The following uses much of the techniques mentioned by @Brits. They present some very good information, so I'll not repeat but suggest you review it (and the links).
I do however take a slightly different approach. First a couple table changes. I use the ISO day of week 1-7 (Monday-Sunday) rather than the day name. The day name is easily extracted for the dater later.
Also I use interval instead to time for start and end times. ( A time data type works for most scenarios but there is one it doesn't (more later).
One thing your description does not make clear is whether the ending time is included it the available time or not. If included the last interval would be 11:00-11:15. If excluded the last interval is 10:45-11:00. I have assumed to excluded it. In the final results the end time is to be read as "up to but not including".
-- setup
create table availabilities (weekday integer, start_time interval, end_time interval);
insert into availabilities (weekday , start_time , end_time )
select wkday
, start_time
, end_time
from (select *
from (values (1, '09:00'::interval, '11:00'::interval)
, (1, '13:00'::interval, '17:00'::interval)
, (2, '08:00'::interval, '17:00'::interval)
, (3, '08:30'::interval, '10:45'::interval)
, (4, '10:30'::interval, '12:45'::interval)
) as v(wkday,start_time,end_time)
) r ;
select * from availabilities;
The Query
It begins with a CTE (next_week) generates a entry for each day of the week beginning Monday and the appropriate ISO day number for it. The main query joins these with the availabilities table to pick up times for matching days. Finally that result is cross joined with a generated timestamp to get the 15 minute intervals.
-- Main
with next_week (wkday,tm) as
(SELECT n+1, date_trunc('week', current_date) + interval '1 week' + n*interval '1 day'
from generate_series (0, 6) n
)
select to_char(gdtm,'Day'), gdtm start_time, gdtm+interval '15 min' end_time
from ( select wkday, tm, start_time, end_time
from next_week nw
join availabilities av
on (av.weekday = nw.wkday)
) s
cross join lateral
generate_series(start_time+tm, end_time+tm- interval '1 sec', interval '15 min') gdtm ;
The outlier
As mentioned there is one scenario where a time data type does not work satisfactory, but you may not nee it. What happens when a shift worker says they available time is 23:00-01:30. Believe me when a shift worker goes to work at 22:00 of Friday, 01:30 is still Friday night, even though the calendar might not agree. (I worked that shift for many years.) The following using interval handles that issue. Loading the same data as prior with an addition for the this case.
insert into availabilities (weekday, start_time, end_time )
select wkday
, start_time
, end_time + case when end_time < start_time
then interval '1 day'
else interval '0 day'
end
from (select *
from (values (1, '09:00'::interval, '11:00'::interval)
, (1, '13:00'::interval, '17:00'::interval)
, (2, '08:00'::interval, '17:00'::interval)
, (3, '08:30'::interval, '10:45'::interval)
, (5, '23:30'::interval, '02:30'::interval) -- Friday Night - Saturday Morning
) as v(wkday,start_time,end_time)
) r
;
select * from availabilities;
Hope this helps.