NYC Subway Interdiction

1. NYC Subway Interdiction LCDR Sean McCrink LT Dustin Crawford LT Lewis Anderson

2. Background • New York City Rapid Transit System • Numbers • Motivation

3. Scenario • New York Metropolitan Museum theft • Positive identification on Perpetrator • Last known location • Allies working with Perpetrator

4. Assumptions / Constraints • Restricted to the subway system • Entry locations • Shortest path • Exit locations • Interdiction strategy

5. Network Development • Current Network • Design Network

6. NYC Network • Operating Stations: 468 • Length of Total Track: 209 mi • Subway Lines: 34 • 2012 Numbers: • 5.4 million rides (M-F) • 3.2 million rides (Sat) • 2.5 million rides (Sun)

7. The Network • Nodes: 42 • Edges: 158 • Start Nodes: 4 • Ending Nodes: 5

8. (cost = # Stops) 38 1 . . . . . . . . . . . . . . (0, 0, 1) 39 (0, 0, 1) 2 40 t s The Network (Min-Cost Flow) 3 41 4 42 (lb = 1) 38. 168th St. (GW) 39. Howard Beach (JFK) 40. Sutphin Blvd. (JFK) 41. Jackson Heights (LGA) 42. South Ferry Grand Central Station Times Square / 42nd St. 47th / 50th / Rockefeller 34th St.

9. Interdiction • No Interdiction • One Interdiction • Two Interdictions • Three Interdictions • Four Interdictions • Five Interdictions • Six Interdictions • Seven Interdictions • Eight Interdictions • Nine Interdictions • Ten Interdictions Start: Grand Central Escape: LaGuardia Airport # of stops: 4

10. Interdiction • No Interdiction • One Interdiction • Two Interdictions • Three Interdictions • Four Interdictions • Five Interdictions • Six Interdictions • Seven Interdictions • Eight Interdictions • Nine Interdictions • Ten Interdictions Start: Rockefeller Escape: LaGuardia Airport # of stops: 5

11. Interdiction • No Interdiction • One Interdiction • Two Interdictions • Three Interdictions • Four Interdictions • Five Interdictions • Six Interdictions • Seven Interdictions • Eight Interdictions • Nine Interdictions • Ten Interdictions Start: Grand Central Escape: LaGuardia Airport # of stops: 6

12. Interdiction • No Interdiction • One Interdiction • Two Interdictions • Three Interdictions • Four Interdictions • Five Interdictions • Six Interdictions • Seven Interdictions • Eight Interdictions • Nine Interdictions • Ten Interdictions Start: 34th St. Escape: South Ferry # of stops: 9

13. Interdiction • No Interdiction • One Interdiction • Two Interdictions • Three Interdictions • Four Interdictions • Five Interdictions • Six Interdictions • Seven Interdictions • Eight Interdictions • Nine Interdictions • Ten Interdictions Start: 34th St. Escape: South Ferry # of stops: 10

14. Interdiction • No Interdiction • One Interdiction • Two Interdictions • Three Interdictions • Four Interdictions • Five Interdictions • Six Interdictions • Seven Interdictions • Eight Interdictions • Nine Interdictions • Ten Interdictions Start: 34th St. Escape: South Ferry # of stops: 11

15. Interdiction • No Interdiction • One Interdiction • Two Interdictions • Three Interdictions • Four Interdictions • Five Interdictions • Six Interdictions • Seven Interdictions • Eight Interdictions • Nine Interdictions • Ten Interdictions Start: Times Square Escape: George Washington Bridge # of stops: 13

16. Interdiction • No Interdiction • One Interdiction • Two Interdictions • Three Interdictions • Four Interdictions • Five Interdictions • Six Interdictions • Seven Interdictions • Eight Interdictions • Nine Interdictions • Ten Interdictions Start: Rockefeller Escape: George Washington Bridge # of stops: 15

17. Interdiction • No Interdiction • One Interdiction • Two Interdictions • Three Interdictions • Four Interdictions • Five Interdictions • Six Interdictions • Seven Interdictions • Eight Interdictions • Nine Interdictions • Ten Interdictions Start: 34th St. Escape: JFK Airport # of stops: 22

18. Interdiction • No Interdiction • One Interdiction • Two Interdictions • Three Interdictions • Four Interdictions • Five Interdictions • Six Interdictions • Seven Interdictions • Eight Interdictions • Nine Interdictions • Ten Interdictions Start: Grand Central Escape: JFK Airport # of stops: 27

19. Interdiction • No Interdiction • One Interdiction • Two Interdictions • Three Interdictions • Four Interdictions • Five Interdictions • Six Interdictions • Seven Interdictions • Eight Interdictions • Nine Interdictions • Ten Interdictions No Escape

20. Validation • Due diligence • No other models to verify • Visual verification

21. Interdiction without interdicting arcs leading into exit nodes. • No Interdiction • One Interdiction • Two Interdictions • Three Interdictions • Four Interdictions • Five Interdictions • Six Interdictions • Seven Interdictions • Eight Interdictions • Nine Interdictions • Ten Interdictions Start: Grand Central Escape: George Washington Bridge # of stops: 15

22. Interdiction without interdicting arcs leading into exit nodes. • No Interdiction • One Interdiction • Two Interdictions • Three Interdictions • Four Interdictions • Five Interdictions • Six Interdictions • Seven Interdictions • Eight Interdictions • Nine Interdictions • Ten Interdictions • Eleven Interdictions No Escape

23. Conclusions • We needed 10 interdictions. • Interdictions made sense • Typically arcs leading to exit nodes • Arcs interdicted differed as interdictions increased

24. Future Research • Other Objectives: • Subway time schedule. • Minimizing transfers instead of stations. • Different probabilities per escape node.

25. References • "Subway and Bus Ridership Statistics 2012". New York Metropolitan Transportation Authority. April 2, 2013. http://mta.info/nyct/facts/ridership/index.htm