1. Workshop PRIXNET – 11/12 Mars 2003 1 CONGESTION PRICING IN AIR TRANSPORTATION Karine Deschinkel Laboratoire PRiSM – Université de Versailles

2. Workshop PRIXNET – 11/12 Mars 2003 2 OUTLINE Problem Assignment theory Congestion pricing Strategy adopted Numerical experiment

3. Workshop PRIXNET – 11/12 Mars 2003 3 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.

4. Workshop PRIXNET – 11/12 Mars 2003 4 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 control  By finding a slot allocation (Ground delay programs)  By finding a route-slot allocation (Works of Oussedick and Delahaye)

5. Workshop PRIXNET – 11/12 Mars 2003 5 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.

6. Workshop PRIXNET – 11/12 Mars 2003 6 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 assignment Uncertainties in the costs  stochastic model Traffic assignment theory (1)

7. Workshop PRIXNET – 11/12 Mars 2003 7 - Airport charges currentlyresearch 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)

8. Workshop PRIXNET – 11/12 Mars 2003 8 Marginal cost pricing Tax = marginal social cost – marginal private cost Bi-level optimisation Leader : Min U F(u, v(u)) s. to G(u,v(u))  0 (u: prices) Users : Min V 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)

9. Workshop PRIXNET – 11/12 Mars 2003 9 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)

10. Workshop PRIXNET – 11/12 Mars 2003 10 Model Formulation (1) Structure of the model Price model for an option Airline choice model Prices of sectors (P S ) Prices of options (P O ) Delay and flying costs (C) Utilities of options (U) Expected number of flights (NE) List of sectors crossed by a route Scheduled flights (NP) P O =A P S U=C+P O P S : price of sector k during time period n (P S (k,n)) Option : a route and a takeoff period

11. Workshop PRIXNET – 11/12 Mars 2003 11 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) + P O (o) C(o,u) : cost of the option : flying cost : depends only on o delay 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 qv u time

12. Workshop PRIXNET – 11/12 Mars 2003 12 Criterion Min J =   ( NO(option) - NE(option)) 2 , ,  Origin- Destination option pair (OD) Identification Problem Observed number of flights (NO) Criterion Expected 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 planned d(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)

13. Workshop PRIXNET – 11/12 Mars 2003 13 Criterion Min J =   ( ND(option) - NE(option)) 2 0  P S  P MAX OD option Criterion Expected number of flights (NE) Desired number of flights (ND) Model Prices of sectors (P S ) Optimization Problem (1)

14. Workshop PRIXNET – 11/12 Mars 2003 14 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

15. Workshop PRIXNET – 11/12 Mars 2003 15 Model of simulation sorting random values with the discrete choice model Sector Capacity C S (k,n) Prices of sectors (P S ) Workload = W(k,n) W(k,n)=p I I(k,n) + p O O(k,n) + p M M(k,n) Congestion indicators Q 1 = number of sector  period saturated Q 1 =   W(k,n)- C S (k,n)) k n Q 2 = total excess load Q 2 =   W(k,n)- C S (k,n))  W(k,n)- C S (k,n)) k n Input volume + Output volume + Number of aircraft Simulation

16. Workshop PRIXNET – 11/12 Mars 2003 16 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

17. Workshop PRIXNET – 11/12 Mars 2003 17 Simulation results

18. Workshop PRIXNET – 11/12 Mars 2003 18 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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