You'll forgive me for being cynical here, but I seriously doubt that any
Linux-derived operating systems could truly qualify as 'real-time'. To meet
the requirements for an RTOS, Linux would have to be so heavily mutated that
it would no longer be Linux.
Um... The rtl kerenel runs the linux kernel as a pre-ementible low
priority thread, has proveable worst case timing around 15uSec between
assertion of interrupt and execution of the realtime handler, and is
Realtime stuff is not only about process rescheduling times.
The definition of real-time system is: a system which can guarantee
execution of tasks within specified time limits.
I've seen a real-life real-time system with guaranteed reaction time of
two hours (it was controlling irrigation water gates).
For routers, the "real-time" limits one needs is in 0.1 second-range;
making a system like that from a general-purpose OS is certainly doable.