Cost-minimized design for Hyperloop networkwith heuristically optimized

location and numberof the stations

1Hansol Yoo, 1Ikki Kim , 2B. Brian Park, 3Jong-hak Kim1 Hanyang University at Ansan, South Korea

2 University of Virginia at Charlottesville, VA., U.S.A.

3 Korea Research Institute for Human Settlements (KHRIS), South Korea

5th Annual Summer Conference on Livable Communities (ACLC)

Hosted by the Transportation Research Center for Livable Communities (TRCLC)

June 21 - 22, 2018 at Western Michigan University, Kalamazoo, Michigan

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1 Research motivationNew technology / Needs of Infrastructure

2Characteristics of Hyperloop and other transportation modes

Speed / Vehicle capacity / Line capacity / Acceleration and deceleration

3 Type of transit network systemOne-to-one / Many-to-many system

4 The process of heuristic optimized network designMinimum spanning tree problem / Heuristic network design process

7 Mode choice analysis and share of HyperloopMultinomial Logit model / Mode shift analysis

5 Minimum spanning tree analysis with various number of citiesFinding a set of major corridors with given travel demand

6 Heuristic refinement and simplification of the networkCombining the MSP results of all corridors / Refinement and Simplification

Hanyang University2

Hanyang University

Research motivation

• Hyperloop technology has become more and more actualized and

applicable into real world since Elon Musk suggested in 2012.

• Many scientists have concentrated their researches mostly on

vehicle technologies and mechanical structure of the vacuum

tube itself based on the assumption of completion of a network.

• However, a network plan for effective and convenient usage

should be preceded. The network plan will be followed by the

infrastructure plan and its construction including land acquisition

which is expected to take about 10 to 20 years.

• That is why the research on the Hyperloop network design is

needed in advance before the Hyperloop technology completion.

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ModeSpeed

Km/h (Mile/h)

VehicleCapacitypersons

Headwaysecond

LineCapacity

Accel/decel distanceKm (Mile)

Walk 12.7 - 4.1

(1.7 - 2.6)1 2.6 900 - 1,380prs/h/ft 2 -

Bicycle 1 20.6 (12.8) 1 2.3 1,600prs/h/lane -

Car 1110 - 120 3

(68 - 75)1 - 5 1.5 3 2,400 - 12,000prs/h/lane 3

0.14 - 0.19(0.09 - 0.12)4

Bus 5 90 (56) 80 - 125 75 - 96 3,000 - 6,000prs/h 0.22 (0.14)

Rail 580 - 130(50 - 81)

800 - 1,750 120 - 360 8,000 - 45,000prs/h 0.51 (0.32)

High speed rail (HSR)

300 - 320(186 - 199)

508 - 935 6 150 - 180 7 10,160 - 22,440prs/hAccel: 15.2 (9.4)

Decel: 6.4 (4) 6

Airplane 8829 - 903

(515 - 561)132 - 544 61 - 72 9 7,790 - 27,200prs/h

3 (1.9)(take off distance)

Hyperloop 1,220 (758) 28 10 30 - 120 11 840 - 3,360prs/h 12 (7.5)

1 HCM20102 LOS E, pedestrians per minute per foot of walkway width,3 Freeway, LOS E4 hypertextbook.com/facts/2001/MeredithBarricella.shtml5 Vuchic, V. R. (2007)6 Suh, Sunduck D. et al. (2005), en.wikipedia.org/wiki/TGV

7 Emery, D. (2011)8 Airbus318, Airbus380, en.wikipedia.org9 Hourly capacity of runway, Horonjeff, R., et al. (2010)10 Musk, E. (2013). 11 Taylor, C. L ., et al. (2016)

Characteristics of Hyperloop and others

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• Super-high speed as a ground transport mode

▷ Broader regions can be served with high accessibility to a CBD.

▷ Safety issues need to be seriously considered (The line radius should be

sufficiently large).

• Fully automated operation

▷ smaller-capacity vehicles can be adoptable safely even in high speed.

▷ Very frequent dispatch (short headway) can be possible.

• Relatively small capacity of a vehicle

▷ It can serve OD pairs having relatively small travel demand where the

service was not available by a mass transit mode such as train or airplane.

• Exclusive right-of-way from other type of vehicles

▷ There in no vehicle congestion by interruption of other type of vehicles

Characteristics of Hyperloop service

and network design

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• Requirement of relatively shorter distance to reach the maximum speed

▷ It can keep higher operating speed because it reach quickly to the maximum

speed after departure.

▷ Safe operation is possible in case of an unexpected accident due to

relatively short stopping distance.

• Relatively small passenger’s space of the vehicle inside for stretching and

walking

▷ It is very difficult to travel between OD pairs that are very distant from each

other without any intermediate rest places.

▷ The maximum travel time, that a traveler tolerates, might be two to three

hours (about 2,400 – 3,600 Km (1,500 – 2,250 miles) by Hyperloop)

Characteristics of Hyperloop service

and network design

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Hyperloop station concept and network design

These graphics came from : https://www.archdaily.com/799341/rb-systems-proposes-cutting-edge-hyperloop-station

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Travel time by a Hyperloop in the United States

Los Angels – Chicago (1 hr. 44 min.)2,085 Km (1743 miles), 104 minutes

New York – Los Angels ( 3 hr. 15 min.)3,940 Km (2,448 miles), 195 minutes

Los Angels – San FranciscoElon Musk estimated 35 minutes560 Km (348 miles), 29 minutes

New York – Chicago1,147 Km (713 miles), 58 minutes

※ The travel times were ideally calculated with the maximum speed of 2,200 Kim/h (763 miles/h)

while considering the acceleration and deceleration at both ends of OD.

Musk, E., "Hyperloop alpha.“, SpaceX. August 13, 2013

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Basic concept of transit network design :

One-to-one system

A

B

C

D

E

H

I

J

K

L

Origin city Destination city

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Basic concept of transit network design :

Many-to-many (hub-and-spoke) system

A

B

C

D

E

H

I

J

K

L

NM

Collecting process Line-haul process Distributing process

SMALL

CITIES

SMALL

CITIES

Departure Hub Arrival Hub

LARGE CITY LARGE CITY

Modes : Walk, bicycle, car, bus Modes : regional bus, rail, HSR, airplane Modes : Walk, bicycle, car, bus

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Accessibility and speed :

Number of stops/stations within a line

M B C EN

Express line

Normal line

LARGE CITY

SMALL CITY SMALL CITY SMALL CITY

LARGE CITY

Express line : Less accessibility, higher speed, less travel time

Normal line : higher accessibility, Lower speed, more travel time

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Proposed one-to-one network

by separating access branch from by-pass tube

By-pass

By-pass

CityStation

CityStation

Access branch

Access branch

Fully automated operation makes it possible to have a small capacity vehicle. As a

result, direct service of a Hyperloop without intermediate stops and transfer is

possible for each OD pair having relatively small demand if the station of each city

has a egress and ingress access branch separately from the main by-pass tube.

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Proposed Hyperloop network system :

Satisfaction in both of accessibility and speed

M B C EN

LARGE CITY SMALL CITY SMALL CITY SMALL CITYLARGE CITY

= Station

The proposed network system provided a direct connection service without transfer for each

OD pair even in case of a small city if the demand is sufficient for its economic operation.

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Process of the heuristic optimized network design

The set of major corridors were combined

all together into as a whole network, and it

was refined and simplified with

professional knowledge.

Step 1

Selecting candidate sets

of cities to be served

Step 2

Running minimum spanning

tree(MST) algorithm and

finding a set of major corridors

The alternative sets of cities, which will be

served by Hyperloop, was selected by

ordering cities from the biggest population.

The MST analysis was performed for each

candidate set of cities to find a cost-

minimized network. Then, a set of major

corridors was selected heuristically.

Step 3

Combining all of major corridors

and refining and simplifying the

combined network

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Cities of the top 60 in the population, South Korea(Selecting candidate sets of cities )

GyunggiProvince

GangwonProvince

ChungcheongProvince

GyungbukProvince

Jeon-laProvince

GyungnamProvince

Gangneung

Ulsan

Busan

Daegu

Daejeon

Gwangju

IncheonSeoul

• The cumulated populations of

the top 30 and the top 60 cities

in aspect of the population are

74.8 % and 88.7 % of the total

population of the South Korea

respectively.

• In this study, 60 cities were

selected as the largest number

of candidate cities for the

Hyperloop service that can

serve about 90 % of the total

population.

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Concept of minimum spanning tree (MST)

𝑀𝑖𝑛. 𝑧 =

𝑖𝑗∈𝐸

𝑐𝑖𝑗𝑥𝑖𝑗

𝑆𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜

𝑖𝑗∈𝐸

𝑥𝑖𝑗 = 𝑛 − 1

𝑖𝑗∈𝐸:𝑖∈𝑆,𝑗∈𝑆

𝑥𝑖𝑗 ≤ 𝑆 − 1 ∀𝑆⊆𝑉

𝑤ℎ𝑒𝑟𝑒 𝑥𝑖𝑗 ∈ 0, 1 𝑎𝑛𝑑 𝑐𝑖𝑗 = cost of link 𝑖𝑗

https://en.wikipedia.org/wiki/Minimum_spanning_treeMathematical formulation

The MST problem is to find a tree that is the minimum total cost of links

connecting all the nodes in a given graph.

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Objective function used in this study

𝑀𝑖𝑛. 𝑧 =

𝑖

𝑗

𝛼 𝑉𝑖𝑗 + 𝛽 𝐶𝑖𝑗 𝑥𝑖𝑗

𝛼 + 𝛽 = 1𝑤ℎ𝑒𝑟𝑒 𝑉𝑖𝑗 = 1 −𝑇𝑖𝑗

𝑚𝑎𝑥 𝑇𝐼𝐽,

𝑇𝑖𝑗 ∶ 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑟𝑖𝑝𝑠 𝑏𝑒𝑤𝑒𝑒𝑛 𝑐𝑖𝑡𝑦 𝑖 𝑎𝑛𝑑 𝑐𝑖𝑡𝑦 𝑗 𝑝𝑒𝑟 𝑑𝑎𝑦

𝐶𝑖𝑗 =𝑑𝑖𝑗

𝑚𝑎𝑥 𝑑𝐼𝐽, 𝑎𝑛𝑑

𝑑𝑖𝑗: 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑐𝑖𝑡𝑦 𝑖 𝑎𝑛𝑑 𝑐𝑖𝑡𝑦 𝑗 (km)

Distance of links are directly proportional to the infrastructure construction

cost. Therefore, the above objective function is intended to simultaneously

reflect travel demand and construction cost in the network design.

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MST analysis for candidate sets of cities

10 cities 13 cities 16 cities 20 cities 25 citiesTotalcost:3.795 Totalcost:4.1978 Totalcost:5.5619 Totalcost:6.9814 Totalcost:9.0771

30 cities 35 cities 40 cities 50 cities 60 citiesTotalcost:11.4901 Totalcost:13.4482 Totalcost:15.8013 Totalcost:20.7758 Totalcost:25.5511

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Finding a set of major corridors heuristically

Overlapped MST results of the representative candidate sets

Desire line of OD travel demand

Overlapping the results of the MST analyses for several candidate sets of cities graphically

and identifying the corridors that are used redundantly in serval candidate sets. The study

also considered travel demands of OD pairs with the desire lines.

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A schematic and conceptual set of corridors

①

②

③

④

②

①

③

④

Overlapped MST results of the representative candidate sets

Desire line of OD travel demand

It is worth to note that relatively large number of travel demand are concentrated on

the corridor 1 compared to the other corridors.

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The selected set of six corridors

West seaNS Corridor

North EW Corridor

East sea NS Corridor

Busan NS Corridor

Gwangju NS Corridor

SouthEW Corridor

1. North EW corridor

2. West-sea NS corridor

3. Gwangju NS corridor

4. Busan NS corridor

5. East-sea NS corridor

6. South EW corridor

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MST analysis for each corridor independently

4. Busan NS corridor

3. Gwangju NS corridor1. North EW corridor 2. East-sea NS corridor

6. South EW corridor5. West sea NS corridor

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Combining all of major corridor’s MST results

to a national-wide composite network

4. Busan NS corridor

3. Gwangju NS corridor1. North EW corridor 2. East-sea NS corridor

6. South EW corridor5. West sea NS corridor

MST results for each corridor A combined network

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Network refinement and simplification

for the Seoul metropolitan area

Busa

n

NS C

orr

idor

Westcorridor

Mid.corridor

Eastcorridor

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National-wide network refinement and simplification

Final proposed national-wide network

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Multinomial Logit Model for a mode choice analysis

𝑃𝑚 =exp 𝑉𝑚

σ𝑘 exp 𝑉𝑘

Where Pm = probability to choose mode m

Vk = a utility function of the alternative mode k

𝛽0𝑘 = mode specific constant for mode k

𝛽𝑛𝑘 = a parameter for the nth explanatory variable of mode k

𝑉𝑘 = 𝛽0𝑘 + 𝛽1 𝑇

𝑘 + 𝛽2 𝐶𝑘

Logit model A utility function

𝑉𝑘 = 𝛽0𝑘 + 𝛽1 𝑥1

𝑘 + 𝛽2 𝑥2𝑘+ . . . . .

This study used following utility function that the Korean government officially

distributed for feasibility study of transportation infrastructure construction plan.

where 𝑇𝑘 = travel time of mode k

𝐶𝑘 = travel cost of mode k

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Results of mode choice analysis and

the share of Hyperloop

Seoul

Daejeon

Daegu

Busan

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