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I've got a massive dataset (~30 billion rows):

host_id | usr_id | src_id | visit_num | event_ts

where any user from their parent host can visit a page on a source (src_id), where the source is, say, their phone, tablet, or computer (unidentifiable). The column vis_num is the ordered number of visits per source per user per host. The column event_ts captures the timestamp of each visit per source per user per host. An example data set for one host might look like this:

   host_id | usr_id  | src_id |  vis_num  |      event_ts
----------------------------------------------------------------
   100     |   10    |  05    |     1     |  2017-08-01 14:52:34
   100     |   10    |  05    |     1     |  2017-08-01 14:56:00
   100     |   10    |  05    |     1     |  2017-08-01 14:58:09
   100     |   10    |  05    |     2     |  2017-08-01 17:08:10
   100     |   10    |  05    |     2     |  2017-08-01 17:16:07
   100     |   10    |  05    |     2     |  2017-08-01 17:23:25
   100     |   10    |  72    |     1     |  2017-07-29 20:03:01
   100     |   10    |  72    |     1     |  2017-07-29 20:04:10
   100     |   10    |  72    |     2     |  2017-07-29 20:45:17
   100     |   10    |  72    |     2     |  2017-07-29 20:56:46
   100     |   10    |  72    |     3     |  2017-07-30 09:30:15
   100     |   10    |  72    |     3     |  2017-07-30 09:34:19
   100     |   10    |  72    |     4     |  2017-08-01 18:16:57
   100     |   10    |  72    |     4     |  2017-08-01 18:26:00
   100     |   10    |  72    |     5     |  2017-08-02 07:53:33
   100     |   22    |  43    |     1     |  2017-07-06 11:45:48
   100     |   22    |  43    |     1     |  2017-07-06 11:46:12
   100     |   22    |  43    |     2     |  2017-07-07 08:41:11

Per each source id, a change in visit number implies a log-off time and a subsequent log-on time. Note that activity from different sources may overlap in time.

My goal is to calculate how many (non-new) users logged in at least twice within some time interval, say 45 days. My ultimate end goal is:

1) Identify all users who repeated the critical event at least twice within a certain time period (45 days).

2) For those users, measure the length of time they took between completing the event the first and second time.

3) Plot a cumulative distribution function – i.e., the percentage of users who performed the second event over different time intervals.

4) Identify the time interval at which 80% of users have completed the second event—this is your product usage interval.

Page 23 of:

http://usdatavault.com/library/Product-Analytics-Playbook-vol1-Mastering_Retention.pdf

Here is what I've tried:

with new_users as (

select host_id || ' ' || usr_id as host_usr_id,
       min(event_ts) as first_login_date

   from tableA
   group by 1
)
,

time_diffs as (
select a.host_id || ' ' || a.usr_id as host_usr_id,
       a.usr_id,
       a.src_id,
       a.event_ts,
       a.vis_num,
       b.first_login_date,  

   case when lag(a.vis_num) over 
                    (partition by a.host_id, a.usr_id, a.src_id 
                      order by a.event_ts) <> a.vis_num
        then a.event_ts -  lag(a.event_ts) over 
                                 (partition by a.host_id, a.usr_id, 
                                               a.src_id 
                                   order by a.event_ts)
        else null end 
          as time_diff                     


    from tableA a
    left join new_users b
    on b.host_usr_id = a.host_id || ' ' || a.usr_id


      where a.event_date > current_date - interval '45 days'
      and a.event_date > b.first_login_date + interval '45 days'

)

select count(distinct case when time_diff < interval '45 days'
                  and event_ts > first_login_date + interval '45 
days'
                  then host_usr_id end) as cnt_45


   from time_diffs

I've tried multiple other (very different) queries (see below), but performance is definitely an issue here. Joining on date intervals is also a new concept to me. Any help is appreciated.

Another approach:

with new_users as (

select host_id,
       usr_id,
       min(event_ts) as first_login_date

   from tableA
   group by 1,2

),

x_day_twice as (

select a.host_id, 
       a.usr_id,
       a.src_id,
       max(a.vis_num) - min(a.vis_num) + 1 as num_logins

    from tableA a
    left join new_users b
    on a.host_id || ' ' || a.usr_id = b.host_id || ' ' || b.usr_id
    and a.event_ts > b.first_login_date + interval '45 days'

where event_ts >= current_timestamp - interval '1 days' - 
interval '45 days' and first_login_date < current_date - 1 - 45

group by 1, 2, 3
)


select count(distinct case when num_logins > 1 
                           then host_id || ' ' || usr_id end)
   from x_day_twice
boldbrandywine
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