mysqlでDATETIMEをTIMESTAMPに変換する方法は？

試してみてください：

select 
  o1.id, 
  o1.operation_date_time, 
  (unix_timestamp(o2.operation_date_time) - unix_timestamp(o1.operation_date_time)) 
    as duration 
from operations as o1 
  inner join operations as o2
where o1.operation = "START" 
  and o2.operation = "STOP"
  and o1.id = (o2.id - 1);

出力として提供する必要があります：

+------+---------------------+----------+
| id   | operation_date_time | duration |
+------+---------------------+----------+
|    1 | 2000-01-01 06:30:45 |     4455 |
|    3 | 2000-01-01 08:18:12 |    11146 |
|    5 | 2000-01-01 15:45:01 |    11792 |
+------+---------------------+----------+
3 rows in set (0.00 sec)