In the UK at least, router (in a computing context) _does_ rhyme with hooter. It is, after all, something that routes traffic -- exactly like your first example.
A router pronounced 'rowter', on the other hand, is a device for cutting grooves in wood.
http://dictionary.cambridge.org/us/dictionary/english/route
Contrast http://dictionary.cambridge.org/us/dictionary/english/legiti... , which correctly notes that the adjective and verb are pronounced differently.
Route 66 -> sounds like root
My usual route to work -> rhymes with doubt
Can someone reset the router -> rhymes with doubter.
In other meanings the pronunciations vary.
> Router as in the hardware always rhymes with doubter.
> I have never heard any other pronunciation for it.
Neither had I, until I lived in the UK.I'm Australian, and we use the owl sounding router.
In the UK, it's very much a rooter sounding router.
Always funny, as here in AU root is slang for the act of copulation.
The pronunciation made Akamai's SureRoute product especially droll.
'to get into a row with someone'
It's only in a computing context that 'router' rhymes with 'doubter'. I'd suggest female staff would likewise get the wrong idea if one pronounced it 'rooter'.