Hey Bob,
Good to see you making use of the forums and I hope you had a good Thanksgiving holiday!
As you may remember, the MII transaction engine relies heavily on the NetWeaver JMS engine and the JMX threadpool. Your instance may be maxing out this thread pool which is causing the transactions (which use Message Driven Beans for the Message Processing rules) to queue up and wait for a new thread to become available. I explain a lot of this on pages 20-22 of this document:
The Performance of SAP MII on Intel Xeon Hardware Analysis Summary
Also, depending on your NetWeaver release you may have to update your ENGINEAPI version and some other SCAs as there are continuous improvements made to the JMS engine by the NetWeaver team in order for it to perform better under heavy load. Which SP of NW 7.11 are you using?
I also think that there is a profiler for the JMS engine built into NetWeaver which Mike talks about on page #9 of this document:
Hope this helps,
Sam