Random Ramblings to 24 April 2010

Cascading failure
A failure of a system where one component's failure causes a chain-reaction failure of other components. A system bearing a load is susceptible to this type of failure, where an overloaded component shifts its load to other components upon its individual failure. In an electrical grid, a cascading failure occurs when a transformer's failure requires the other transformers to bear the electrical load, increasing the chance that one of those transformers will also fail due to overloading.

Where the components are fully interconnected and handle a fixed load, the per-component load trend is a rectangular hyperbola. This signifies that the per-component load increases at an increasing rate as components fail. As a result, the chance of any individual component's failing also increases at an increasing rate.

A graph illustrating a cascading failure in a World of Warcraft boss encounter. The trend is a rectangular hyperbola.

WoW Mathematics: Sharing the (DPS) load

In any (conventional) boss encounter, a certain number of damage dealers (dps) need to whittle down the boss' health to zero over a certain time period. Barring any extraordinary tinkering by Blizzard, the health level remains constant between attempts.

This fixed DPS burden needs to be shared between all dps. I will examine the DPS burden per dps and how it changes with the number of dps that happen to die during the encounter.

Summary:

• Given a total DPS burden (total raid DPS) of D and a total number of dps of d, the average DPS burden per dps B, where x players are dead, is B = ^D/_{d - x}.
  

Insanity: The Yogg-Saron Soundtrack

I am surprised as to the number of songs written and sung about the mental state, and how diverse in musical style that collection is. This inspired me to compile a selection of those songs into an alternative soundtrack for the Yogg-Saron encounter in Ulduar.

Since actually mixing a full track would require me to pay royalties (and my disk jockey (DJ) skills are rudimentary), I will simply describe it. I will first present the entire list, then attach some commentary after it for those interested in the reasons for my choices.

The playlist

• Phase 1: Flo Rida, Ke$ha 2009, 'Right Round', R.O.O.T.S., Atlantic Recording Corporation, track 5.
• Start of Phase 2: Lady Gaga 2008, 'LoveGame', The Fame, Interscope Records, track 2.