. (For flow chart see Figure A.l2.)

Subroutine ERDEL

This subroutine is associated with determining the amount of enroutedelay an aircraft will encounter for a given flight leg. It generatesthis delay time from a normal distribution using a mean and a variance

72

selected by the analyst. It uses the normal process generator as given

in Simulation and Analysis of Industrial Systems by Schmidt and Taylor.

(For flow chart see Figure A.l3.)

Function VECT

This function is associated with calculating the vectoring distance

for a given flight once it departs. It generates this distance from a

normal distribution using a mean and a variance selected by the analyst.

It also uses the normal process generator as described by Schmidt and

Taylor.i (For flow chart see Figure A.l4.)

Subroutine SERDES

This subroutine will assign an aircraft a position in the waiting

stack at a given terminal and perform the necessary adjustments to

aircraft's status and next event time. The subroutine will also increase

the number of aircraft that must wait, or the number of aircraft that

must hold, based on the previous status of the aircraft. (For flow chart

see Figure A.l5.)

Subroutine UNSTAC

Subroutine UNSTAC will service an aircraft which leaves the waiting

stack after an aircraft has cleared the runway. In effect, this subroutine

will remove the first aircraft from the waiting stack and allow it to

occupy a runway. In addition, it will call subroutine DELAY to calculate

delay statistics for their aircraft. (For flow chart see Figure A.l6.)

73“I

Subroutine DELAY

This subroutine calculates the amount of delay which an aircraft

may encounter while waiting for service, either departure or arrival.

The basic concept is that the amount of delay encountered will be equal

to the difference between the actual time of service and the desired

time of service. (For flow chart see Figure A.l7.)

Subroutine FUTCAP

This subroutine is associated with the tagging scheduling algorithm.

It estimates the enroute time for a flight and then predicts the time

interval, T, in which that flight will arrive at its destination. Based

on the terminal's hourly acceptance rate, it will determine if the

flight would be allowed service during that time interval, T. If so,

the flight is allowed to depart at the present time; otherwise, the

flight will be tagged and must wait. (For flow chart see Figure A.l8.)

Subroutine OPWRIT

Subroutine OPNRIT will write the appropriate information relative

to the present aircraft event. This subroutine is only called when the

IWRIT parameter is equal to zero. (For flow chart see Figure A.l9.)

Subroutine WRIDEL

Subroutine WRIDEL calculates hourly delay statistics for each

terminal at the end of the simulation. This includes the number of air-

craft that demand departure (arrival) service, the number of aircraft

I‘I

74 II

that wait (hold), and the average delay encountered by an aircraftand standard deviation. (For flow chart see Figure A.20.)

Subroutine TODEL

Subroutine TODEL accumulates the total delay statistics for each

terminal at the end of the simulation. Also, it gives total departuredelay, total arrival delay, and average enroute delay. (For flow chart

see Figure A.2l.)

Subroutine TWRIT

Based on whether or not all "write" statements are being written,

this subroutine will write the appropriate information each time aperiodic review is taken. This subroutine is called only when IWRIT isequal to zero. (For flow chart see Figure A.22.)

Subroutine PUSHUP

Subroutine PUSHUP will advance all aircraft occupying positions inthe waiting stack at a given terminal one position. This advancing will

occur after the aircraft occupying the first position has been removed

from the waiting stack and allowed to occupy the runway. (For flow

chart see Figure A.23.)

Subroutine NEXFLI

Subroutine NEXFLI is used to determine the information relative to

an aircraft's subsequent flight leg once that aircraft has completed itsprevious flight leg. The subroutine determines the departure terminal,

. 75

the destination, and the time at which the aircraft will demand departure

service. (For flow chart see Figure A.24.)

Subroutine TCAPYf

Subroutine TCAPY controls the steps in reviewing the acceptance rate

of the terminals when a periodic review is found to be the next event.

It controls the calling of the subroutine CHANG, which determines the new

hourly acceptance rate when appropriate. (For flow chart see Figure

A.25.)

· Subroutine CHANG

This subroutine determines the new hourly acceptance rate for a

given terminal at each periodic review. (For flow chart see Figure A.26.)

Function RAND

This function generates a uniformly distributed random number between

zero and one. It is taken from Simulation and Analysis of Industrial

Systems by Schmidt and Taylor. (For flow chart see Figure A.27.)

lI

l76

START

INLTIALIZEVARIABLES

A

CALLSUBROUTINE

TERCAP

CALLSUBROUTINE 7

FLIGHT

PEAKCALL g CALLSUBROUTINE UNIFORM DEMAND SUBROUTINE

UNIFM PDUNIF

Figure A.l Macro Flow Chart of Main Program

77 Y

CALLSUBROUTINE

UNIFM

DETERMINENEXT

EVENT

END OF DAY YES

°NO

Figure A.1 (continued)

I

78 'I

ALLAIRCRAFT IDLE NO

IN SYSTEM?

YES

SUMMARY OFDELAY

STATISTICS

END DE YES 0vERALLSIMULATION SUMMARY

NO

Figure A.I (continued)

79

SUBROUTINEFLIGHT

READ INFLIGHTDATA _INITIALIZEAIRCRAFTVARIABLES

IS TYES TAGGING

ALGORITHM BEINGUSED?

CALLSUBROUTINE

TAGSCHNO

RETURN

Figure A.2 Macro Flow Chart of Subroutine FLIGHT

l80 l

SUBROUTINEADFLT

DETERMINEAIRCRAFT

T0 BEADDED

DETERMINEDEPARTURE

TERMINAL ANDDESTINATION

SET STATUSVARIABLES

ACCORDINGLY

CALCULATEDEPARTURE

TIME

Figure A.3 Macro Flow Chart of Subroutine ADFLT

1181

‘PROCEEDT0 NEXTAIRCRAFT

RETURN

Figure A.3 (continued)

82

SUBROUTINEUNIFM

DETERMINEFLIGHT

INFORMATION ”

CALCULATE· HOUR OF

DEPARTURE

NIFORMOR UNIFORM SQHEDULE

SIMULTANEOUS? ACCORDINGLY

T SIMULTANEOUST UNIFORM

SCHEDULEACCORDINGLY

Figure A.4 Macro Fiow Chart of Subroutine UNIFM

uY

83

DETERMINENEW TIME OFDEPARTURE

RETURN

Figure A.4 (continued)

84

SUBROUTINEPDUNIF

DETERMINEFLIGHTINFORMATION Y

DURINGPEAK DEMAND NO

INTERVAL?

° YES

UNIFORMOR UNIFORM SCHEDULESIMULTANEOUS? TCCORDINGLY

SIMULTANEOUSh UNIFORMSCHEDULEACCORDINGLY

4Figure A.5 Macro Flow Chart of Subroutine PDUNIF

I

85

DETERMINENEW TIME OFDEPARTURE

RETURN

Figure A.5 (continued)

II

86

SUBROUTINETAGSCH

DETERMINEDEPARTURE

TERMINAL

CALCULATETIME

INTERVAL

E INCREASET PROJECTEDEOPERATIONS

RETURN

Figure A.6 Macro Flow Chart of Subroutine TAGSCH

87

SUBROUTINETERCAP

READTERMINAL

VARIABLES

CALLSUBROUTINE

CHANG

INITIALIZEARRAYS

RETURN

Figure A.7 Macro Flow Chart of Subroutine TERCAP

88 I

SUBROUTINENEXT

CALLSUBROUTINE

ACNEXT

CALLSUBROUTINE

TERNEX

COMPARE TIMES

OPERATE ONNEXTEVENT

RETURN

Figure A.8 Macro Flow Chart of Subroutine NEXT

l•

1

891

SUBROUTINEACNEXT

INITIALIZEVARIABLES

SEARCH FORMINIMUM

AIRCRAFTTIME

SAVEAIRCRAFT

STATUS ANDTIME

RETURN

Figure A.9 Macro Flow Chart of Subroutine ACNEXT

90 Q

SUBROUTINETERNEX

INITIALIZEVARIABLES

SEARCH FORMINIMUM

TERMINALTIME

I SAVEMINIMUM

TERMINALTIME

RETURNC

Figure A.lO Macro Flow Chart of Subroutine TERNEX

I

9lSUBROUTINEAOPER

DETERMINEAIRCRAFT

ON WHICH TOOPERATE

DETERMINETERMINAL

ASSOCIATED ·WITH AIRCRAFT

YES FDEPARTURE?

IF POSSIBLE„ALLOW

AIRCRAFT TO NODEPART T

DEPARTURECLEARING°RUNWAY? ·

AIRCRAFTI BEGINSNO EuraouisFLIGHT

Figure A.ll Macro Flow Chart of Subroutine AOPER

92

YES ARR1vAL2

IF POSSIBLE,9 ALLON

AIRCRAFT TO NOLAND

ARRIVALCLEARING YESRUNNAY?AIRCRAFTTERMINATES

NO FLIGHT LEG

TAGGEDYES AIRCRAFT?ALL

IF POSSIBLE, FLIGHT LEGSALLON E COMPLETED?

AIRCRAFT TODEPART NO YESPnoceso IDEETO NEXT

EVENT NEN NEXTEVENT TIME

RETURN

°Figure A.1T (continued)

R 93

SUBREi<llé6ö‘FE

DETERMINEDEPARTURETERMINAL ANDDESTINATION

CALCULATEENROUTE

TIME

CALLSUBROUTINE MERDEL

CALCULATENEW NEXT

EVENTTIME

RETURN

· Figure A.l2 Macro Flow Chart of Subroutine ENROUT

I

94

SUBROUTINEERDEL

DETERMINEMEAN AND

STANDARDDEVIATION

GENERATEUNIFORM

RANDOMNUMBER

CALCULATEENROUTE

DELAY

RETURN

Figure A.l3 Macro Flow Chart of Subroutine ERDEL

I .

I

95

FUNCTIONVECT

DETERMINEMEAN AND

STANDARDDEVIATIDN

GENERATEUNIFORM· RANDOM

NUMBER

CALCULATEVECTORING

DISTANCE

RETURN

Figure A.l4 Macro Flow Chart of Function VECT

I96

9 SUBROUTINESERDES

SET AIRCRAFTNEXT EVENTTIME TO ALARGE NUMBER

INCREASE THE NUMBERIN THE NAITING STACKAND ASSIGN AIRCRAFT

A POSITION

CHANGESTATUS

OF AIRCRAFT

RETURN

Figure A.I5 Macro Flow Chart of Subroutine SERDES

I

I

97

SUBROUTINEUNSTAC

DETERMINEFIRST

AIRCRAFTIN STACK

MOVE THEREMAINING

AIRCRAFT UP ONEPOSITION

CALLSUBROUTINE

OELAY

Figure A.l6 Macro Flow Chart of Subroutine UNSTAC

98 i

CALLYES SUDRDUTINE

CALCULATE NEXT EVENTTIME AND NEW STATUSOF AIRCRAFT DEINGSERvIcED

RUNNAY YESAVAILABLE?

NO

RETURN

Figure A.16 (continued)

u99

SUBROUTINEDELAY

CALCULATEHOUR DF DAY

IN WHICHDELAY DCCURS

ARRIVAL ARRIVAL DEPARTUREOR

DEPARTURE?

CALCULATE CALCULATEARRIVAL DEPARTURE

STATISTICS STATISTICS

RETURN

Figure A.l7 Macro Flow Chart of Subroutine DELAY

LL

l00

N SUBROUTINEFUTCAP

DETERMINEDEPARTURETERMINAL AND

DESTINATION

CALCULATEENROUTE

TIME

DETERMINEPROJECTEDTIMEINTERVAL

LESS THAN PROJECTEDOPERATIONS:

ACTUALALLOW

AIRCRAFT TT0 DEPART GREATER

RETURN GFigure A.l8 Macro Flow Chart of Subroutine FUTCAP

IO] Q

TAGAIRCRAFT

CALCULATENEW NEXTEVENT TIME

RETURN

Figure A.18 (continued)

u

lO2

SUBROUTINEOPWRIT

DETERMINETYPE

OF AIRCRAFTEVENT

WRITESTATUS

OF AIRCRAFT

RETURN

Figure A.l9 Macro Flow Chart of Subroutine OPWRIT

—————————————————————————"———————‘""""""‘iii'iiiCECCEEETTT"————————————“'"——————————i

103

SUBROUTINENRIDEL

sr HounorTHEDAYIN NHICH

DELAY OCCURS

DETERMINETERMINAL

UNDERCONSIDERATIDN

CALCULATEDEPARTURESTATISTICS

CALCULATEARRIVAL

STATISTICS

Figure A.20 Macro F1ow Chart of Subroutine WRIDEL

104WRITEDELAY· STATISTICS

RETURN

Figure A.20 (continued)

105

SUBROUTINETODEL

INITIALIZE NOVARIABLES QDETERMINET TERMINAL

RETURN

CALCULATEDELAY

STATISTICS

WRITE DELAYSTATISTICS

Figure A.21 Macro F1ow Chart of Subroutine TODEL

106

ALLNO TERMINALS

CONSIDERED?

lYES

CALCULATEENROUTE

DELAYSTATISTICS

NRITE TOTALSYSTEM DELAY

RETURN

Figure A.21 (continued)

107 ;

SUBROUTINETWRIT

NRITESTATUS

OF TERMINAL

RETURN

Figure A.22 Macro Flow Chart of Subroutine TNRIT

106 Z1

SUBROUTINEPUSHUP

DETERMINETHE NUMBEROF AIRCRAFT

TO MOVE UP

ARE NOTHERE AIRCRAFTIN STACK? RETURN

YES

MOVEAIRCRAFT UPONE POSITION

RETURN

Figure A.23 Macro Flow Chart of Subroutine PUSHUP

P

T09

I*• INENEXFLI

DETERMINENEW FLIGHT

DATA

APPLYE SCHEDULE

ISNEW TIME YES

GREATER THAN RETURN3D?

N0

ADJUSTTIME

RETURN

_F1gure A.24 Macro Fiow Chart of Subroutine NEXFLI

110

SUBROUTINETCAPY

DETERMINETERMINAL

BEINGREVIEWED

DETERMINENEW

ACCEPTANCERATE

CALCULATETIME

0F NEXTREVIEW

SERVICEAIRCRAFT

IF NECESSARY

RETURN

Figure A.25 Macro F1ow Chart of Subroutine TCAPY

1aao.---

111 I

CALCULATEHOUR OF

THE DAY

DETERMINENEw

ACCEPTANCERATE

CALCULATERANDOM

ERROR

ASSIGN NENACCEPTANCE

RATE

RETURN

Figure A.26 Macro F1ow Chart of Subroutine CHANG

ll2 E

FUNCTIONRAND

GENERATEUNIFORM

RANDOMNUMBER

RETURN

Figure A.27 Macro Flow Chart of Function RAND

l

APPENDIX B: SAMPLE OF INPUT FLIGHT DATA

113

I

I

H4

(ULOC• (\!(\!C (U(\|LO

NCULO(*7 RO• IZN(\lN°'O\

2 CC1 L1.!G‘$|_;_1 Lu „1- ¤. ..1an ut <E<[ ZLL; LL] y-4 ••

¤.CL1.!L1.I··•—•>-¤fCC1I—·ZI·—I—L.JE C•• DLL};-4|_L|

(/7I·—I·"·Z¤C|·—·Z1.11.1..1;. ::•<E:z<§1—1—-z1—1-10: ';E¤c•-•¤c..1<.>•'.>c¤<CI·-<C¤:¤:¤:•—«¤.(/>c1.1-1-—•1·—•..1L1.!»L1.IL1.J<<Z<EL1.CCC

(")r—LD ¢‘("7LO ZNC• CUCU ·• (\! r- • (\1 (\!C N C C LO C NN N (*7 (ULO 1.0 LO LO

CCUC (UGNLO N<!'LO (*7<1‘LO(\1 N (\1RO (\!N C\I(\|• LO • LO (U RON N ' •

(U (*7 (\! (\1N N N NZ •'RD Z ·•<I" Z •••·· Z ••(\!

1 C1- 1 C(\| CZ CC 1 Cd)L1.! L1JRO Ln! LL-IRO Lu L1.107 L1.! LIJO71... LL; „ 1... Lu .. 1.. LU .. 1. Lu „L/7 Q. ..1 V) O. ...1 (/) CL .1 (/7 Q. ..1<E U') < <C (/7 <E <E L/1 <C < (/7 <ELL! Z I.1.! Z L1J Z L1J Z|__g_|

p-4 •• |_;_„| 9-• •• LL] y-g •• |_;_| 9-• ••••(/°)••§ LL] ••m••Z LL] LL.1.1.11-•¤: Z 1.1.1»-•¤1:¤c E L!J•—41 Z LIJI··-Ox ZQCLI-JLLJ•••-·• O.DL!JLL1•••·-• O.2L1JL1.!•••-• Q.2L1.1L1J•••-—•>-¢Z§I·—ZI—— >—1@I·—Z|—-· >—(Iml—-Z}- >-CZ®|—~Zl·—1-—-L) ° C !·•LJZ C 1-LJZ C 1-(JZ C•· :DLlJV""l-IJ •• :>u.I•—•L1.! •~ ·• Z>L1J•—4LLJ(/)|——EZQ¢|—1 (/7I····I·—ZQ¢I·—-OC ¢/7}-1-21}-1 (/)}—I—·ZCZ}——C£u.11.1. :<:> 1.1.11.1.1;. :<: 1.1.11.1.LL :<1::> 1.1.11.1.1.1. ZD<D•—·• I¤t•-4QC •-4 I1•—*Q£ 1-1 IQf•—•I •-( 1:1:1r-111..1(.JL>L'J<EI——<E ..!(.J<..JL5<II—-<E ..ILJ(.>L'J<Z|·—-<C ...!L.>(.>(D<Z!——<E1QC1•·—•Q.(/)O. ¤f111—«1C!.(/7¤. 11QCr-•¤.(/7¤. tZCZ¤:>—1¤.(/7¤.•-—••—••—•_|L1.|L1„JI..1J Z1!-1U—C—JIJJLL]LIJ UZ!.-·'|U**¢ZJLIJLlJLIJ •-••·—••-—•..1L1.JL1.!L1.!<1:<<1.1.c¤c¤¤ <1:<1:<c1.L.c:¤c1 <<£<cLL.::1¤¤ <<E<1.L1:¤¤c::

APPENDIX C: SAMPLE OUTPUT

115

I

II

116 '

>•r··· C7 G I'- N G LOLLI (*7 G (*7 LO r- C7 r-Q OW LO Q (*7 (*7 LO LO

• Q Q N ¤*I C3 O CD _G N (*7 N r— (*7 LOI-- 1- •— r-(/7

LLJE•-—•I-CD Ü G N G (*7 r- I-(7Z N (Ü N G (*7 I- LOfü • • • • • • •I- N cs LO I- M LO cwI-I r- Ü LO I3 V7 Ür- r- I-3

L1.!i><E

LLJZ•-—•I'-

N LD G C7 1-CD 77 G LD ® r-· C7 C7Z LO N LO N •— C7 €\I>—

-* Ü (*7 Ü 1-<E I'- •—·Q •-1

<ELI-! 3II-

, L1.‘ CDQtECDI /'\ /'\ IN /'\ ZN IN IN• N (*7 0- G LD G7 ÜI- •—— N N N r-Q.I LL!'- NI \-I \-I ~•/ N.! \-/ \-I[O •

E =¤= O N N LO M N no~ LO (*7 G N (*7 (*7 N<Z

I-LII!-·[-1--Qt!Gj_|_ •

EUI • #3:L.)<EV-! _]I-G(/7r— Z•-—• r-• I- N (*7 Q LO LO N’“ E<1- !.1.!(/> I-

I

I

>· d‘ LO N G LO (Y) NL1.. Ch LO LO G N UD GG LO Ü G Ü (Y) IG• O) G O) G O') LO O'}

G 1- O') G 1—_ Q' NI- fi 1- •—(/3

L1.!E•—-1I·-LDZ G G G G N <I‘ IGE G N (Y) G N IG N.1 U') LO LO G LO r- G)G G IG LO NI IG 1-· r-

L1.J><E

LL!Z•—-1I- G <" LO G (Y) <' ¢'LD N 1- LD ¢' N NZ N 1·- N r- IG LOI"" Ü (Y) r-

>- G<E .1G GI

L1.!II-

I u.GZG

/N /N /N f'\I O) <1' G G LO LD LD• IG (Y) IG 1--G

ZI

__|L!$/I-

LO • =N= G G N LC) LO IG IGE (Y) N O') N N N<EL1.!

I1-I-!-Qt!GLL O

_ ZU) • #8:f..J<[•-• .!

I-GI-! I-I 1-· N (Y) Q' LD LO NI- E< 1I- L1.!tf) I-

u

APPENDIX D: TABLES OF RESULTS

} H8

1119

Tab1e 0.1Resu1ts of SAS_Three—Nay Ana1ysis of Variance

for 1750 Aircraft Based on Departure De1ay

Source df SS MS F Va1ue

Schedu1e 2 200273.98 100136.992 480.39*Termina1 6 154830.38 25805.063 123.79*Hour 23 258949.93 11258.69 54.01*(Schedu1e)(Termina1) 12 230899.97 19241.66 92.31*

(Schedu1e)(H0ur) 46 341085.40 7414.90 35.57*

(Termina1)(Hour) 138 1001554.70 7257.643 34.81*

(Schedu1e)(Termina1)(Hour) 276 1763683.65 6390.158 30.65*

within Ce11 1008 210113.35 208.44Corrected Tota1 1511 4161391.36 2754.06

* Significaht at the .995 1eve1.

1

120

Table D.II

Results of SAS_Three—Way Analysis of Variancefor 2250 Aircraft Based on Departure Delay

(Synthesized flights added in the morning)

Source df SS MS F Value

Schedule 2 171361797 85680898.4 385.5*

Terminal 6 205586928 34264487.9 154.1*

Hour 23 349230898 15183952.1 68.3*

(Schedu1e)(Termina1) 12 504251036 42020919.7 189.1*

(Schedu1e)(Hour) 46 477958870 10390410.2 46.7*

(Terminal)(Hour) 138 455249561 3298909.9 14.8*

(Schedule)(Termina1)(Hour) 276 1056337347 3827309.2 17.2*

within Cell 1008 223991724 222214.0

Corrected Total 1511 3443968160 2279264.2

A * Significant at the .995 level.

Tl2l I

Table D.IIIResults of SAS_Three-way Analysis of Variance ·for 2250 Aircraft Based on Departure Delay

(Synthesized flights added in the afternoon)

Source df SS MS F Value

Schedule 2 l30209792 65l04896 922.9*Terminal 6 28064407 467740l.2 66.3*Hour 23 l95523487 850l02l.2 l20.5*(Schedule)(Terminal) l2 6l553806 *5l29483.9 72.7*

(Schedule)(Hour) 46 35l496l56 764l220.8 l08.3*

(Terminal)(Hour) l38 82024324 594379.2 8.4*

(Schedule)(Terminal)(Hour) 276 l74262673 63l386.5 8.9*

within Cell l008 7ll0ll0l 70536.8Corrected Total l5ll l094235747 724l79.8

* Significant at the .995 level.

l22

[ Table D.IV

Results of SAS_Three-way Analysis of Variancefor 2750 Aircraft Based on Departure Delay(Synthesized flights added in the morning)

Source df SS MS F Value

Schedule 2 ll9575896l 597879480 4003.l*

Terminal 6 5264645l3 87744086 587.4*Hour 23 l63l597ll7 70939005 474.9*

(Schedule)(Terminal) l2 l05890798l 88242332 590.8*

(Schedule)(H0ur) 46 2936055l49 63827286 427.3*

(Terminal)(Hour) l38 l42475878l l0324339 69.l*

(Schedule)(Terminal)(Hour) 276 306657l78l llll0767 74.3*

within Cell l008 l50547554 l49353

Corrected Total l5ll ll99066l837 7935580

*Significant at the .995 level.

I

Il23

Table D.VResults of §AS_Three-Way Analysis of Variancefor 2750 Aircraft Based on Departure Delay

(Synthesized flights added in the afternoon)

Source df SS MS F Value

Schedule 2 6l6540498 308270249 3247.5 *Terminal 6 2ll2460l3 35207669 370.9 *Hour 23 l440754l68 6264l486 659.9 *(Schedule)(Terminal) l2 l36l62464 ll364872 ll9.5 *

(Schedule)(Hour) 46 20l2778856 43756062 460.9 *

(Terminal)(Hour) l38 648486497 4699l78 49.50*

(Schedule)(Terminal)(Hour) 276 7l7300086 25989l3 27.3 *

within Cell l008 9568l9l2 94923Corrected Total l5ll 5878950494 3890768

* Significant at the .995 level.

124 E

Table D.VI

Results of SAS_Three-way Analysis of Variancefor 1750 Aircraft Based on Arrival Delay

Source df SS MS F Value

Schedule 2 2994.33 1497.16 51.68*Terminal 6 31511.09 5251.84 181.31*Hour 23 13596.03 591.13 20.40*

(Schedule)(Terminal)4

12 4020.48 335.04 11.56*(Schedu1e)(Hour) 46 6023.66 130.94 4.52*(Termina1)(Hour) 138 48150.57 348.91 12.04*

(Schedu1e)(Termina1)(Hour) 276 36962.80 133.92 1 4.62*Within Cell 1008 29196.95 28.96

Corrected Total 1511 172455.94 114.13

* Significant at the .995 level.

1125, Table D.VII

Results of SA§_Three-way Analysis of Variancefor 2250 Aircraft Based on Arrival Delay

(Synthesized flights added in the morning) i

Source df SS MS F ValueSchedule 2 17788517 8894258.2 1941.1*Terminal 6 23963650 3993941.7 871.6*

1 Hour 23 36225101 1575004.4 343.7*(Schedule)(Terminal) 12 29892006 3324333.8 725.5*

(Schedu1e)(Hour) 46 59590465 1295444.8 282.7*

(Termina1)(Hour) 138 72496647 525338.0 114.6*

(Schedu1e)(Terminal)(Hour) 276 123902630 448922.5 97.9*

within Cell 1008 4618617 4581.96Corrected Total 1511 378477633 ·250481.5* Significant at the .995 level.

1u

V 126

Table D.VIII C

Results of SAS_Three-Way Analysis of Variance 1for 2250 Aircraft Based on Arrival Delay

(Synthesized flights added in the afternoon)

Source df SS MS F Value

Schedule 2 43418.5 21709.2 6.4*Terminal 6 637606.3 106267.7 31.5*Hour 23 1203537.0 52327.6 15.5*(Schedule)(Terminal) 12 171536.9 14294.7 4.2*

(Schedule)(Hour) 46 510659.9 11101.3 3.2*

(Termina1)(Hour) 138 2800186.2 20291.2 6.0*

(Schedu1e)(Termina1)(Hour) 276 1421958.0 5152.0 1.5*

within Cell 1008 3394508.2 3367.5Corrected Total 1511 10183411.0 6739.51

* Significant at the .995 level.

il27 C

Table D.IXResults of SAS_Three-way Analysis of Variance

for 2750 Aircraft Based on Arrival Delay(Synthesized flights added in the morning)

Source df SS MS Value

Schedule 2 l79970l7 8998508.6 ll70.3*Terminal 6 —3605ll59 6008526.5 78l.4*Hour 23 473800l5 2060000.6 267.9*(Schedule)(Terminal) l2 43375577 36l463l.4 470.l*(Schedule)(Hour) 46 67l96852 l46080l.l l89.9*

(Terminal)(Hour) l38 ll5l06977 834l08.5 l08.4*

(Schedule)(Terminal)(Hour) 276 l562304l5 566052.2 73.6*Within Cell l008 7750046 7688.54Corrected Total l5ll 49l088059 325008.6

* Significant at the .995 level.

II

128

Table D.XResults of §A§_Three—Way Analysis of Variancefor 2750 Aircraft Based on Arrival Delay(Synthesized flights added in the afternoon)

Source df SS MS F Value

Schedule 2 14965320 7482659.8 480.3*Terminal 6 127636024 21272670.7 1365.6*Hour 23 218470651 9498723.9 609.7*(Schedu1e)(Termina1) 12 26068280 2172356.7 139.4*(Schedu1e)(Hour) 46 73891381 1606334.4 103.1*(Terminal)(Hour) 138 444203629 3218866.9 206.6*(Schedu1e)(Terminal)(Hour) 276 132627745 480535.3 30.8*Within Cell 1008 15701784 15577.2Corrected Total 1511 1053564812 697263.3

* Significant at the .995 level.

I

I

Appendix E I

TERMINALS INCLUDED IN THE DISTANCE MATRIX

'I29

120n1. New York 27. Minneapolis2. Chicago 28. Montreal

3. Atlanta 29. Nashville4. Los Angeles 30. New Orleans5. washington 31. Norfolk

A

6. Dallas 32. Oklahoma City

7. Denver 33. Omaha8. Baltimore 34. Ottawa

I9. Boston 35. Philadelphia

10. Buffalo 36. Phoenix11. Charlotte 37. Pittsburgh12. Cincinnati 38. Portland13. Cleveland 39. Rochester

14. Columbus, Ohio 40. St. Louis15. Dayton 41. Salt Lake City16. Detroit 42. San Antonio17. Hartford 43. San Diego

18. Houston 44. San Francisco19. Indianapolis 45. Seattle

20. Jacksonville 46. Syracuse

21. Kansas City 47. Tampa

22. Las Vegas 48. Toronto,

23. Louisville 49. Vancouver

24. Memphis 50. winnipeg

25. Miami26. Milwaukee

u

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Ü „THE EFFECT OF SCHEDULING ÄON AIR TRAFFICOELAYby

Randal R. Crockett

(ABSTRACT)

At the present time, millions of dollars are being lost by majorairlines each year because of the inability of high density air terminalsto efficiently service all of the demands placed upon them during peakperiods of demand. Up to the present time, studies involving congestionhave been aimed primarily at the implementation of computerizedtechniques to aid the air traffic controller during peak demand periods.By scheduling aircraft in a given system in a different manner, delay,causedrby congestion, could possibly be reduced at high density terminalseven more than it has been reduced by the results obtained from previousstudies.

The approach taken in this study involves testing differentheuristic scheduling algorithms, based on what has been done previously,to determine what extent total system delay can be reduced. The methodof approach which was followed was based on a simulator which modelsaircraft movement between N major terminals. For each schedulingalgorithm developed, hourly statistics related to the number of aircraftdemanding service, average departure delay, and average arrival delaywere calculated along with total system delay times for arriving anddeparting aircraft. The results obtained from these algorithms were

analyzed and compared with the scheduling algorithm which resulted ina reduction in delay being examined in greater detail to determinewhether or not such a schedule would actually be feasible and worthwhile.