The Collaborative International Dictionary of English v.0.48:

Rout \Rout\, v. t. [imp. & p. p. Routed; p. pr. & vb. n.
   Routing.]
   To break the ranks of, as troops, and put them to flight in
   disorder; to put to rout.
   [1913 Webster]

         That party . . . that charged the Scots, so totally
         routed and defeated their whole army, that they fied.
                                                  --Clarendon.
   [1913 Webster]

   Syn: To defeat; discomfit; overpower; overthrow.
        [1913 Webster]

The Free On-line Dictionary of Computing (30 December 2018):

routing

    /row'ting/ Using a kind of rotating cutting tool called
   a router, pronounced /row't*/.  In the USA a router,
   pronounced /row't*/, is also a network device that performs
   "routing".  In the UK, the network device is pronounced
   /roo't*/ and what it does is spelled "routeing".

   (2002-07-31)