Michael Kupfer. San Jose State University Research Foundation NASA Ames, Moffett Field, CA. 8 th USA Europe ATM Seminar June 29 th July 2 nd Napa, CA

Transcription

1 Michael Kupfer San Jose State University Research Foundation NS mes, Moffett Field, C 8 th US Europe TM Seminar June 29 th July 2 nd Napa, C 0

2 SFO Motivation: Dependent Simultaneous runways Offset Instrument single runway pproaches operations SOI FOG FOG OM Non Transgression Zone FOG 28R 28L 28R 1

3 Objective: Development of a scheduling model for very closely spaced parallel approaches Investigation of the merits of various scheduling methods Throughput increase of ~ 5-10% over first-come-first-served scheduling with pairing 2

4 Scope: First-come-first-served: with/without pairing allowed Genetic algorithm: with/without greedy algorithm Mixed integer linear program Model based on Terminal rea Capacity Enhancement Concept 3

5 Methodology: Input: earliest and latest possible arrival time of aircraft Objective: minimize arrival time at coupling point of last aircraft in set (i.e. makespan) Constraints: temporal, pairing, sequencing, separation, route and grouping 4

6 Temporal constraints: SFO Coupling Point Shortest route Max. speed Longest route Min. speed Latest possible ET Delay Nominal ET Time advance Earliest possible ET ET Window ET [s] 28L 5

7 Pairing constraints: SFO 6

8 Sequencing constraint: SFO 7

9 Separation constraint: H H H H H L L H L 8

10 Separation constraint: Very Closely Spaced Parallel Runways Pairing Time Window Collision potential Safe Wake Hazardous Region Unsafe because of wake intrusion 9

11 Precedence constraint: From same route + paired: change of sequence is ok From same route + not paired: change of sequence is not ok 10

12 11 Grouping constraint: /C Type Group # B727 B73 B73C B74 B757 B767 B777 DC10 DC8 DC9 L101 MD11 MD80 /C Type Group # BE20 B C560 B F28 B B707 C C130 C C550 C CRJ C CL60 C F100 C F900 C F10 C F20 C F50 C H25B C LJ35 C C421 D B46 E

13 Independent Variables: Scheduling method: FCFS with pairing [FCFSwP] FCFS without pairing [FCFSwoP] Genetic lgorithm with Greedy [GwG] Genetic lgorithm without Greedy [GwoG] Mixed Integer Linear Program [Optimal] Pairing Time Window: 5-10 sec 5-15 sec 5-20 sec ET window: sec sec sec Collision potential Pairing Time Safe Window Unsafe because of wake intrusion Very Closely Spaced Parallel Runways Wake Hazardous Region 12

14 Dependent Variables: Makespan (throughput) verage delay Computation time Number of pairs in schedule ctual spacing between paired aircraft 13

15 pproach: One randomly generated traffic sample 20 aircraft / 30 min 3 wake categories 3 routes 3 groups One run per scenario: 45 runs Constant ET window for all aircraft in a run Constant pairing time window for all aircraft in a run 14

16 ssumptions: ll aircraft have capabilities to perform very closely spaced parallel approaches: ircraft surveillance and aircraft-aircraft communication using DS-B High precision navigation systems (D-GPS) Enhanced avionics (primary flight display, navigation display) 2 parallel runways Computation of earliest ET and latest ET: trajectory predictor available 15

17 Makespan 37:28 FCFSwoP min 32:13 FCFSwP min Relative Throughput 105% 30:36 min Upper Pairing Bound [s] Max. Delay per aircraft [s] Scheduling method Optimal GwoG GwG 16

18 Relative verage Time Deviation from Earliest Possible ET 03:24 FCFSwoP min Relative verage Delay 02:14 FCFSwP min 01:20 min Upper Pairing Bound [s] Max. Delay per aircraft [s] Scheduling method Optimal GwoG GwG 17

19 verage Computation Time verage Computation Time [s] Upper Pairing Bound [s] Max. Delay per aircraft [s] Scheduling method Optimal GwoG GwG 18

20 Computation Time G without Greedy: 2% improvement Optimal solution G with Greedy: 82% improvement 19

21 Concluding remarks: dvanced scheduling methods improve throughput 5-6% Genetic lgorithm with Greedy shows better makespan and delay than FCFS with pairing Optimal solutions: computation times sensitive to changes of independent variables For simulations consider genetic algorithm with greedy improvement heuristic Future research: More runs Other optimization objectives Other optimization methods Robust schedules 20

22 Thank you for your ttention! 21

23 Decision variables: z ij y ij 1 if i and if i and jarej are paired paired, and i is leading j 0 0 otherwise 1 if i and if i and jare j are paired not paired, and i is leading j 0 0 otherwise 22

24 Constraints: Temporal constraint: ST needs to be within earliest and latest ET Pairing constraint: Two aircraft per pair t i N j N i t, t ] i ( 1,..., N ) [ i, E ET i, L ET z 1 {0,1 } ij z ij i ( 1,..., N) z 1 z {0,1 } j ( 1,..., N ). ij ij Sequencing constraint: Paired or not paired ij z z + y + y = 1 z, z, y, y {0,1 } + ji ij ji i, j (1,..., N ) i j ij ji ij ji 23

25 Constraints: Separation constraint: Standard separation between not paired aircraft. Follower in a pair must be between some lower pairing bound (LPB) and upper pairing bound (UPB) behind its lead. t j ti ( y ji + z ji ) M + yij sepij y, z, y {0,1} i, j (1,..., N ) i j ji ji ij t j ti ( y ji + z ji ) M + ( yij + zij ) LPB z ji, y ji {0,1} t j ti ( yij + z ji ) M + z z ji, y ij {0,1} ij UPB Route constraint: If not paired and in trail on same route: no overtaking t j t ( y + z ) M i i, j (1,..., N ) i j if and if ij ji t i, ET < t j, ET r i = r j 24

26 Constraints: VCSP grouping constraint: paired aircraft must have similar performance (same VCSP group) z = 0 z = 0 ij i, j (1,..., N ) ji if i g i g j j 25

27 J1 J12 J234 Nom. ET E-ET FCFS-IMC FCFS-VMC G_wG CPLEX 26