CHARLES N. GLOVERMICHAEL O. BALLDAVID J. LOVELL

Collaborative Approaches to the Application of Enroute Traffic Flow Management Optimization Models

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Weather in the NAS

Weather is unpredictable How long will it last? Where is it headed? How dangerous is it?

These are research questions for meteorologists.

These questions also affect the NAS.

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The Impact on Flights

Suppose many flights are scheduled to travel through a region of airspace.

A weather disturbancein this region can greatly reduce capacity.

This leads to a problem of congestion in the NAS.

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The Implementation of AFPs

Airspace Flow Programs (AFP’s) are generally implemented over volumes of airspace where a capacity reduction is predicted over an extended period of time.

Flights are given the choice of flying around the flow constrained area (FCA) (with or without ground delay), or flying through the FCA with a given amount of ground delay.

Primary Route Bad Weather in Airspace

Secondary Route

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Weather Uncertainty

Given the uncertainty of weather, it is entirely possible that the FCA clears earlier than anticipated.

In such a case, flights still grounded have the possibility of reducing their

delays by departing sooner. flights that have rerouted around the FCA can possibly have

their route length shortened by now flying through the FCA.

Primary Route Bad Weather in Airspace

Secondary Route

Hybrid

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Approaches to this Problem

The problem of how best to allocate flights to FCA arrival slots in under a reduced capacity situation was studied by Ganji and later by Glover.

Two different IPs were proposed which seek to minimize the total expected delay of all flights scheduled to fly through the FCA.

Both IPs assume a probability distribution of possible weather scenarios and give outputs which include courses of action based on the weather outcomes.

Unfortunately, neither of these models take CDM into account.

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Collaborative Decision Making

Collaborative Decision Making (CDM) originates from an understanding that neither side (the FAA/EUROCONTROL, nor the airlines) has all the information necessary to solve air traffic flow problems.

Most, if not any new major ATFM system proposed either in the US or Europe must adhere to Collaborative Air Traffic management principles.

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GG Model and CDM

In seeking to minimize the total expected delay, the GG model assumes that the air navigation service provider (ANSP) can exercise universal control, which is a rare occurrence.

So although the model they propose is powerful from a mathematical point of view, they are unlikely to be accepted as currently proposed.

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Accounting for CDM

Here, we analyze two alternative approaches for incorporating these models into a CDM-like setting.

In both cases, the ANSP allocates certain resources to the flight operators, and the flight operators then optimize the use of the resources they are given.

This gives the flight operators the final decision on which flights are rerouted and to adjust the ground delay amounts.

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Overview of IP

Here we will describe the GG model. This is a two-stage stochastic IP. Stage one represents the initial assignment

of delay and reroutes under the assumption that the weather lasts the entire duration. One constraint set says that

each flight must be given an initial assignment The other says that

the FCA capacity must be respected.

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Overview of IP

Here we will describe the GG model. This is a two-stage stochastic IP. Stage two represents a set of weather

clearance times (called scenarios) addressing the possibility that the weather clears early. In each scenario,

each flight must be reassigned In each scenario,

the FCA capacity must be respected. In each scenario,

we cannot violate the laws of geometry or physics.

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Modification to the GG Model

The adjustments we made to the GG model were based on bringing in line with CDM principles. Each flight now has a flight operator. Instead of assigning FCA arrival times to flights, these

assignments are made to flight operators, who then have the ability to distribute the delay as needed.

The basic fairness mechanism is still Ration-by-Schedule, which is accepted.

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The First Mechanism

The ANSP executes RBS and allocates to each flight operator a bundle of FCA arrival times.

Each flight operator then makes decisions regarding which flights will stay on their primary routes and experience ground delay and which will be rerouted around the FCA.

This is functionally equivalent to the CDM cancellation and substitution process.

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The Second Mechanism

The ANSP executes RBS and allocates to each flight operator a bundle of FCA arrival times.

Each flight operator then makes decisions regarding which flights will stay on their primary routes and experience ground delay and which will be rerouted around the FCA.

The ANSP then executes an inter-airline exchange.

This is functionally equivalent to the CDM compression algorithm.

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Flight Operators Using the GG Model

The flight operator decision step can take advantage of the GG model.

However, because the flight operator only knows about their flights, this gives a limited viewpoint of the utilization of the NAS.

This implies that the flight operators are using an approximate objective function, where they are estimating future ANSP behavior.

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Experiment

We tested the two mechanisms versus the system optimal (provided by the GG model).

The input to the model consisted of 400 flights and an FCA whose duration was expected to last 5 hours.

We also assumed seven airlines and four aircraft types:

ERJ-170

737-300

757-200

767-400

Carrier 1

64 64 16 16

Carrier 2

30 12 6 12

Carrier 3

0 70 0 0

Carrier 4

20 8 0 12

Carrier 5

0 10 10 0

Carrier 6

20 0 0 0

Carrier 7

12 9 9 0

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Airline Costs

Flight operator decisions are based on minimizing expected airline cost of delay.

The aircraft operation cost per minute of airborne delay is $64 and $32 for ground delay.

We used a cost per minute of delay per passenger of $3.00, of which airlines consume 1/6th of this cost.

Thus in our model for the cost of ground delay for an airline is 32 + 0.5Psn(f)

The cost for airborne delay for an airline is 64 + 0.5Psn(f)

Psn(f) is the number of passengers on flight f.

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Thank You!

Questions?

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ANSP Costs

To determine the efficiency of the solutions produced, we executed the GG model on this input, ignoring the carriers.

This gives a system optimal. We assumed that the ANSP’s objective is to

reduce the overall expected cost of delay, using the same figures from the previous slide.

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Modeling Compression

Compression can also be modeled by an objective function (after the airlines have individually run the algorithm themselves) via a superlinear cost function:

Let md = Maxf {time (goal(f)) – earliest(f)}. Then the cost of assigning flight f to the FCA

arrival time i is cst(f, i) = (time(i) – (time(goal(f)) + md))1+e

Where goal(f) is the time that the f’s carrier wishes to assign to flight f and earliest f is the earliest time that f can arrive at the FCA.

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Total Expected Costs of Delay

1 2 3 4 5 6 7 8960000

980000

1000000

1020000

1040000

1060000

1080000

1100000

1120000

1140000

Mechanism Performance Comparison

SysOptMech1Mech2

Executions

Tota

l E

xpecte

d C

ost

of

Dela

y

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Results & Conclusions

As expected, neither MECH1 nor MECH2 received the optimal cost, but both provided within 10% of the system optimal.

MECH2 does achieve a small, but noticeable advantage over MECH1.

Although MECH1 provides airlines with more power in controlling their flights, it also requires more information, particularly when these flights will be at the FCA boundary which can be difficult to compute.

MECH2 only requires a priority listing of the flights. Both mechanisms reduce the role of the ANSP to one of

allocating a set of FCA arrival times to airlines and allowing the flight operators to optimize the resources they are given.