Hard question you have there
I don't have very detailed knowledge about how the CPU interrupt is generated, and I also didn't found any documentation in regard to this, but look what I know:
as i known,
when router receive a packet in some interface,
the interface interrupt a cpu to process the packet.
This is true, but not in every cases. If in the routing process the switching part is the one called "process switched" then yes, for every packet arriving on the interface an interruption is sent to the CPU. If it's direct proportional with the number of packets arriving on the interface, I would have to say yes. In this case, if you have a lot of traffic, then you are stuck with 100% CPU utilisation. That's why process switched method is not so common this days.
So, this method will involve the CPU all the time.
Next method is fast-switching which still uses the CPU, but only for the first packet that arrive on the interface with a certain destination. After this packet has been forwarded the information how to reach that destination is stored in the fast-switching cache, so all other packets with the same destination will be forwarded based on the cached information. No interruption to CPU is needed anymore. In this case I believe that there is no direct proportion between packets entering the interface and interrupts sent to the CPU.
Then it is CEF, which builts the FIB table in which it stores all the information needed to forward packets, so no interrupt to the CPU is needed. It will consume more memory (due to FIB table), compared with the previous method, but less CPU. This the most common method used today. Totally no proportion between packets entering on the interface and CPU interrupts.
Of course there are other processes on the router that can request CPU interrupts, like in any PC, but I believe that the answer above is related to your question.
I hope this helps!
