Huge number of active database sessions with "SQL*Net message from client" wait event

"SQL*net message from client" suggests the Oracle DBMS is waiting for the client to send new commands to the DBMS, and therefore any time spent in this event should be client-side time and not consume DB server CPUs. In other words, normally, if a session is in this event, it should be "INACTIVE" rather than "ACTIVE".

What's puzzling to us is that starting from this week (after we started using connection pools [we use Tomcat]), we occasionally see sessions in the "SQL*net message from client"

event and showing "ACTIVE" at the same time for extended periods of times. And during all this time, CPU usage on the DB is high.