Finding free timeslots between appointments with preferred beginning - mysql

Question

I have 2 tables...
appointments:
id (int)
start (datetime)
end (datetime)
timeslots:
id (int)
timeslot (time)
The table timeslots has records like this...
00:00:00
00:05:00
00:10:00
...
23:55:00
The table appointments has one record...
start: 2017-05-15 01:30:00
end: 2017-05-15 02:00:00
With the following simplified query I try to get the first free starting timeslot each hour if there is no prefered hourly begin time while respecting existing appointments...
SET #mandatory=true, #parallel=1, #targetdate="2017-05-15", #begin='30', #duration='00:30:00', #time_start="00:00:00", #time_end="03:00:00";
SELECT MIN(timeslot) AS free_slot FROM timeslots
INNER JOIN
appointments
ON 1=1
WHERE timeslots.timeslot BETWEEN #time_start AND #time_end
AND (ADDTIME(timeslot, #duration) BETWEEN #time_start AND #time_end)
AND ((#mandatory AND MINUTE(timeslot)=#begin) OR (NOT #mandatory))
AND ((
SELECT COUNT(*) AS anzahl
FROM appointments
WHERE (concat(date(#targetdate)," ",timeslots.timeslot) BETWEEN appointments.start AND appointments.end - INTERVAL 1 SECOND
OR concat(date(#targetdate)," ", ADDTIME(timeslot, #duration) ) BETWEEN appointments.start AND appointments.end - INTERVAL 1 SECOND)
) < #parallel)
GROUP BY HOUR(timeslot)
Explanation of parameters:
#mandatory:
TRUE means, I only allow timeslots matching #begin. FALSE means, I prefer(!) timeslots matching #begin, but if there is no match, I would like to get the first free timeslot each hour.
#parallel:
Number of parallel appointments allowed. The value 1 means, that there should be no overlapping appointments. The value 2 means, that there should be only 2 appointments at the same time.
#targetdate:
The query should return timeslots only for the targetdate.
#begin:
The prefered beginning of the free timeslots. '30' means, that I would like to get timeslots starting "half past ..." every hour.
#duration: The needed duration of consecutive free timeslots.
#time_start and #time_end:
The result should only contain records within this time range.
My problem is, that I get either free timeslots only starting at half past ... or the first free timeslot for every full hour - depending on setting #mandatory to TRUE or FALSE.
When setting #mandatory to TRUE I think I get the desired result (only timeslots starting at the defined begin time). But I want to set #mandatory to FALSE and get first free timeslot every hour ONLY when there is no free timeslot beginning with half past (I would like to PREFER the matching begin timeslots, but offer alternative timeslots...
This is what I would like to get:
00:30:00
01:00:00 (this row respects the existing appointment at half past one and returns the first free timeslot for this hour only when the duration of the remaining timeslots fits)
02:30:00
Is there an easy way to get these results?
Best regards