The user agent string format "Mozilla/5.0 (X11; Linux i686 on x86_64; rv:14.0) Gecko/20100101 Firefox/14.0.1" is from a Mozilla Firefox browser e.g. see this Mozilla reference: Gecko_user_agent_string_reference
The Real Browser Monitor (RBM) executes in a Firefox instance on the App Synthetic Monitor (ASM) monitoring stations. So if that user agent string is being observed in the web server log at the frequency which matches the RBM run interval e.g. 5/10 minutes, then the RBM is probably the source of the user agent strings.
For further details of RBMs see the ASM Wiki page: Real Browser Monitor (RBM) for Firefox