Planes, trains and polymers, the statistical physics of ... · Chi Ho Yeung1, David Saad1, K. Y....
Transcript of Planes, trains and polymers, the statistical physics of ... · Chi Ho Yeung1, David Saad1, K. Y....
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
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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)