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MySQL:soma datas sem contar períodos sobrepostos duas vezes


Ok, eu insisto seriamente que você teste isso de todas as maneiras antes de usá-lo em produção. Teste especialmente o que acontece se houver MÚLTIPLAS sobreposições por 1 período de tempo.

O que essa consulta faz é calcular a duração de cada intervalo de tempo e quanta sobreposição existe com outros intervalos de tempo que têm um ID mais alto.
select
    t1.id,
    t1.start_time,
    t1.end_time,
    t1.end_time - t1.start_time as duration,
    sum(
          if(t2.start_time <  t1.start_time and t2.end_time >  t1.end_time  , t1.end_time - t1.start_time, 0) -- t2 completely around t1
        + if(t2.start_time >= t1.start_time and t2.end_time <= t1.end_time  , t2.end_time - t2.start_time, 0) -- t2 completely within t1
        + if(t2.start_time <  t1.start_time and t2.end_time >  t1.start_time and t2.end_time   < t1.end_time  , t2.end_time - t1.start_time, 0) -- t2 starts before t1 starts and overlaps partially
        + if(t2.start_time <  t1.end_time   and t2.end_time >  t1.end_time   and t2.start_time > t1.start_time, t1.end_time - t2.start_time, 0) -- t2 starts before t1 ends and overlaps partially
    ) as overlap
from
    times t1
    left join times t2 on
        t2.id > t1.id --  t2.id is greater than t1.id
        and (
               (t2.start_time <  t1.start_time and t2.end_time >  t1.end_time  ) -- t2 completely around t1
            or (t2.start_time >= t1.start_time and t2.end_time <= t1.end_time  ) -- t2 completely within t1
            or (t2.start_time <  t1.start_time and t2.end_time >  t1.start_time) -- t2 starts before t1 starts and overlaps
            or (t2.start_time <  t1.end_time   and t2.end_time >  t1.end_time  ) -- t2 starts before t1 ends and overlaps
        )
group by
    t1.id

Então o que você quer ter no final é isso:
select
    sum(t.duration) - sum(t.overlap) as filtered_duration
from
    (
        OTHER QUERY HERE
    ) as t

Então, no final, você tem esta consulta:
select
    sum(t.duration) - sum(t.overlap) as filtered_duration
from
    (
        select
            t1.id,
            t1.start_time,
            t1.end_time,
            t1.end_time - t1.start_time as duration,
            sum(
                  if(t2.start_time <  t1.start_time and t2.end_time >  t1.end_time  , t1.end_time - t1.start_time, 0) -- t2 completely around t1
                + if(t2.start_time >= t1.start_time and t2.end_time <= t1.end_time  , t2.end_time - t2.start_time, 0) -- t2 completely within t1
                + if(t2.start_time <  t1.start_time and t2.end_time >  t1.start_time and t2.end_time   < t1.end_time  , t2.end_time - t1.start_time, 0) -- t2 starts before t1 starts and overlaps partially
                + if(t2.start_time <  t1.end_time   and t2.end_time >  t1.end_time   and t2.start_time > t1.start_time, t1.end_time - t2.start_time, 0) -- t2 starts before t1 ends and overlaps partially
            ) as overlap
        from
            times t1
            left join times t2 on
                t2.id > t1.id --  t2.id is greater than t1.id
                and (
                       (t2.start_time <  t1.start_time and t2.end_time >  t1.end_time  ) -- t2 completely around t1
                    or (t2.start_time >= t1.start_time and t2.end_time <= t1.end_time  ) -- t2 completely within t1
                    or (t2.start_time <  t1.start_time and t2.end_time >  t1.start_time) -- t2 starts before t1 starts and overlaps
                    or (t2.start_time <  t1.end_time   and t2.end_time >  t1.end_time  ) -- t2 starts before t1 ends and overlaps
                )
        group by
            t1.id
    ) as t