CENTER FOR AIR CENTER FOR AIR TRANSPORTATION SYSTEMS TRANSPORTATION SYSTEMS RESEARCHRESEARCH

A Transparent and Economically Efficient Process for Determining

Planned Airport Capacities

Phil Railsback

Center for Air Transportation Systems Research

George Mason University

CACATSRTSR

Why Determine Planned Capacities?

Delays Are a Function of Planned (Scheduled) Airport Capacity

Economic Cost of Reliability to• Passengers• Airlines

Recognizing Property Rights of Slots to Holders• Slots Can Be A Scarce Resource• Codification of Rights Helps Establish Value• Slots Being Claimed as Financial Assets

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Choosing a Planned Capacity

“Planned” v. “Scheduled”

Planned Capacity Must IncludeScheduled Operations (Airlines)

Unscheduled (“Pop-Up”) Airline Operations

General Aviation Operations (US Part 135 and 91)

Unscheduled Operations Must be Taken Into Account in Policy and Planning

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Definitions

Time PeriodSlots Are Considered Fungible Within a Time Period

Airport StateOpen v. Closed, IMC v VMC, Runways in Use

Planned CapacityPolicy-Established Upper Bound on Operations

Realized CapacityActual Maximum Number of Operations Possible in a

Specific Time Period on Day of Operations

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Definitions (continued)

Slot AvailabilityProbability of a Planned Slot Being Realized on Day

and Time of Operations

Slot FailureEvent Where a Planned Slot is Not Realized

Priority ClassSub-grouping of Slots Within a Time Period to

Support Multiple Slot Priorities

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Randomness and Capacity

Capacity is a Function of Random Processes• Weather• Inter-Arrival Rate Randomness• Departure-Arrival Interference• Fleet Mix Dependence (Wake Vortex)

Therefore Capacity is a Random Process• Capacity is Properly Described as a Probability

Density Function (PDF)

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Airport State Identification

{Closed, IMC, VMC} X {Runway Configurations}e.g.

IMC using 22/13 (Arrival/Departure)VMC using 13/13 etc.

Randomness Leads to a Capacity Distribution by StateCan be Determined by Analysis or Empirical Measurement

Inter-Arrival Randomness, Arrival-Departure Interference, Fleet Mix Variation

Each State Has a Probability of OccurringState Frequencies are Empirically Measurable

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Airport Capacity

Airport States Form a Partitioning

Each State Has a Capacity Distribution

Probability of a Realized Capacity (RC) is(by Law of Total Probability)

)_()_()(_

StateAirportRCpStateAirportpRCpStatesAirport

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Example: LGA

•State-Specific Capacity PDFs•Based on Historical Data by State•Selected only Time Periods When Operating at Capacity•Shows Very Little Weather Dependence

0

0.05

0.1

0.15

0.2

0.25

Arrivals per 15 Minutes

Prob

abili

ty

vmc_4_4 vmc_4_31 vmc_4_13 vmc_31_31

vmc_31_4 vmc_22_31 vmc_22_22 vmc_22_13

vmc_13_13 vmc_13_4 imc_4_4 imc_4_31

imc_4_13 imc_31_31 imc_31_4 imc_22_31

imc_22_22 imc_22_13 imc_13_13 imc_13_4

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Planned Capacity and Slot Availability

There is a Relationship Between Planned Capacity and the Realized Capacity Distribution

The Relationship Results in• Slot Availability (%)• Expected Number of Unplanned Slots

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Derivation of Slot Availability

Partition By Possible Realized Capacities

Each Combination of Realized Capacity (RC) and Planned Capacity (PC):• RC >= PC, p is 1• RC < PC, p is RC / PC

Slot Availability:

)()0

,1min()_( RCpRC PC

RCPCnrealizatioslotp

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Unplanned Slots

Reducing Planned Capacity Increases System Reliability at Cost of Reduced Utilization

U(PC): Expected Number of Unplanned Slots

e.g.: 9 Planned Slots, 12 Realized Slots• 3 Unplanned Slots – Opportunity Cost

The Expected Value is:

0),0max()()(

RCPCRCRCpPCU

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Example: LGA

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 2 4 6 8 10 12 14 16 18 20

Planned Arrivals per 15 Min

Slo

t A

vailab

ilit

y

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Example: LGA

0

2

4

6

8

10

0 2 4 6 8 10 12 14 16 18 20

Planned Arrivals per 15 Minutes

Exp

ecte

d N

um

ber

of

Un

pla

nn

ed

Slo

ts

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Economic Efficiency

What is the Most Efficient Planned Capacity?• Maintain System Reliability v. Maximize Throughput

We Need Slot Valuation as a Function of Slot Availability

Then Maximize Summed Slot Valuation:• e.g.: 5 Slots at 98% valued at 900 € each• 10 Slots at 85% valued at 400 € each• 4500 € > 4000 € → Plan 5 Slots

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Auctions Can Provide Valuation

Auctions Provide Value Discovery Across Multiple Operators

We Can Integrate Desired Availability into a Slot Auction• Auction Availability/Priority Classes, or• Have Bidders Specify Desired Availability in Their

Packages– Might be Prone to Auction Gaming

Necessary Condition for Operators’ Product Differentiation by On-Time Performance

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LGA Example: Priority 2 Slots

Compare:

5 Priority 1 Slots, 98% Availability and

(from previous plot)

5 Priority 2 Slots, 71% Availability; or

(from this plot)

10 Priority 1 Slots, 84%(from previous plot)

0

0.2

0.4

0.6

0.8

1

1 3 5 7 9 11 13 15 17 19

Priority 2 Planned Arrivals per 15 Minutes

Prio

rity

2 Sl

ot A

vaila

bilit

y

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Conclusions

Provides Simple, Transparent Relationship Between Availability and Planned Capacities

Shows How Market Mechanisms (Auctions) Can Provide Answer to Trading Off Throughput and Reliability

Data Are Critical to Results

Insights Into Airport Behavior

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Questions

Phil Railsback

George Mason University

prailsba@gmu.edu