sessionize.sql

SELECT chat,sender,text,
       message_date,
       SUM(is_new_session) OVER (ORDER BY chat, message_date) AS global_session_id,
       SUM(is_new_session) OVER (PARTITION BY chat ORDER BY message_date) AS chat_session_id
      FROM (
        SELECT *,
              CASE WHEN EXTRACT('EPOCH' FROM message_date) - EXTRACT('EPOCH' FROM last_event) >= (60 * 120) 
                     OR last_event IS NULL 
                   THEN 1 ELSE 0 END AS is_new_session
         FROM (
              SELECT chat,sender,text,
                     message_date,
                     LAG(message_date,1) OVER (PARTITION BY chat ORDER BY message_date) AS last_event
                FROM messages
              ) last
       ) final