The 'Verse isn't anything like Traveller universe, in that it appears to be some sort of multiple star system with multiple habitable planets. FTL is fuzzy on details--if in fact it actually happens and isn't just intersystem travel (again, Firefly is vague on the details...), as it is implied. FTL communications however appears to be a real thing, unlike Traveller, and terraforming seems to be something that the Alliance can do with relative ease, whereas in Traveller it takes many years and can go horribly wrong, even when the Ancients do it.
Objectively speaking however, there are too many parallels between Traveller and Firefly for Traveller not to have been an influence (heck I can essentially lift the plot of a Firefly episode and use it in Traveller with minimal effort). This is not to say that Joss owes Marc money, not even close. There are clearly enough unique elements in Firefly that is a clearly something new.
Objectively speaking however, there are too many parallels between Traveller and Firefly for Traveller not to have been an influence (heck I can essentially lift the plot of a Firefly episode and use it in Traveller with minimal effort). This is not to say that Joss owes Marc money, not even close. There are clearly enough unique elements in Firefly that is a clearly something new.