In the database logging we see that the Analytic reports are being generated at random times during the day. These query's can be quite long and heavy causing performance issues.
Further investigation turned out that users can schedule these reports themselves, not realizing that this has performance impact.
The workaround is to do a SQL update to delete, or reschedule at night-time, and set up a cron job to script the delete/resched task.
Proposal to restrict Analytic reports from being run every hour, or only at night.