Brain Lint

I had a request the other day: how many simultaneous users are on the site, by time of day. I already have a session database that’s computed nightly from weblogs: it contains the times at which each session started and ended.

CREATE TABLE sessions
(
  user_id integer NOT NULL,
  start_at timestamp without time zone,
  end_at timestamp without time zone,
  duration double precision,
  views integer
)

I thought for sure the next step would be to dump some data, then write some Ruby or R to scan through sessions and see how many sessions were open at a time.

Until I came up with a nice solution in SQL (Postgres). Stepping back, if I can sample from sessions at say, one-minute intervals, I can count the number of distinct sessions open at each minute. What I need is a row per session per minute spanned. Generate_series is a “set returning function” that can do just that. In the snippet below, I use generate_series to generate a set of (whole) minutes from the start of the session to the end of the session. That essentially multiplies the session row into n rows, one for each of the minutes the session spans.

From there, it’s easy to do a straight forward group by, counting distinct user_id:

with rounded_sessions as (
select user_id, start_at, end_at,
generate_series(date_trunc('minute',start_at), end_at, '1 minute') to_the_minute from sessions
where start_at between '2012-01-21' and '2012-01-28'
)
select to_the_minute, count(distinct user_id) from rounded_sessions group by 1

The date_trunc call is important so that session rows are aligned to whole minutes, if that’s not done, then none of the rows will align for the counts.

That set won’t include rows that had no users logged in. To do that, the query below will use generate_series again to generate all the minutes from the first minute present to the last, then left join the counts to that set, coalescing missing entries to zero.

with rounded_sessions as (
select plm_users.user_id, start_at, end_at,
generate_series(date_trunc('minute',start_at), end_at, '1 minute') as to_the_minute
from sessions
where start_at between '2012-01-21' and '2012-01-28'
),
counts_by_minute as (
select to_the_minute, count(distinct user_id) from rounded_sessions
group by 1
),
all_the_minutes as (
select generate_series(min(to_the_minute), max(to_the_minute), '1 minute') as minute_fu from rounded_sessions
)

select to_the_minute , coalesce(count, 0) as users from all_the_minutes
left join counts_by_minute on all_the_minutes.minute_fu = counts_by_minute.to_the_minute

As a member of PatientsLikeMe‘s Data team, from time to time we’re asked to compute how many unique users did action X on the site within a date range, say 28 days, or several date ranges (1,14,28 days for example). It’s easy enough to do that for a given day, but to do that for every day over a span of time (in one query) took some thinking. Here’s what I came up with.

One day at a time

First, a simplified example table:

create table events (
  user_id integer,
  event varchar,
  date date
)

Getting unique user counts by event on any given day is easy. Below, we’ll get the counts of unique users by events for the 7 days leading up to Valentine’s day:

select count(distinct user_id), event from events
where date between '2011-02-07' and '2011-02-14'
group by 2

Now Do That For Every Day

The simplest thing that could possibly work is to just issue that query to compute the stats for the time span desired. We’re looking for something faster, and a bit more elegant.

Stepping back a bit, for a seven day time window, we’re asking that an event on 2/7/2011 count for that day, and also count for the 6 following days – effectively we’re mapping the events of each day onto itself and 6 other days. That sounds like a SQL join waiting to happen. Once the join happens, its easy to group by the mapped date, and do a distinct count.

With a table like the one below

This SQL becomes easy.

select to_date, event, count(distinct user_id) from events
join dates_plus_7 on events.date = dates_plus_7.from_date
group by 1,2

You’ll then need to trim the ends of your data to adjust for where the windows ran off the edge of the data.
That works for me on Postgresql 8.4. Your mileage may vary with other brands.

How Do I Get One of Those?
A dates table like that is a one-liner using the generate_series method:

select date::date as from_date, date::date+plus_day as to_date from
 generate_series('2011-01-01'::date, '2011-02-28'::date, '1 day') as date,
 generate_series(0,6,1) as plus_day ;

There we get the cartesian product of the set of dates in the desired range, and the set of numbers from 0 to 6. Sum the two, treating the numbers as offsets and you’re done.