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Interdicting Tradeflow on the U.S. Rail Network. LTC Brian Axelsen MAJ Steve Jones. U.S. Rail Network. Vital to moving large amounts of goods between large population centers. a network of more than 140,000 miles 43 percent of intercity freight volume - PowerPoint PPT Presentation
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Interdicting Tradeflow on the U.S. Rail Network
LTC Brian AxelsenMAJ Steve Jones
U.S. Rail Network
• Vital to moving large amounts of goods between large population centers.
• a network of more than 140,000 miles • 43 percent of intercity freight volume• Shippers would pay $69-95 billion more per year
if all freight moved by rail were shifted to truck• On average, railroads are four times more fuel
efficient than trucks.
Source: http://www.aar.org - Association of American Railroads
US Rail Network
Class 1 Rail Network
Model Scenario
• Determine the impact of a “dirty bomb” attack on the tradeflow between the two largest U.S. cities and the rest of the country.
• Multi-commodity (NYC and Los Angeles)– “New York” and “LA” commodities– Two of the most populous cities and busiest ports– Demand from each node is the tradeflow between
that node and NYC and LA– Supply is sum of all demand for each commodity
Gravity Model
Tradeflow between nodes i and j
= Constant to adjust for scale
Economic mass of city (pop.)
GC Distance between nodes i and j
ij
ij
F
G
M
D
2i j
ijij
M MF G
D
• Basic theoretical model for trade• Used to evaluate NAFTA and WTO
Model Scenario
• Nodes: 50 largest Metropolitan Statistical Areas (MSA) and 20 key rail intersections.
• Edges: Represent multiple rail lines between two nodes.– Cost = $1 per tradeflow unit per mile– Very large capacity
US Rail Network
US Rail and Abstract Networks
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4
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89
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1211
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1819
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3136
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4849
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Abstract Network
5
4
3
2
1
67
10
89
17
15
14
13
1211
16
20
1819
27
25
24
23
22
21
26
30
28
29
37
35
34
33
32
3136
40
38
39
47
45
44
43
42
41
46
50
4849
5152
53
54
55
5657
58
5960
6162
64
Measure of EffectivenessTotal economic cost of the supply and demand
model for tradeflow.– Shipping costs along usable edges– Cost of unsatisfied demand– Both NYC and LA commodities
Operator’s/Attacker’s Problem
• Operator wants to satisfy all demand for each commodity at the minimum cost
• Attacker uses dirty bombs to maximize the cost of tradeflow between the two largest population centers and the rest of the country.
• Attacking an edge represents the incapacitation of the rail network between two MSA’s.
• Additional Constraint to Attacker: Edges originating from a supply node cannot be attacked.
Operator Resilience Curve
Detroit Isolated
D.C Isolated
Pittsburg Shipping Restricted
Seattle Isolated
Boston Isolated
1 Attack
No City Isolated; increased cost to meet demand.
2 Attacks
Detroit Isolated
3 Attacks
Washington D.C Isolated
4 Attacks
Washington D.C and Virginia Beach Isolated; there is now “excess” supply in NY.
5 Attacks
No City Isolated; significantly increased cost; ¼ of supply cannot leave NY.
6 Attacks
No City Isolated; significantly increased cost; ¼ of supply cannot leave NY.
7 Attacks
Seattle Isolated; significantly increased cost; 1/4 of supply cannot leave NY.
8 Attacks
Boston Isolated; significantly increased cost; 1/3 of supply cannot leave NY.
Model Extension
• Removed constraint that arcs coming from supply nodes cannot be attacked.– New York isolated first: consistent with Gravity
Model– Solutions are not nested– Costs increase by orders of magnitude upon
isolation of a supply node– Consistent with securing supply nodes
Open Ended Analysis
• Total Economic activity: All nodes have supply to and demand from all other nodes.
• All Port Economic activity: All nodes with a port have supply to and demand from all other nodes.
• Split nodes in two to model attacking a city’s population as well as the network (Multi-objective model for the attacker)
• Adjust capacity based on number of nodes between two cities.
Summary and Conclusions
• Overall Resiliency of Rail Network– High physical capacity, especially east of
Mississippi– No single point of failure– No point of extreme vulnerability: Solutions not
nested.• Greatest increase in cost incurred by isolating
a transportation hub, not a city.
