Where did you get idea that a router must keep track of session response time. This is not really a function of a router. If you really want to learn networking you will know a router operates on layer 3 and sometimes on layer 4 but it is not concerned with higher layer protocols that would include caring about response times.
A routers only real function is to sort traffic between paths. It looks at the destination IP address and selects which interface to send it on. This does not really apply to home router since it really only has 1 path to and from the internet. It is better called a gateway. The only time a router would place traffic in a buffer is if the connection it wanted to send the data on was being used at that moment. How large this buffer is is not a function of latency.
Home "routers" gateways have a addition function in the nat that to a point keeps track of the sessions but it does not actually care about the actual round trip time. This session information is kept in memory not so much a buffer and is discarded when the session is closed or after a period of time of inactivity. The length of time it is kept and the size are not affected by the round trip time.
You must be misreading the book or it is wrong. The concept of RTT is more of a end device/application function. Even more so for UDP session since only the application knows which data packets actually make up which session.
Yes, you are right and that is my concern as I know RTT is related to end application or host. I am reading Computer Networking A Top Down Approach by Kurose. It says:
"How much Buffering at Output Port of Router is Required
..... For many years, the rule of thumb [RFC 3439] for buffer sizing was that the amount of buffering (B) should be equal to an
average round-trip time (RTT, say 250!msec) times the link capacity (C). Thus, a 10-Gbps link with an
RTT of 250 msec would need an amount of buffering equal to B = RTT # C = 2.5 Gbits of buffers".
Which RTT is this book talking about?