a-results.txt

...
 2017-07-14 12:52:00+00 |     2
 2017-07-14 12:53:00+00 |     2
 2017-07-14 12:54:00+00 |     2
 2017-07-14 12:55:00+00 |     2
 2017-07-14 12:56:00+00 |     2
 2017-07-14 12:57:00+00 |     2
 2017-07-14 12:58:00+00 |     2
 2017-07-14 12:59:00+00 |     2
 2017-07-14 13:00:00+00 |     3
 2017-07-14 13:01:00+00 |     3
 2017-07-14 13:02:00+00 |     3
 2017-07-14 13:03:00+00 |     3
 2017-07-14 13:04:00+00 |     3
 2017-07-14 13:05:00+00 |     3
 2017-07-14 13:06:00+00 |     3
 2017-07-14 13:07:00+00 |     2
 2017-07-14 13:08:00+00 |     2
 2017-07-14 13:09:00+00 |     2
 2017-07-14 13:10:00+00 |     2
 2017-07-14 13:11:00+00 |     2
 2017-07-14 13:12:00+00 |     2
 2017-07-14 13:13:00+00 |     2
 2017-07-14 13:14:00+00 |     2
...

a-schema.sql

DROP TABLE events CASCADE;
CREATE TABLE events(
    id serial primary key
  , device_id int not null
  , start_at timestamp with time zone
  , end_at timestamp with time zone
  , unique(device_id, start_at)
);

/* DEVICE    9   10   11   12   13   14   15   16
 *   1            |---|          |--------|
 *   2       |-------------|
 *   3                 |--------|
 *   4                      |----------------|
 *
 *   In other words, there was 1 device at 9, 2 at 10, 1 at 11 and so on...
 */
INSERT INTO events(device_id, start_at, end_at) VALUES
  (1, '2017-07-14 10:00', '2017-07-14 11:00')
, (1, '2017-07-14 13:00', '2017-07-14 15:00')
, (2, '2017-07-14 09:00', '2017-07-14 12:00')
, (3, '2017-07-14 11:00', '2017-07-14 13:07')
, (4, '2017-07-14 12:08', '2017-07-14 15:31')
;

a-solution.sql

-- Tested with PostgreSQL 9.6.3
WITH device_presences AS (
    SELECT device_id, tstzrange(start_at, end_at, '[)') presence
    FROM events)

SELECT minute, count(distinct device_id)
FROM generate_series((SELECT min(start_at) FROM events), (SELECT max(end_at) FROM events), interval '1 minute') AS minutes(minute)
CROSS JOIN device_presences
WHERE presence @> minute
GROUP BY minute
;