Network Robustness Analysis Based
on Current Road Incident Data
R. Vodák1, M. Bíl 2, R. Andrášik 2, J. Sedoník 2
This work was financed by the Transport R&D Centre (OP R&D for Innovation No. CZ.1.05/2.1.00/03.0064) by
project no. VG20102015057 provided by the Ministry of the Interior and by the grant IGA_PrF_2015_013
Basic nomenclature
• Robustness
• Redundancy
• Randomness
• Hazard
Example of a vulnerable network
Each removed link will
cause the instantaneous
network break-up
Example of a robust network
All links must be
removed to disconnect
the nodes
How to compare two or more
networks?
Robustness measure
𝑅=
1
𝑘
𝑘 𝑐𝑜𝑚𝑝 𝐺𝑖 −1
𝑖=1 𝑙𝑖𝑛𝑘(𝐺 )
𝑖
∈ (0,1]
• k is the number of all combinations of links which can be removed from
the network
•
comp(Gi) is the number of components of the network which emerge
after the removal of the i-th combination of links
• link(Gi) is the number of links in the i-th combination of links removed
from the network.
• Gi represents the network after the removal of i-th combination of links.
Total hazard
The total hazard consists of two main classes:
• hazards induced by nature (floods, landslides
and snow)
• hazards produced by people
The total hazard is computed as an occurrence
of at least one of the particular hazards.
Particular hazards
• Road segments were separated into two groups – with or
without a historical disruption by a particular event.
• A particular hazard for segments with a historical disruption
was estimated empirically (e.g. 3 events within 14 years led to
4/16 as a Bayesian estimate of the probability of the event).
• A logistic regression model was constructed for the rest of the
road segments
Přerušení provozu
v důsledku
vážných
dopravních nehod
Silnice I/52. Foto: HADN CDV, 2012
Silnice I/52. Foto: HADN CDV, 2013
Dálnice D2. Foto: HADN CDV, 2012
Stupně poškození silnic
vlivem přírodních pohrom
1
1. Přerušení dopravy
2. Poškození úseku
3. Celková destrukce
Rok 2002: Karlín, okres Hodonín, zdroj: archiv SUS JMK
2
3
Silnice II. tř. Koryčany – Jastřabice, 2010. Foto: SUS ZLK
Bystřička, červenec 1997. Foto: Karel Kirchner
Strategy 1
All combinations of removed links without any
restriction.
Each link can be removed
Strategy 2
A link can only be removed if at least one
connection between each of its end nodes with
another node is preserved.
The rule would be violated here
Strategy 3
There is one or no interrupted link coming out of
a node.
The rule would be violated here
Monte Carlo method
• Choose randomly a link.
• Check whether the link can be interrupted
• Decide on the interruption or repair
Application to actual road networks
Networks no. 1 and 2.
Real road networks schematically depicted in the simplest way
1
2
Results
Strategy 1
Strategy 2
Strategy 3
Network 1
0.2885
0.2414
0.2361
Network 2
0.0365
0.0194
0.0147
1
2
Improvements
Strategy 1
Strategy 2
Strategy 3
Network 1
0.2885
0.2414
0.2361
Network 2
0.0365
0.0194
0.0147
Strategy 1
Strategy 2
Strategy 3
Network 1
0.1843
0.1394
0.1216
Network 2
0.0138
0.0025
0.0019
Improvement - strategy 1
Improvement – strategy 2
Improvement – strategy 3
Final remarks