So I've come up with a way to kill what I think is the most elite packs per minute thus far, I've done it alot over the last week with a high success rate and I wanted to share what I do and see some insight from other that are farming Act 3/4.
Concepts Behind my run:
1) Small areas minimize run back time if you happen to die, which does happen.
2) Elite packs love to be near entrances and way points for what ever reason, I'm generally able to find them inside the entrance to somewhere or ontop of the way point itself at times.
3) Quick, fast, elite kills per minute.
4) I run past most trash, depending on what it is and if it has a chance to kill me. Obviously running will be faster elites but you don't "HAVE" to run past everything.
I'll explain my route in parts and explain it as I go along. Start at the quest Heart of Sin: Second Heart, it'll give you Cydea alive.
Keep Depths Level 3 > Keep 2 Back Entrance > Keep 1 WP Entrance > Keep 2 Front Entrance.
Starting at Keep 3 because of how small it is (You'll notice small areas are something I love) and because of its the only place that can have 4 Elite packs in it that you can clear in <5 Minutes, from there taking the exit to Keep Level 2 back entrance and rushing to the first pack you find, from there TP and take Keep 1 WP looking for the first pack, then back to Keep 1 WP and go inside Keep 2 front entrance this time to find the next. Chest available in Keep 2 which can be at the entrance.
There is a chance that you won't find one at the entrances and still won't find one quite deep in if you're unlucky enough to not find one quickly, it happens. I generally search fairly deep for one but do some times not find one at all, its rare not to find one though.
Progress: 8 - 10 Minutes in. 5 - 8 Packs killed. 3 possible goblins. 1 Chest chance.
Rakkis Crossing WP; Head north to The Underbridge > Rakkis Crossing; head south to The Bridge Stores.
Start off by taking the Rakkis Crossing WP and head north to The Underbridge, if its up kill the elite and look for a goblin, TP and head back to the Rakkis WP and head south to the bridge stores. A man will crawl out of the door and it will be shiny before you click it if there's a pack inside. On your way to both areas there can be elites too, plus a goblin outside if you're lucky.
Progress: 10 - 15 Minutes in. 8 - 12 Packs killed. 5 possible goblins. 1 Chest chance.
Arreat Crater 1 WP > Tower of the Damned 1 WP: Take Back Entrance to Arreat Crater 1 > Arreat Crater 2 > Tower of the Cursed 1; Take back entrance to Arreat Crater 2.
Same as all the others, kill your first pack and TP out following my route. There's a possibility for you to encounter a pack while WPing to each tower but for simplicity I'm not counting it in this part of the route. Chest available at Arreat Crater 2 some times.
Progress: 15 - 25 Minutes in. 12 -16 Packs killed. 7 possible goblins. 2 Chest chances.
Tower of the Damned 1 > 2 > Heart of the Damned > Tower of the Cursed 1 > 2 > Cydea > Core of Arreat > Azmo.
Unlike the rest of the run you'll be clearing the entire way down all of these floors killing everything in your path because these areas are very small and if you die you have almost no run back what so ever, each floor has a chance at a goblin and 3 elite packs.
Complete Progress: 40 - 60 Minutes. 17 - 37 Packs killed. 13 possible Goblins. 2 Chest chances. 2 Bosses killed.
My average run is 48 Minutes long, 32 Elite packs and 4 Goblins. Usually don't get any chests.