California High-Speed Rail Initiative

Lieutenant Commander J Ryan “Slappy” McLaughlin, USNMajor Greg Whelan, USA

OA 4204 Red Team ProjectNetwork Flows and Graphs

2

CA High-Speed Rail Initiative

“California’s high-speed rail project will create hundreds of thousands of jobs, linking California’s population centers and avoiding huge problems of massive airport and highway expansion” - CA Governor Brown, November 1, 2011

“It’s a huge infrastructure but it’s absolutely necessary for our future” - SF Mayor Lee, May 23, 2012

“It’s an overall approach to building tomorrow’s transportation system” - Dorothy Rothrock, VP CA Technology Association

3

Outline

• Background– CA High-Speed Rail overview– Benefits / Concerns

• Problem Statement • Network Design

– Graph Design– Assumptions / Limitations

• Analysis– Shortest Path– Multi-Commodity– Modified Multi-Commodity

• Concluding Remarks

4

Project Highlights

• Rail Line Linking S-N• 800 Miles of Track• 24 Stations• $68.4 Billion

• Electrically Powered• Fastest Train in U.S.• L.A. to San Francisco in

Two Hours and 40 Minutes

5

Projected Route

• Initial investment is for the line in dark green primarily through the central valley region

• Future routes continue into San Francisco, San Diego and Sacramento

6

Proponents

• Environmentally Sound• Ease/Cost of travel• Infrastructure Improvements• More Travel Options• Improved Trade• Jobs• Decrease Congestion

7

Population Distribution

• $1.9 Trillion Economy

• 38 Million People• 170,000 Miles of

Roads• 6 of the Most

Congested Urban Areas in U.S.

8

Opposition

• Road Infrastructure• Right of Way• Lack of Coherent Plan• Inaccurate Ridership Estimates• Cost

9

Funding Concerns

10

Problem Statement

• Do Californians need the California High Speed Rail initiative?

• Consider real world interdiction of phases of the project through budget cuts.– Quantify the effect on travelers– Effectiveness of the current transportation network– Effects of adding High-Speed rail network

11

Network Design

• California Transportation Network

12

Network Design

• (City, Transportation) pairs– (Monterey, Bus) – (Monterey, Train)

• Start and End nodes ~ (City)• 28 Cities modeled

SanDiego

SanDiegoBS

SanDiegoAR

SanDiegoHS

SanDiegoTR

13

Network Design

• Connect nodes if transportation exists or is planned (as the case for High-Speed Rail)

• Cost ~ Time Required

LosAngelesBS

SanDiegoAR

SanDiegoBSSanDiego

LosAngelesAR

LosAngeles

SacramentoBS

SacramentoAR

Sacramento

High Speed Rail Amtrak Bus Airplane

San Luis Obispo

Ventura

Sylmar

Burbank

Los Angeles

Fullerton

AnaheimUniversity City

San Diego

Palmdale

Ontario

Riverside

Murrieta

Escondido

Industry

Oakland

San Francisco

Palo Alto

San Jose

Gilroy

Salinas

Sacramento

Stockton

Modesto

Merced

Fresno

Hanford

Bakersfield

AirAmtrakHigh Speed RailBus

15

Assumptions / Limitations

• Direction of Travel• Standardized Transfer/Connection Times• No Capacity Limits• No Private Transportation• Oversimplified Network

16

Analysis

• Shortest Path• Multi-Commodity Flow with Interdiction• Multi-Commodity Flow (adding arcs)

17

Shortest Path

Cost (Time)

Flow(On Arc)

Delay (Time)

Interdiction (Arc)

• Measure of Effectiveness ~ Time• Cost ~ Time• Interdict ~ Remove Travel Leg

18

• Shortest Time from San Diego ~ San Francisco

• Interdictions

Shortest Path

19

Shortest Path

• High-Speed Rail Not a Huge FactorLA-SAC Comparison

SD-SF Comparison

20

Shortest Path

• More Remote the City– Bigger Factor

BF-SJ Comparison

21

Multi-Commodity Flow

• Primary Measure of Effectiveness– Time Factor

• Capacities• “Commodities”• 627,464 total

22

Multi-Commodity Flow

• Gravity Model of Trade– Employed in 1954 by Walter Isard– Predictions of economic trade flows

• G – constant• Pi – population factor• Dij – distance factor

23

Multi-Commodity Flow

• Current Network vs. Network with HSR HSR Addition Comparison

24

Multi-Commodity Flow

• Only Interdict HSR

HSR Interdiction Comparison

25

MCF with no Interdiction(Adding HS Rail Arcs)

*primal ij ijkZ C Y

. . *ijk ij iks t Y X S 1 if HS Rail arc ij is used,

0 if notTotal Supply Available of

Commodity k

High Speed Rail

High Speed Rail Amtrak Bus Airplane

1 165.42 157.23 144.44 135.15 124.56 114.57 106.18 98.09 92.710 89.611 87.112 85.313 83.514 82.515 81.916 81.217 80.718 80.319 79.920 79.721 79.622 79.523 79.524 79.425 79.426 79.427 79.4# Arcs Minutes

0 182.7 San Luis Obispo

Ventura

Sylmar

Burbank

Los Angeles

Fullerton

AnaheimUniversity City

San Diego

Palmdale

Ontario

Riverside

Murrieta

Escondido

Industry

Oakland

San Francisco

Palo Alto

San Jose

Gilroy

Salinas

Sacramento

Stockton

Modesto

Merced

Fresno

Hanford

Bakersfield

0 2 4 6 8 10 12 14 16 18 20 22 24 260

20406080

100120140160180200

Average Travel Time

# High Speed Rail Arcs

Min

utes

27

Conclusion

• High-Speed Rail will decrease the average time to travel

• Makes current transportation network more resilient

• CA should start construction in the LA area

28

Future Considerations

• Expand graph (more realism)– Integrate $ cost per segment– Integrate option for POV transportation– Additional arcs/nodes– # of trains/bus/airplane per day– Capacity constraints

• Consider addition/deletion of stops– Changing routing of track

29

Questions