How to load balance thick clients based on HTTP parameter?

Universal persistence:

http://support.f5.com/kb/en-us/solutions/public/7000/300/sol7392.html

Your iRule would look something like:

when HTTP_REQUEST { 
 set cid [findstr [HTTP::uri] "cid" 4 ";"] 
 if { $cid != "" } { 
 persist uie $cid 
 } 
}

The ";" value is the terminator signifying the end of the parameter value, so you will need to adjust as needed.

You would create a universal persistence profile that references the iRule and assign it to the desired virtual server