CONGESTION PRICING IN AIR TRANSPORTATION

1. CONGESTION PRICING IN AIR TRANSPORTATION Karine Deschinkel Laboratoire PRiSM – Université de Versailles

2. OUTLINE Problem Assignment theory Congestion pricing Strategy adopted Numerical experiment

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. Problem (2) Congestion of airports and sectors (8 % of delays > 15 mn). High controller workload. Growth of air traffic demand (between 5 % and 12 % since 1985) 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. 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. Traffic assignment theory (1) 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

7. currently research = f(origin,destination,service,weight,…) f(…, departure time) - Route charges f(route, departure time) f(distance, weight, unit rate) = Overview of congestion pricing in air transportation (1) - Airport charges

8. Overview of congestion pricing in air transportation (2) • Marginal cost pricing • Tax = 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

9. Strategy (1) 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

10. Delay and flying costs (C) Prices of options (PO) Utilities of options (U) Prices of sectors (PS) Expected number of flights (NE) Price model for an option Airline choice model List of sectors crossed by a route Scheduled flights (NP) Model Formulation (1) Structure of the model 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

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) + PO(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) = S NP(u) exp(-a U(o,u)) Route 1Route 2 SS exp(-a U(q,v)) u q v u time

12. Observed number of flights (NO) Delay and flying costs (C) Expected number of flights (NE) Model Criterion Identification Problem 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) Criterion Min J = SS ( NO(option) - NE(option)) 2 , ,  Origin- Destination option pair (OD)

13. Optimization Problem (1) Prices of sectors (PS) Desired number of flights (ND) Expected number of flights (NE) Criterion Model Criterion Min J = SS ( ND(option) - NE(option)) 2 0PS PMAX OD option

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. Simulation Workload = W(k,n) W(k,n)=pI I(k,n) + pO O(k,n) + pM M(k,n) + Output volume + Number of aircraft Input volume Sector Capacity CS(k,n) Model of simulation sorting random values with the discrete choice model Congestion indicators Prices of sectors (PS) Q1= number of sectorperiod saturated Q1= SS H(W(k,n)- CS(k,n)) k n Q2= total excess load Q2= SS (W(k,n)- CS(k,n)) H(W(k,n)- CS(k,n)) k n

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 Numerical experiments TARGET • target constructed manually • reduction of congestion

17. Simulation results

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