"Queue times shouldn't be this high during peak hours" (How a queue works)

I'm reposting this in its own thread because it ended up being a longer post than I expected and I think it deserves a little visibility.

Well there should NEVER be 30 minute queue times, no matter what positions you are looking for. Hell there shouldnt even be 5 minute queue times in primetime NA. As i said, im gold not challenger. When it was solo duo, find games in 20 seconds. Now we are looking at 8 minute average queues purely cause people dont want to play support? I'm calling absolute BS on that, im sure out of 3 million players in primetime, at least 200000 are playing support as one of their two roles. I dont care if im matched against challenger or bronze, at least give me a game.

You are not actually thinking about how a queue works. Being in 'primetime' has no benefit when the role selector is a thing. The only way to fix queue times is to go back to no role selector (or for you to be willing to play support) which means you would have decent odds of getting stuck in support for a full 40 minute game, which honestly sounds worse to me if you are someone who doesn't like playing support (I usually play support and have instant queue times).

Let's assume you are correct, there are 3 million players and 200,000 are willing to play support. I'm pretty sure the numbers aren't THAT bad but the numbers you chose will illustrate my point perfectly.

So the rest of that queue, 2.8 million are in line to play a game, let's assume they are evenly divided between all 4 other roles, there are no other imbalances that could slow down the game (I am pretty sure top and mid are most popular, jungle is less popular, and bot is almost as unpopular as support, which further complicates and slows down matters)

That means there are 700,000 groups of 4 waiting on supports, 200,000 of them get supports right away and the other 500,000 are now waiting in queue. That's 500,000 4-man groups, so 2 million players.

the first 200,000 waiting will be able to get their game when the supports all finish their first game (let's assume all games are equal length, 30 minutes for simplicity) and the 800,000 non-supports they were playing with go to the end of the line as 200,000 more groups

Another game, another rotation in, we've now gotten 600,000 groups into games

Another game, another rotation in, we've now gotten 800,000 groups into games, meaning everyone has had at least one game at this point.

TL;DR: with the numbers you gave, it takes the length of 4 games for everyone to play at least one game (support players get to play in all 4 games and the lucky players first in line got to play a second game at the end) meaning that the longest queue time was a 3 game wait of 1 and a half hours.

But what about more support players joining the queue during this process? Well given the ratio you gave, for every one support player, there are going to be 14 non-supports joining the queue, so the queue for non-supports grows by 14 while the queue for support grows by one, maintaining the ratio of a 2.5x full game wait before someone joining at the end of the line will be able to play a game.

But what about if it's a busy or light load at the time? When there are less other players for me to compete with or more supports available? Changes to player load in the queue should still maintain the same ratio of supports to non-supports. If you assume only 300,000 total players with 20,000 supports, that still results in only 2/7 of the non-supports getting into a game each time the supports are available for a game.