Monday, February 27, 2012

Would an Isolated Network Suppress its Load by Connecting to Another Network?

Yes, but only up to a critical point. A group of mathematicians from University of California Davis has recently built a model to analyze how interconnection between networks could amplify large global cascades by spreading failure. It is a surprise because conventional wisdom suggests that having more interconnections provides more routing options to handle unexpected high loads. A failed connection could divert its loads to neighbors with lower loads, using the whole system more effectively.

This topic relates to the materials we are currently studying in class: Braess’ paradox, load balancing, and routing game. Generally, people believe that having more resources and options are better than nothing. For example, one could imagine that building a new freeway could reduce traffic on another freeway that has similar destinations. Examples seen in class showed that when a better resource is provided, every individual chooses that option. Because each person is selfish and not willing to give up the best benefit, it reduces overall performance. ('s_paradox) Although there are benefits to creating interconnections, having an interdependent network could increase the chance of weakening the entire network.

For each interconnection that is added, additional load is expected, thus resulting in greater total capacity and average capacity. When one connection fails, it will divert its load by passing it to neighboring networks. Neighboring networks need to suddenly handle excess loads and as a result, have a higher chance of failing as well. In this way, having one failed connection in a network could cause a cascade of loads in the whole system.

The paper published by Charles Brummit’s group studied the topologies of the interacting networks. They analyzed topological data on two interdependent power grids from the US Federal Energy Regulation Commission (FERC). Additionally, Brummit’s team developed a multitype branching process approximation as a theoretical tool to formulate the cascade spreading in interconnected networks, which is justified to be the ideal model for power grids in this paper.

One of the important results they found in the paper is, “What amplifies the global cascades most significantly is the increase in total capacity (and hence average load available for cascades) and not the increased interdependence between the networks.” This explains why people observe network failure cascades happening in real life. Since it’s more common to open a connection from one network to others than to rewire a connection to connect to other networks, the former increases the overall loads of the system, thus more vulnerable to cascades. Load balancing and determining the optimal configuration of interconnection of networks are very challenging yet useful topics to study.


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