NYC Subway Interdiction

1

NYC Subway Interdiction

LCDR Sean McCrinkLT Dustin CrawfordLT 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

The Network (Min-Cost Flow)

s

4

3

2

1

38

t

1. Grand Central Station2. Times Square / 42nd St.3. 47th / 50th / Rockefeller4. 34th St.

38. 168th St. (GW)39. Howard Beach (JFK)40. Sutphin Blvd. (JFK)41. Jackson Heights (LGA)42. South Ferry

.

.

.

.

.

.

.

.

.

.

.

.

.

.

(0, 0,

1) 39

40

41

42

(cost = # Stops)

(0, 0, 1)

(lb = 1)

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 CentralEscape: 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: RockefellerEscape: 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 CentralEscape: 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 SquareEscape: 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: RockefellerEscape: 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 CentralEscape: 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 CentralEscape: George Washington Bridge# of stops: 15

22

• 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

Interdiction without interdicting arcs leading into exit nodes.

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