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CONGESTION PRICING IN AIR TRANSPORTATION

Karine Deschinkel

Laboratoire PRiSM – Université de Versailles

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OUTLINE

Problem

Assignment theory

Congestion pricing

Strategy adopted

Numerical experiment

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03 Problem (1)

• Airspace under control is divided into sectors.

• A sector is a volume of space defined by a floor, a ceiling and vertical borders

• Sectors are assigned to controllers that ensure safety of the flights.

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Growth of air traffic demand (between 5 % and 12 % since 1985)

Problem (2)

Congestion of airports and sectors (8 % of delays > 15 mn).

High controller workload.

How to reduce congestion?

• To modify the structure of airspace (by increasing the number of runways and sectors)but : increase of coordination workload and additionnal costs.

• To perform flow controlBy finding a slot allocation (Ground delay programs)By finding a route-slot allocation (Works of Oussedick and Delahaye)

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03 Problem (3)

Proposed approach

Context• A target route-slot allocation is supposed to be known and calculated so that air traffic congestion is reduced.

• Companies choose, for each flight, an option An option : a combination of a departure time and a route.

Objective is• Find a pricing policy to reach this target allocation assign fees to each option airline companies modify the departure times and the routes of their flights.

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Choices of departures times and routes by airlines =

Distribution of the users in the network

Wardrop’s principles

• System approach (-> system equilibrium)routes and departure time are assigned to each user by a central organism• User approach (-> user equilibrium)users are free to choose their route and their departure time

Traffic assignment models

• Deterministic assignment Transportation costs supposed to be known• Stochastic assignmentUncertainties in the costs stochastic model

Traffic assignment theory (1)

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- Airport charges

currently research

f(origin,destination,service,weight,…) f(…, departure time)=

- Route charges = f(distance, weight, unit rate) f(route, departure time)

Overview of congestion pricing in air transportation (1)

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• Marginal cost pricingTax = marginal social cost – marginal private cost

• Bi-level optimisation

Leader : MinU F(u, v(u)) s. to G(u,v(u)) 0 (u: prices)

Users : MinV f(u,v(u)) s. to g(u,v(u)) 0 (v: flows)

• Queuing model

• Priority pricing

• Peak pricing

• Auctions

Overview of congestion pricing in air transportation (2)

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How to compute prices ?

Model formulation : to develop a model describing the relation between fees charged to aircraft and the choices of routes and takeoff time

Identification problem : to estimate the parameters of the model by using statistics of observed traffic flows

Optimization problem : to minimize the difference, in terms of takeoff time and route, between the target assignment and the assignment resulting from fees

Simulation : to evaluate the impact of pricing on congestion

Strategy (1)

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Model Formulation (1)

Structure of the model

Price model foran option

Airline choicemodel

Prices ofsectors

(PS)

Prices ofoptions

(PO)

Delay and flying costs (C)

Utilities ofoptions

(U)

Expected numberof flights (NE)

List of sectors crossed by a route Scheduled flights (NP)

PO=A PS U=C+PO

PS : price of sector k during time period n (PS(k,n))Option : a route and a takeoff period

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Model Formulation (2)

Model of airline choices

Logit model (probabilistic discrete choice model for stochastic traffic assignment) Utility of an option (o) for a flight planned on period u: U(o,u) = C(o,u) + PO(o)

C(o,u) : cost of the option :flying cost : depends only on odelay cost : depends on the difference between the scheduled

take off period u and the take off period of the option

NE(o) = NP(u) exp(- U(o,u)) Route 1 Route 2

exp(- U(q,v))u

q v

utime

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Criterion

Min J = ( NO(option) - NE(option)) 2

, , Origin- Destination option pair (OD)

Identification Problem

Observed number of flights (NO)

CriterionExpected number

of flights (NE)Model

Delay and flying costs (C)

Parameters structuring C:o=(i,j) : option (route i, take-off period j)u : take-off period plannedd(i) : duration of the flights on route i cms = cost of ground delay (euros/mn)

C(o,u) = cms (d(i) + (i)) + cms (j-u)

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Criterion

Min J = ( ND(option) - NE(option)) 2

0PS PMAX OD option

CriterionExpected numberof flights (NE)

Desired number of flights (ND)

Model

Prices of sectors (PS)

Optimization Problem (1)

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Optimization Problem (2)

First strategy :To set the price of each sector at each period independently of other prices

continuous optimization

• Method : gradient’s method , simulated annealing• Disadvantage : price table not readable

Second strategy :To limit the number of prices (structure by levels : low, high and medium price)To assign a price level to each sector at each time period

discrete optimization

• Method : gradient algorithm to compute new prices + simulated annealing to find an optimal assignment

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Model of simulationsorting random values with the discrete choice model

Sector Capacity CS(k,n)

Prices of sectors (PS)

Workload = W(k,n) W(k,n)=pI I(k,n) + pO O(k,n) + pM M(k,n)

Congestion indicators Q1= number of sectorperiod saturated

Q1= W(k,n)- CS(k,n)) k n

Q2= total excess load

Q2= W(k,n)- CS(k,n))W(k,n)- CS(k,n)) k n

Input volume+ Output volume + Number of aircraft

Simulation

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NETWORK• 52 Origin-Destination pairs between airports : Bordeaux, Lille, Strasbourg, Rennes,Marseille, Paris Orly, Lyon, Toulouse• 35 sectors

DEMAND• Time horizon : 1 traffic day = 6h00 - 22h15 65 periods of 15 minutes• 433 planned flights

TARGET• target constructed manually reduction of congestion

Numerical experiments

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0,00

0,50

1,00

1,50

2,00

2,50

3,00

3,50

4,00

(Sector, period)

Cap

acit

y o

verl

oadBefore pricing

After pricing

Simulation results

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Conclusion and Perspectives

A simple assignment model for air traffic is proposed. It takes into account dynamic sector prices.

A formulation of 2 problems To identify parameters of the model To get to the desired number of flight at each period and for each route

Solution of the optimization problem by gradient and simulated annealing algorithms

Simulation of air traffic with pricing policy : Significant reduction of congestion

Perspectives Improvement of the optimization process (simulated annealing, tabu search) Direct minimization of congestion (no desired number of flights) Modeling of the traffic which does not follow timetables Calibration of the model on real life data

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