Chi Ho Yeung1 , David Saad1, K. Y. Michael Wong2

1Nonlinearity and Complexity Research GroupAston University, United Kingdom

2Department of Physics, Hong Kong University of Science and Technology, Hong Kong

C. H. Yeung, D. Saad and K. Y. M. Wong, PNAS, 110, 13717 (2013)

Planes, trains and polymers, the statistical physics of routing

HKUST

Motivation: what’s wrong with

current routing methods?

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From one point to another We use GPS, online path finder!

Source: Google Map

An example: Driving from MongKok Central

Route A Route B

Route A

Route B

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An example: MongKok Central

Route A Route B

?

Much longer travel time than the expected! Source: Google Map

Route BRoute A

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Problem? Individual route optimisation

Simultaneously coordinate

routes!

Everyone travels slightly longer

than the shortest option all

benefit!

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Routing in off-peak hours?

Tuen MunTin Shui Wai

Yuen Long

Scenario 1Individual optimisation - shortest path

Tuen Mun

Yuen LongTin Shui Wai

Very empty buses, waste of resources!

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Path sharing in late off-peak hours

Tuen MunTin Shui Wai

Yuen Long

Scenario 2Coordinated paths

Tuen Mun

Yuen LongTin Shui Wai

Discontinue less popular bus routes save resources!

Better use of capacity!

Flight route optimal utilisation

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Relatively under-loaded planesShare flights to

different destinations

and continue with short-haul flights

Advantages of coordinating routes

Peak hours/Peak seasons – load/traffic balancingAdvantages: avoid congestion, save travelling

time

Off-peak hours/Off-peak seasons – discontinue less popular routes

Advantages: encourage sharing, save energy and operational cost, suppress the need for new infrastructure, extend sustainability

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Other applications: internet routing

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P2P networks, instant messengers, online commerce, etc …

Wireless communications Stability, robustness, efficiency Suppress the need for

new infrastructure

efficiency and sustainability save resources

Coordinate path simultaneously, difficult?11

1. Many users, different starting point/destination

2. For each user, there are many alternative path choices

Beijing U Temple of Heaven

Technically Very Difficult

Polymers on Networks

The physics of polymersWhat is a polymer? A long chain of molecules

What is a network?

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PrinceEdward

KowloonTong

Starting point

Destination

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Peak hours – reduce congestion repulsion between polymers

Repulsion!

Repulsion!

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Off-peak hours – consolidate routesattractionbetween polymers

Attraction!

Results: Optimisation algorithm

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London Underground275 stations2316 passengers (polymers) – Oyster card data of 2316 real passengers starting point & destination

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Oyster card

London tube map

Results – London Underground

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Repulsion

Node size/edge thickness traffic amount

2316 passengers (Oyster card data)

Results – London Underground

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Attraction

Node size/edge thickness traffic amount

2316 passengers (Oyster card data)

Results – Our algorithm vs shortest path

Everyone travels on a slightly longer path, overall benefit can be large!

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London subway network with 2316 passengers

Repulsion Attraction

Results – Adaptive routing after breakdown- Node size/edge thickness amount of traffic change

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, - traffic , - traffic

1. More changes2. Changes are smaller

1. Less changes2. Changes are larger

- no change

Results - Air Traffic Network

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Repulsion

Results - Air Traffic Network

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Attraction

Conclusion- Coordination of path is useful:

Peak hours – avoid congestion, balance trafficOff-peak hours – encourage sharing, save resources

- However, it is technically very difficult; applying physics of polymers, we obtain1. readily applicable algorithm2. interesting phenomenon

may lead to next-generation routing software, planning of large scale events

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C. H. Yeung, D. Saad and K. Y. M. Wong, PNAS, 110, 13717 (2013)