Re: 11 millions records : more than 30 seconds to retrieve simple request

[Rick James]

"searching of the first row is very fast" -- IF you have a useful index (and you did in that case)

LIMIT 2000 -- Well, it takes time to deal with 10000 rows.
And note that that these are proportional: 10000:30000 :: 2:6

Did you run each SELECT twice? (The first time may be hitting the disk; the second may not.)

SELECT slower than INSERT -- Let's see the details of the SELECT. And do EXPLAIN SELECT. Lots of things can slow down a SELECT.

How many different values are there for "variable"? (I am curious about how much it is jumping around.)

The latest schema included some of what I recommended, but not some other things.