This topic has been discussed within several strings...usually around the first of the year when we are all confirming that our points rolled properly and wondering if the program will be renewed for the upcoming year.
Here is one link that may answer your questions... rollover nights
You will also find that when you read a discussion the right hand column of the page will include a section called "more like this". That is usually a good place to find similar discussions based on key words.
We've been talking about this since the program began. In a nutshell it is based on nights stayed, not total nights and it rolls over at the start of a year, but does not include those nights you may have rolled over from previous years.
Thus, you've stayed 90 nights in 2011, 15 above Platinum, so you roll over 15 nights as your beginning balance for 2012.
Hope that makes sense, if not let me know