A Model of Load Failures
https://pdfs.semanticscholar.org/f5ba/96369c8990e98a1684b2faa9ee9f510d8309.pdf
This research paper designs a model for cascading failures in a power grid. It starts by modeling a disturbance on device. Then check to see if the device fails. A device is listed as going to fail if it’s load exceeds its capacity to handle the load. When a device fails its load gets picked up by all other devices in the network. Based on this model as a cascade. If the cascade stops then in subsequent steps there will be no other failures. The paper is much more complex than this but I find the model quite interesting. Like those seen in class, this model is a cascade.
Considering the format of the model it’s interesting to consider if this form of network (in its simplified form described above) could get translated to our learnings on network effects. If we can consider doing a similar process of ordering the capacity of each node based on the node’s capacity. If we want to consider each having a different load then we can apply the load to the capacity and then order based on the remaining capacity. Thus we have a model for the reservation price r(x). Next, we need a model for the network effects. One interesting note is that if a node fails then it’s load is displaced to all other nodes. Just quickly thinking, since each node fails at it possible that this would be equivalent to the integral of the failed node’s capacities. Since this is shared by the remaining nodes we divide it by the number of remaining nodes. Thus an equation can be drawn up for the network effects f(x). If we draw the disturbance load as some formulation of the price we now have a model for the network which is quite the fun thought experiment.