When a switch or router becomes really busy will it drop ICMP packet sent both directly to it (i.e. pings) in favour of normal data traffic and also any pings passing through it or will it just drop those sent direcly to it? Or will it firstly drop pings sent directly to it and carry on passing pings through it, and if it becomes busier still will it then drop pings passing through it in favour of normal data traffic (a double tiered approach where normal data is given highest priority, then pings passing through it and last of all pings sent directly to it)?
For example if I try to ping a router that usually responds to pings when it is not busy and then it stops responding to pings but I can ping a switch on the far side of the router. But if I then can't ping the switch on the far side of the router either would that mean that all traffic is not getting through (i.e. does it treat pings passing through it the same as it treats normal data traffic)?
The pings destined to the router itself has lower priority but the pings passing through the router would be handled the same way like all other normal traffic.
Let's say a router is too busy handling large volume of traffic. An ICMP packet arrives destined to the router itself and another ICMP packet arrives at the same time which the router has to forward out another interface it would only drop the ICMP packet destined to itself but the one that's passing through the router would be handled in a normal way.