How to load balance thick clients based on HTTP parameter?

The answer basically depends on the client. HTTP is stateless, so every request MUST contain some unique piece of information that the server can use to derive persistence, session management, etc.

So, if the client WILL ALWAYS add "?cid=" to its request URIs, then Shaggy's original iRule will do the trick.

If, however, the client only sends that cid value once at the beginning of the session, then you need something else to use for ongoing persistence. The best choice, if the client supports it, is cookies, and that would be the last iRule above.