Religious-pilgrimage system

Lecture Notes 2.3 Network Vulnerability HRV KFSC, Fall 2020

I. Introduction: Business Micro View to National Macro View a. Now that we have established why networks are so critical for a

society from both a supply-chain perspective and a distribution-chain perspective, we need to start examining their vulnerability to accidental failure or intentional attack of individual nodes.

b. In other words, how much harm will occur if particular nodes are shut down?

c. This is really important, because if the government is seeking to ensure the security of an entire national network, it needs to know which nodes are really critical for maintaining a functional infrastructure.

d. Governments generally speaking lack the resources to protect all nodes. Besides, the benefits of such protection is probably far lower than the cost, thus resulting in a negative net-utility gain.

e. So, which nodes should be protected to ensure a positive net-utility gain for the security spending?

II. Network vulnerability

a. It turns out that networks have vulnerabilities that go beyond the losses that occur when individual nodes fail.

i. For example, when a fire in a warehouse imposes cost on a business due to a delay in deliveries.

b. They have vulnerabilities due to the structure of the network system. c. Such vulnerabilities can occur especially when the nodes are tightly

connected to other nodes in order to achieve high degrees of efficiency.

d. Electrical Network example i. The distribution network of electricity is tightly connected because electricity cannot be stored.

ii. The generators of electricity must generate precisely enough to match exactly that which gets consumed by users.

iii. So, when demand gets high, like on a hot summer day, more generators get turned on to meet the demand.

iv. But what happens when there is a technical failure in one of the distribution nodes, so that it gets shut down to prevent too much electricity from flowing, thus leading to overheating and burning out the line or capacitor?

v. The needed electricity gets rerouted from other generators. vi. But what happens when that gets too much and also shuts

them down.

vii. The electrical distribution network starts suffering from “cascading” effect, where failure starts spreading throughout the network, ultimately leading to a complete collapse.

viii. This is precisely what happened to the Northeast of the United States in August 2003.

e. Other examples i. Communicable disease cascade: Spanish Influenza pandemic of 1918; COVID 19 pandemic of 2020.

ii. AIDS sexually transmitted disease crisis during the 1980s. iii. Zipper effect in structural failures iv. Los Angeles Riot (1992): Failure to contain a local riot, where

angry people overwhelmed security forces who then elected to retreat, encouraged other angry people to defy security forces and start rioting all over the city. Why? Due to communication connection from television broadcasts.

v. Arab Spring (2011) vi. Economic Recessions: just a few businesses may suffer from a

decline of net revenue function, thus forcing them to cutback on production and lay people off. But other people see such layoffs and fear an economic downturn in happening, so they cut back on their spending over fear of becoming unemployed. But that cutback on spending lowers the net revenue curves of other businesses, whose owners then cutback on production thus laying more people off. Thus the economy endured a systemic collapse due to tight coupling of employment and consumer spending.

vii. Internet: cascading failures due to too much traffic to a server, prompting a surge of frustrating user to overwhelm substitute servers.

viii. Cascading effects of transportation system failures: 1. Overuse of dirt roads (designed for light hores-drawn

wagon use) in Soviet Union by the Germans heavy trucks and tanks in Fall 1941 during initial German invasion.

2. Traffic jams on a main highway causing a cascade of smaller jams to spread on side roads as people seek alternative routes.

III. Random vs. Scale-Free Network Vulnerability a. It turns out that the vulnerability of a network to systemic or

cascading failure depends on a basic feature i. Is it a random network? ii. Is it a “scale-free” network?

b. If it is a random network, then it is more vulnerable to a random accidental failure, but if it is a scale-free network, it is more vulnerable if only a particular set of nodes fail.

i. These nodes are called “hubs.” ii. Hubs are nodes that have a great deal of links that far surpass

the average number of links the nodes throughout the network have.

c. It turns out that a very simple technique exists for determining whether a network is random or scale-free.

IV. Analyzing Networks

a. Analyzing networks with histograms of N(k) versus k, where N(k) is the number of nodes with k links, and k is the number of links.

i. Step one: number each node. ii. Step two: analyze each node to determine how many links it

has. iii. Step three: count the number of nodes for each number of

links. iv. Draw a graph showing link number k is the x-axis and number

of nodes with those links, N(k) in the y axis. b. Random network: resulting curve is a bell-shaped curve

Scale-free network: resulting curve is downward sloping of N(k) = 𝑘!! or N(k) = 1/(𝑘!)

c. Big difference between random and scale-free networks: scale-free has a few nodes with many links, while it also has many nodes with just a few links.

d. Random networks have many nodes with an average number of links, with just a few that have less, and a few that have more, but none that have vastly more as in scale-free networks.

V. Example of Random Network

k Nodes with k links N(k)

1 1, 11, 14 3 2 2, 3 2 3 4, 5, 7, 9, 10, 12, 13 7 4 6, 8 2 Average number of links = (3+2+7+2)/4 = 3.5

3

1 4

2

6

7

1

1 3

5

9

1 2

4

10

8

1 1

k

N(k)

1 2 3 4

1 2 3 4 5 6 7

x x

x

x

Example of Scale-Free Network

k Nodes with k links N(k)

1 1, 5, 6, 9, 12, 14, 16 7 2 2, 4, 7, 11, 13, 15 6 3 0 4 10 2 5 3 1

3

14 2

6 7

1

13

5

9 12

4

10

8 11

15

16

k

N(k)

1 2 3 4

1 2 3 4 5 6 7 x

x

x x