MET CS $535$ OL

Module $3$

Homework $1$

Consider the network of Fig. $5-12($a$).$ Distance vector routing is used, and the following vectors have just come in to router D: from A: $($B:$5,$ E:$4)$; from B: $($A:$4,$ C:$1,$ F:$5)$; and from C: $($B:$3,$ D:$4,$ E:$3)$; from E: $($A:$2,$ C:$2,$ F:$2)$; from F: $($B:$1,$ D:$2,$ E:$3).$ The cost of the links from D to C and F are $3$ and $4$ respectively. What is D$$s new routing table? Give both the outgoing line to use and the cost.

Explain the difference between routing, forwarding, and switching.

For hierarchical routing with $4800$ routers, what region and cluster sizes should be chosen to minimize the size of the routing table for a three$-$layer hierarchy? A good starting place is the hypothesis that a solution with k clusters of k regions of k routers is close to optimal, which means that k is about the cube root of $4800($around $16).$ Use trial and error to check out combinations where all three parameters are in the general vicinity of $16.$

A router is blasting out IP packets whose total length $($data plus header$)$ is $1024$ bytes. Assuming that packets live for $10$ sec$,$ what is the maximum line speed the router can operate at without danger of cycling through the IP datagram ID number space?

A large number of consecutive IP addresses are available starting at $198\mathrm{.}16\mathrm{.}0\mathrm{.}0.$ Suppose that four organizations, A$,$ B$,$ C$,$ and D$,$ request $4000,2000,4000,$ and $8000$ addresses, respectively, and in that order. For each of these, give the first IP address assigned, the last IP address assigned, and the mask in the w$.$x$.$y$.$z$/$s notation.

The set of IP addresses from $29\mathrm{.}18\mathrm{.}0\mathrm{.}0$ to $29\mathrm{.}18\mathrm{.}127\mathrm{.}255$ has been aggregated to $29\mathrm{.}18\mathrm{.}0\mathrm{.}0/17.$ However, there is a gap of $1024$ unassigned addresses from $29\mathrm{.}18\mathrm{.}60\mathrm{.}0$ to $29\mathrm{.}18\mathrm{.}63\mathrm{.}255$ that are suddenly assigned to a host using a different outgoing line. Is it now necessary to split up the aggregate address into its constituent blocks, add the new block to the table, and see if any re$-$aggregation is possible? If not, what can be done instead?

In IP$,$ the checksum covers only the header and not the data. Why do you suppose this design was chosen?

IPv$6$ uses $16-$byte addresses. If a block of $1$ million addresses is allocated every picosecond, how long will the addresses last?

As we saw in class, the IPv$6$ address has been divided into two $64$ bit parts, of which only the top $64$ is assigned by an addressing authority. Using the conditions of Problem $8,$ now how long will it take to allocate the whole IPv$6$ address space?

Assuming that all routers and hosts are working properly and that all software in both is free of errors, is there any chance, however small, that a packet will be delivered to the wrong destination?

Just for 'fun', a little think piece $($actually $2)$ for some extra credit. Starting on Page $472$ Tanenbaum describes ARP.$$ Read it and think about it$.$ We have seen something similar before.

a$)$ What was it and how is it similar?

b$)$ There is a simpler way of seeing the problem that makes it a degenerate case of something else. What is it and how would it work?

This is a hard one. Don't feel you have to attempt it or be disappointed if you don't solve it$.$ But if you do$,$ I think you will enjoy the experience. If you do$,$ there will be extra credit for getting right, but won't take off for not getting it$.$ ;-)