We are in the midst of a huge migration project in which a lot of PST files are imported.
Our archiving task runs from 6 in the evening till midnight. We notice in the MSMQ queues that the server is quite busy and that queues are filling and going down.
However we notice that the A6 queue is not going down.
If you decide to purge, remember to stop the Storage and Taks controller services to avoid the Event log spam.
Before pruging you could try to restart the Admin service and see if you can bring it to life.
A6 is, as RahulG state the Synchronisation queue and be default EV does syncs at midnight and midday. EV will process the queues hierarchically so A1 takes precedence over A2 and so on, A5 is different so ignore that as it only processes during the scheduled run. So if A1 A2 A3 or A4 contain data EV will try to get them done before A6.