'lazy / weighted' sort algorithm

Not sure if this is appropriate for this mailing list, but I'm sure that there
may be others with ideas / opinions out there. I have a list of frequency counts
of categories where a categories count will get updated each time an item in the
category is manipulated. The list needs is sorted slowly over an arbitrary
period of time (possibly days) such that items at eventually appear at the head
of the list will have been accessed the most frequently over the longest period
of time. Newly created list entries get added to the list in such a way
(probably towards the middle of the list?) such that existing items are not
immediately removed from the list.

I’ve been calling this a lazy sorted or weighted sort. Is there a ‘real’ term
for this kind of sorting and an established algorithm? Ideas
are solicited.

Thanks.

Cache algorithms - Wikipedia, the free encyclopedia
Perhaps MRU, or LRU (depending on your point of view I suppose)

yep - it's a L/M RU queue. I'm interested in getting ideas about weighting techniques where items move slowly up/down the queue & if there were any well known techniques / methods for accomplishing that.

The "Completely Fair Scheduler" (CFS) in the linux kernel does something like that; it maintains a red-black tree where process are picked from the left, and move rightward based on how much processor time they've used. However, this measurement is weighted by a priority formula including the "nice" value and whether the process is a "real time" process. There are some other factors, and new processes are placed into a queue with a starting value determined by the activity of the queue itself (ie, they don't necessarily go in at the front).

So not quite the same, but similar.

Thanks for the hint - I didn't consider it to be a form of a scheduler problem but it is in retrospect.