PRESENTATION OVERVIEW

Transcription

1 ATFM PRE-TACTICAL PLANNING Nabil Belouardy PhD student Presentation for Innovative Research Workshop Thursday, December 8th, 2005 Supervised by Prof. Dr. Patrick Bellot ENST Prof. Dr. Vu Duong EEC European Organisation for the Safety of Air Navigation 1

2 PRESENTATION OVERVIEW I. Introduction to ATFM II. Current implementation III. Perturbations and interactions IV. Control loop design V. Example of correction VI. Mathematical resolution VII. Decision VIII. Conclusion 2

3 INTRODUCTION TO ATFM ATM (AIR TRAFFIC MANAGEMENT) ASM (Airspace Management) Definition of resources Sectors and routes design Airspace allocation between military and civilians ATC (Air traffic Control) Available resource constraints Ground controllers (airport towers) Airspace controllers (en-route and approach area) ATFM (Air Traffic Flow Management) Balance demand / resources Ground delay programs Rerouting 3

4 CURRENT IMPLENTATION Controllers Filed Air Traffic Regulation Capacities + Current Air Traffic Operational events 4 Main features Regulation is performed using Flight plans profiles already submitted Activated constraints (declared capacities and traffic volume restrictions) Operational events disrupt the natural outflow of air traffic Controllers adapt opening scheme and regulations with regards to the observed air traffic

5 PERTURBATIONS AND INTERACTIONS Filed Air Traffic Regulation + Ad hoc events Current Air Traffic 5 Main phenomena Airline Operations Ad hoc events disrupts air traffic planning Aircraft mechanical failures Bad weather conditions Airline Operation Centers modify planned allocation in function of the current air traffic state, so as to Recover the nominal schedule of services Minimize the costs of irregularities

6 CONTROL LOOP DESIGN (1) Filed Air Traffic Controllers Capacities Regulation + Ad-hoc events Current Air Traffic Correction Airline Operations Pre-filter Ideas Prediction of tactical measures of airline operation centers Incorporation of air demand change into regulation process Compensation of the demand-dependant part of uncertainty 6

7 CONTROL LOOP DESIGN (2) Flight A Flight B On flight Taxiing On ground Taxiing On flight Taxiing Landing In block Off block Take off Time axis Correction (case of delay propagation through aircraft daily schedule of services) After accomplishing flight A from airport X to airport Y, the aircraft plans to fulfill flight B from airport Y to airport Z The block time may contain a margin (absorber) to alleviate late arrival effects If flight A starts at airport X with a noticeable delay T, given enough knowledge about planned operations in airport Y, we can estimate the amount of delay T flight B would have at airport Y. 7

8 EXAMPLE OF CORRECTION (1) Matching The correct set of pairs is: (3-6), (0-4), (7-5), (12-10), (8-14), (9-11), (13-15), (16-17) and (18-19). Choosing (8-11) (9-14) instead of (8-14) (9-11) gives an infeasible solution (minimum separation between arrival and departure). 8

9 EXAMPLE OF CORRECTION (2) 9 Qualitative Analysis As the flights 12, 8, 9, 13, 3 and 7 are cancelled at Paris LFPG, necessarily the flights 10, 14, 11, 15, 6 and 5 would be cancelled at Frankfurt EDDF. Great margins of (0-4) and (18-19) obviated delay propagation. Margin absence in (16, 17) allowed delay to propagate.

10 EXAMPLE OF CORRECTION (3) AFR251E AFR519T Current Traffic Filed Traffic 10 Quantitative Analysis 17:00 18:00 19:00 20:00 51 min 2h15min 46 min Time axis Flight A from Paris to Frankfurt has taken-off with 51 min of delay With no margin at Frankfurt, it can make up for about 5 min Flight B has had 46 min of delay at take-off in Frankfurt Good information about flight B is available enough time before its scheduled departure

11 MATHEMATICAL RESOLUTION (1) Maximum Coupling in Graph Vertices (nodes) are constituted of scheduled arrivals and departures. Edges (links) match arrival i to departure j if there is a minimum separation time between its scheduled landing and take-off times. Maximum coupling problem aims to find a set of edges of maximum cardinal, such that any two edges don t have a common vertex. Linear programming approach For all (i,j) Є E: X(i,j) = 0 or 1» binary variable (edge selected or nor) For all k Є V: Σ X(i,j) 1 (i,j) Є E s.t. i=k or j=k» no multiple affectation Criterion: argmax Σ w(i,j) X(i,j) s.t. w(i,j) = 1 if Take-Off (j) Landing (i) > min, (i,j) Є E 0 otherwise.» maximum coupling of feasible solutions (minimum separation) 11

12 MATHEMATICAL RESOLUTION (2) Why Maximum Coupling? Commercial airlines aim to keep aircraft airborne insofar as possible, for reason of profit. A plausible coupling shall not leave many aircraft in the airport with no useful activity. Military operations are totally different and don t apply such policy, some other general flights (e.g. humanitarian aids) may provide other specific cases. Uniqueness issue Linear programming formulation of a physical problem has always optimal solutions, but uniqueness is not guaranteed. In our context, two closer departures shall be considered as a single subgroup. If the flights are planned for instance towards London and Liverpool, in cancellation or delay situations it s the flight of minimum cost (here Liverpool) which be scarified.» From abroad airports, routes to London and Liverpool are the same. counting traffic volumes remains correct. If the flights are planned to serve destinations in opposite directions (London and Zurich with departure from Frankfurt), counting traffic volumes becomes uncertain.» Fuzzy or stochastic 12

13 DECISION (1) Deterministic Regulation Model (overall cost minimization) For all aircraft i Є A, T(i) 0 indicates the corresponding ATFM delay required. For each sector k Є S of capacity C(k), for each aircraft i and j planning to enter the area k at estimated time over ETO (k, i) and ETO (k, j), we shall have: [ ETO(k, i) + T(i) ] [ ETO(k, j) + T(j) ] 60 / C(k)» Only one aircraft is accepted to enter at a span time of 60 / capacity Criterion: argmin Σ T(i) for all k Є S: for all (i,j) Є A: T(i) T(j) 60/C(k) + ETO(k, j) ETO(k, i) Linear program of the general form argmin <w, T> A T b Towards Stochastic Regulation (choice of the weight vector w) Airborne aircraft and foreseen subsequent flight demand give an estimated traffic volume in airspace area of a bell form (e.g. Gaussian and Poisson shapes) The weight w(i) can be chosen in function of congestion probabilities in airspace sectors related to the flight of aircraft i 13

14 DECISION (2) Stochastic Regulation Model (overall cost minimization) Criterion: argmin J = <w, T>, w is a stochastic weight A T b Assumptions Expectation: E (w) = µ Covariance: E (w-µ) (w-µ)* = K Consequence E (J) = µ T Cov (J) = T* K T Risk-sensitive criterion: argmin µ T + λ T* K T, λ 0 a parameter A T b Quadratic program, with positive definite matrix K (covariance). 14

15 CONCLUSION New design for ATFM Provides more immunity to operational events Requires deep study (knowledge) of airline control strategies Doesn t pose a problem of solvability Constitute an alternative way to Collaborative Decision Making» No supplementary information is required from airlines Is still under investigation. 15

16 THE END Thank you for your attention! Any remark, question or advise? 16