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Consider a very large network $10000$ routers. Two host $A$ and $B$ connected with this network. Host $A$ sends a data to host $B$. and after some unit of time host $A$ receives $ICMP$ time exceed message for the samedata packet. The number of router that can be travelled by packet when message return back to A _____________

Why ans is $255+254$

Why not after going some distance some ICMP message generated? Say if $ICMP$ message generated in $9999th$ router, then where it give error of time exceed message?

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I think for 255+254 to be the answer the question would be " The maximum number of router that can be travelled by packet when message return back to A"

Since TTL field is 8 bit max value that can be set is 255, so packet goes through 255 routers decrementing TTL field value by 1 at every router and then ICMP message generated and returned, now this ICMP packet can go through max 254(Since one would be original sender(A here)) new routers(NOT on initial path of packet)

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yes, that I know

I just want to know if after say, 9000 packet it gets a ICMP unreachable message then hat happen?
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A packet doesn't travel all routers of network, only those in the shortest path between A and B. Also We might consider a worst case scenario where routers are aligned line by line with every one of the 10000 routers are connected like a chain, In this case packet has to travel all routers but at each router its TTL is decremented by 1 so I think it will never go beyond 255 routers, so if a packet cannot reach 9000 routers then there's no case of sending ICMP unreachable message from there! , Please see the following link for a detailed discussion on a similiar thread

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Also the ICMP packet is always sent back to the original router which has putted it into datagram
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@Anuj Mishra

Still not got it.

Say from A to B there are 10000 router  Say all those router we need to visit to reach destination B. Then after reaching 1000 router TTL message is send, then where this message will receive?

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if the IPv6 Hop Limit is less than or equal to 1 {
send an ICMP Time Exceeded -- Hop Limit Exceeded in
packet
}
else {
decrement the Hop Limit by 1

resubmit the packet to the IPv6 module for transmission
to the new destination
}

The ICMP message is always sent back to orignal source via source address mentioned in packet. Also It will never reach 1000 router Always Hopcount will become 0 or 1 and TTL exceed error will occur.

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then why 10000 router needed, if we cannot find more than 255 router at once?
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10000 routers are connected in a network, we have various connections at routers, not just one, so no need to go in a linear fashion going through every router. Take example of the Internet There's like no limit to how many routers are there but still we can find them, send and receive data from them, Like the thread in the link mentioned the advanced and complex mechanisms of finding shortest paths bound the path length to 30 -35 routers, i.e, we can reach any router/server by making approx 30-35 routers max(in general).
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U mean it is like star topology, So means 10000 router cannot be added in bus topology

right?

Ok it can be.
+1

I haven't seen 10000 "Routers" connected in bus topology, surely other workstations, 2 layer switches and repeaters are possible but wouldn't it be too inefficient to have 10000 "Routers" connected in a linear path, I mean where do we then use our clever algorithms like DVR and LSR. I'm not saying it cannot be arranged like that - just that it won't be functional. Also if we think about what can be the solution in such a case :

1)Routers don't decrement TTL field (Not viable as Infinite looping can occur)

2)TTL field bits should be increased (Also not viable as we have to change IPV4 header format which "changes everything everyone has worked on")

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yes may be that the case
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@Anuj Mishra

i know that packet forwarded by router the TTL value will be decremented by one unit.

but ur 1st statement say...its wrong plz explain??

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@Gateasp2020 TTL value will be decremented by 1 at router, no doubt about that. Actually, I used this fact to prove my point that we can't have a functional model where 10000 routers are connected in a path like fashion(Kind of proof by contradiction). Don't get confused what you know is correct, read the whole thread again you'll get the idea of what I'm saying,

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@Anuj Mishra