Tokyo Metro system during disasters or attacks

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Abstract

• Public transportation is a kind of networks closely related to our daily life. In this research, I would use the data from Tokyo Metro to generate the network of Tokyo Metro. After that, I would analyze the change of global efficiency and connected passengers, during node attacks and node failures.

Background

• The security and stability of public transportation are always the most concerned issues. As a kind of networks, what will happen if some stations are destroyed due to natural disasters or terrorist attacks? We could concern in two ways. First, the general view of the whole system would be the change of the cost from one station to another. Second, the stations might be entirely separated to multiple groups of stations even if they still work well.

• Also, as the graph theory, the removement of nodes could be in two ways, which are node attack and node failure. We could concerned node attack as intentionally attacks to the system, node failure as a random shutdown of some stations in the system.

Research Question

1. What is the change of the cost when the network of Tokyo Metro system experiences a sequence of node attacks and node failures?

2. What is the change of the remaining passengers’ in connections when the network of Tokyo Metro experiences a sequence of node attacks and node failures ?

Dataset

• The data was all web-crawled from Tokyo Metro websites, including the stations, lines, average passengers of each station in 2017.

• The nodes represent the stations. The stations connected in lines represent the edges, only the previous and next stations would be concerned as edges.

• 1. Nodes(stations): 142.*
• 2. Edges(connections): 175.

(*Kokkai-gijidomae and Tameike-sanno are concerned as one node(station) in the data of Tokyo Metro.)

Network Figure

Fig.1. Tokyo Metro Network

Method

1. Approach

A. Modified Node Attack

• Step 1. Find the node(s) with highest degree. (Original)

• Step 2. Remove the node with highest average passengers among them.

B. Node failure

• Randomly remove one nodes from the network.

2. Measurement

A. Global Efficiency

• Denotes \(n\) as the # of nodes, \(d(i,j)\) as the length of the shortest path between node \(i\) and \(j\).

\[E(G)=\frac{1}{n(n-1)}\sum_{i\neq j\in{G}}\bigg(\frac{1}{d(i,j)}\bigg)\]

\[E_{glob}(G)=\frac{E(G)}{E(G^{ideal})}\]

B. Application: Largest Connected Passengers

• Step 1. Summarize the number of passengers of nodes(stations) in each component.

\[CP_{k}=\sum_{i\in{C_{k}}}(Popu_{i})\]

• Step 2. Find the one with most passenges.

\[LCP(G)=\max_{C_{k}\in{G}}{CP_{k}}\]

Results

• Since after node-attacking on 53 nodes, the network would have no nodes with degree higher than 1, the node attack and node failure would stop in that time.

1. Network Figure

• Following graphs are the network figure during modified node attack and node failure.

Fig.2. Node Attack on the network

Fig.3. Node Failure on the network

2. Example of the component with largest amount of passengers during node attack and node failure.

Fig.4. Comparison.

• We could easily see the difference on the speed of change. Node attack could decrease the largest amoint of passengers in connections faster, by removing transfer stations and separating the system.

• Since the node failure is by random, we should run many times to get the average result. Following is the comparison of \(LCP\) and \(E_{glob}\), during the sequences of node attack and average of node failure (1000 times).

3. Comparison of LCP and global efficiency

Fig.5. Ratio of Largest Connected Passengers.

Fig.6. Global Efficiency.

• As the figure 5 and 6 revealed, both the LCP and global efficiency decreased faster if the network experienced node attacks.

Discussion

• In conclusion, we can say that the network of the Tokyo Metro system is more vulnerable to node attacks, no matter from the perspectives of the cost (global efficeincy) or passengers in connections. In the real life, this implies the Tokyo Metro system might be influenced more in the shutdown of the transfer stations.

• Back to our previous course, we also know that the scale-free network is more fragile to node attacks. Although there are some differences between theory and reality, we could also know that the Tokyo Metro system shared some characteristics with the scale-free network.

References

1. 路線・駅の情報.(2018, December 29th). Retrieved from https://www.tokyometro.jp/station/index.html

2. 各駅の乗降人員ランキング.(2018, December 29th). Retrieved from https://www.tokyometro.jp/corporate/enterprise/passenger_rail/transportation/passengers/index.html

3. Traffic Performance by Station.(2018, December 29th). Retrieved from https://www.tokyometro.jp/lang_en/corporate/enterprise/transportation/ranking/index.html

4. Wikipedia - Efficiency (network science).(2018, July 26th). Retrieved from https://en.wikipedia.org/wiki/Efficiency_(network_science)

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