TSQL get overlapping periods from datetime ranges

Question

I have a table with date range an i need the sum of overlapping periods (in hours) between its rows.

This is a schema example:

create table period (
    id int,
    starttime datetime,
    endtime datetime,
    type varchar(64)
  );

insert into period values (1,'2013-04-07 8:00','2013-04-07 13:00','Work');
insert into period values (2,'2013-04-07 14:00','2013-04-07 17:00','Work');
insert into period values (3,'2013-04-08 8:00','2013-04-08 13:00','Work');
insert into period values (4,'2013-04-08 14:00','2013-04-08 17:00','Work');
insert into period values (5,'2013-04-07 10:00','2013-04-07 11:00','Holyday'); /* 1h overlapping with 1*/
insert into period values (6,'2013-04-08 10:00','2013-04-08 20:00','Transfer'); /* 6h overlapping with 3 and 4*/
insert into period values (7,'2013-04-08 11:00','2013-04-08 12:00','Test');  /* 1h overlapping with 3 and 6*/

And its fiddle: http://sqlfiddle.com/#!6/9ca31/10

I expect a sum of 8h overlapping hours: 1h (id 5 over id 1) 6h (id 6 over id 3 and 4) 1h (id 7 over id 3 and 6)

I check this: select overlapping datetime events with SQL but seems to not do what I need.

Thank you.

Answer 1

select sum(datediff(hh, case when t2.starttime > t1.starttime then t2.starttime else t1.starttime end,
    case when t2.endtime > t1.endtime then t1.endtime else t2.endtime end))
from period t1 
join period t2 on t1.id < t2.id
where t2.endtime > t1.starttime and t2.starttime < t1.endtime;

Updated to handle several overlaps:

select sum(datediff(hh, start, fin))
from (select distinct
case when t2.starttime > t1.starttime then t2.starttime else t1.starttime end as start,
case when t2.endtime > t1.endtime then t1.endtime else t2.endtime end as fin
from period t1 
join period t2 on t1.id < t2.id
where t2.endtime > t1.starttime and t2.starttime < t1.endtime
) as overlaps;