Does Oracle limit session kill commands to about one per second?

I am running Oracle Database Server 11gR2 on AIX 7.2.

We have a problem in one application that causes it to abandon already created sessions that are in a pool and to create new sessions to use in place of the ones it abandoned. The old sessions stay around in the database instance. We are working with the software vendor on the application issue but are making little process.

My initialization parameters include the following:

process=1700

sessions=2576

There have been times when the application's usual pool of 40 to 64 sessions increases at a rate of two hundred a minute. We scramble to kill sessions to keep from reaching the maximum allowed by initialization parameters. On two occasions we reached the limit. The listener returned message, "TNS-12520: TNS:listener could not find available handler for requested type of server" for connection requests until we got rid of the excess sessions.