Cómo devolver todos los periodos de tiempo libres de una cita establecida

Es difícil decir si la solución a continuación funcionará para usted, dada la pequeña muestra de datos, pero con suerte lo ayudará a comenzar.

IF OBJECT_ID('tempdb..#sked') is not null
DROP TABLE #sked

IF OBJECT_ID('tempdb..#tmpResults') is not null
DROP TABLE #tmpResults

create table #sked(
    ID int,
    time_start datetime2,
    time_end datetime2,
    duration int)

insert into #sked (ID,time_start,time_end,duration) values
(4,'2016-06-06 00:30:00','2016-06-06 01:30:00',3600000),
(2,'2016-06-06 04:00:00','2016-06-06 04:20:00',1200000),
(1,'2016-06-06 10:00:00','2016-06-06 11:00:00',3600000),
(6,'2016-06-06 11:30:00','2016-06-06 12:30:00',3600000)

declare @startRange datetime2
declare @endRange datetime2
declare @slotDurationInMinutes int

set @startRange = '2016-06-05T00:00:00.000'
set @endRange = '2016-06-07T21:59:00.000'
set @slotDurationInMinutes = 30

select
    time_end as free_from,
    isnull(lead(time_start) over (order by time_end),@endRange) as free_until
into #tmpResults
from
    #sked
where
    time_end >= @startRange 
    and time_end <= @endRange
    --and duration <= (@slotDurationInMinutes * 60000) --conversion to milliseconds

union all

select
    case when @startRange < min(time_start) then @startRange end as free_from,
    case when @startRange < min(time_start) then min(time_start) end as free_until
from
    #sked
where
    time_end >= @startRange 
    and time_end <= @endRange
    --and duration <= (@slotDurationInMinutes * 60000) --conversion to milliseconds
order by
    free_from

select 
    *,
    DATEDIFF(minute,free_from,free_until) 
from 
    #tmpResults
where
    free_from is not null
    and DATEDIFF(minute,free_from,free_until) >= @slotDurationInMinutes