If this is a web application, then it's possible you can pull this information from WebTrends or something some server that can analyze each log file from the web server.
You can also probably write up an irule to count each HTTP trigger to track the connections. Here is a link to a forum post talking about using Profile STATS which can store custom counter information
(http://devcentral.f5.com/Default.aspx?tabid=53&forumid=5&tpage=1&view=topic&postid=33148).
In the post they are tracking Web content but, it's possible to track sessions on clients.
I hope this helps
thanks,
CB