For a hotspot user we can set some limits in the profiles.
This page about different limits and different traffic priorities of the wiki site gives a good overview of the different options.
The minimum rate should be the data rate that is guaranteed to a target
On the wiki page about Queue under HTB properties it is called limit-at (NUMBER/NUMBER) : normal upload/download data rate that is guaranteed to a target
There is the remark that

Good practice suggests that: Sum of children's limit-at values must be less or equal to max-limit of the parent.

The problem is that the simple queues of the hotspot users are not children of a parent.
So how can there then be a minimum data rate ?.

Yes I do know how to set the max limit, burst limit, burst threshold and burst time for a hotspot profile.
For normal hotspot user profile we use the line at rate limit 128k/256k 256k/1024k 100k/200k 64/64 for high web browsing speed but slow downloading. Works very good to limit the hotspot users that constant download.
We would like to have some sort of guarantee bandwidth for al the hotspot users when there is a heavy load on the hotspot bandwidth.

Extending the line to 128k/256k 256k/1024k 100k/200k 64/64 8 64k/128K should give the hotspot users at least 64K/128K bandwidth.
The question is does this work, and if so how ?.

The problem is that the simple queues of the hotspot users are not children of a parent.

from the http://wiki.mikrotik.com/wiki/Manual:Qu ... ple_Queues :

One configuration item in /queue simle' can create from 0 to 3 separate queues - one queue in global-in, one queue in global-out and one queue in global-total.

so parents are global queues