Process timespan for each start/end pair using Hive script - hadoop

Question

I have a service that can be started or stopped. Each operation generates a record with timestamp and operation type. Ultimately, I end up with a series of timestamped operation records. Now I want to calculate the up-time of the service during a day. The idea is simple. For each pair of start/stop records, compute the timespan and sum up. But I don't know how to implement it with Hive, if possible at all. It's OK that I create tables to store intermediate results for this. This is the main blocking issue, and there are some other minor issues as well. For example, some start/stop pairs may span across a single day. Any idea how to deal with this minor issue would be appreciated too.
Sample Data:
Timestamp Operation
... ...
2017-09-03 23:59:00 Start
2017-09-04 00:01:00 Stop
2017-09-04 06:50:00 Start
2017-09-04 07:00:00 Stop
2017-09-05 08:00:00 Start
... ...
The service up-time for 2017-09-04 should then be 1 + 10 = 11 mins. Note that the first time interval spans across 09-03 and 09-04, and only the part that falls within 09-04 is counted.

Answer 1

select to_date(from_ts) as dt
,sum (to_unix_timestamp(to_ts) - to_unix_timestamp(from_ts)) / 60 as up_time_minutes
from (select case when pe.i = 0 then from_ts else cast(date_add(to_date(from_ts),i) as timestamp) end as from_ts
,case when pe.i = datediff(to_ts,from_ts) then to_ts else cast(date_add(to_date(from_ts),i+1) as timestamp) end as to_ts
from (select `operation`
,`Timestamp` as from_ts
,lead(`Timestamp`) over (order by `Timestamp`) as to_ts
from t
) t
lateral view posexplode(split(space(datediff(to_ts,from_ts)),' ')) pe as i,x
where `operation` = 'Start'
and to_ts is not null
) t
group by to_date(from_ts)
;
+------------+-----------------+
| dt | up_time_minutes |
+------------+-----------------+
| 2017-09-03 | 1.0 |
| 2017-09-04 | 11.0 |
+------------+-----------------+