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10.7: Epilog and Exercises

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  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

  • CIDR was a deceptively simple idea. At first glance it is a straightforward extension of the subnet concept, moving the net/host division point to the left as well as to the right. But it has ushered in true hierarchical routing, most often provider-based. While CIDR was originally offered as a solution to some early crises in IPv4 address-space allocation, it has been adopted into the core of IPv6 routing as well.

    Interior routing – using either distance-vector or link-state protocols – is neat and mathematical. Exterior routing with BGP is messy and arbitrary. Perhaps the most surprising thing about BGP is that the Internet works as well as it does, given the complexity of provider interconnections. The business side of routing almost never has an impact on ordinary users. To an extent, BGP works well because providers voluntarily limit the complexity of their filtering preferences, but that seems to be largely because the business relationships of real-world ISPs do not seem to require complex filtering.

  • 10.8 Exercises

    Exercises are given fractional (floating point) numbers, to allow for interpolation of new exercises. Exercise 5.5 is distinct, for example, from exercises 5.0 and 6.0. Exercises marked with a ♢ have solutions or hints at 24.9 Solutions for Large-Scale IP Routing.

    0.5.♢ Consider the following IP forwarding table that uses CIDR.







    For each of the following IP addresses, indicate to what destination it is forwarded. 64 is 0x40, or 0100 0000 in binary.


    1.0. Consider the following IP forwarding table that uses CIDR. IP address bytes are in hexadecimal here, so each hex digit corresponds to four address bits. This makes prefixes such as /12 and /20 align with hex-digit boundaries. As a reminder of the hexadecimal numbering, “:” is used as the separator rather than “.”













    For each of the following IP addresses, give the next_hop for each entry in the table above that it matches. If there are multiple matches, use the longest-match rule to identify where the packet would be forwarded.

    (i) 81:3b:15:49
    (ii) 81:3c:56:14
    (iii) 81:3c:85:2e
    (iv) 81:4a:35:29
    (v) 81:47:21:97
    (vi) 81:43:01:c0

    2.0. Consider the following IP forwarding table, using CIDR. As in exercise 1, IP address bytes are in hexadecimal, and “:” is used as the separator as a reminder.











    (a). To what next_hop would each of the following be routed? 63:b1:82:15, 9e:00:15:01, de:ad:be:ef
    (b). Explain why every IP address is routed somewhere, even though there is no default entry. Hint: convert the first bytes to binary.

    3.0. Give an IPv4 forwarding table – using CIDR – that will route all Class A addresses (first bit 0) to next_hop A, all Class B addresses (first two bits 10) to next_hop B, and all Class C addresses (first three bits 110) to next_hop C.

    4.0. Suppose a router using CIDR has the following entries. Address bytes are in decimal except for the third byte, which is in binary.



    37.149.0000 0000.0/18


    37.149.0100 0000.0/18


    37.149.1000 0000.0/18


    37.149.1100 0000.0/18


    If the next_hop for the last entry were also A, we could consolidate these four into a single entry → A. But with the final next_hop as B, how could these four be consolidated into two entries? You will need to assume the longest-match rule.

    5.0. Suppose P, Q and R are ISPs with respective CIDR address blocks (with bytes in decimal), and P then has customers A and B, to which it assigns address blocks as follows:


    Q has customers C and D and assigns them address blocks as follows:

    (a).♢ Give forwarding tables for P, Q and R assuming they connect to each other and to each of their own customers.
    (b). Now suppose A switches from provider P to provider Q, and takes its address block with it. Give the changes to the forwarding tables for P, Q and R; the longest-match rule will be needed to resolve conflicts.

    5.5 Let P, Q and R be the ISPs of exercise 5.0. This time, suppose customer C switches from provider Q to provider R. R will now have a new entry → C. Give the changes to the forwarding tables of P and Q.

    6.0. Suppose P, Q and R are ISPs as in exercise 5.0. This time, P and R do not connect directly; they route traffic to one another via Q. In addition, customer B is multihomed and has a secondary connection to provider R; customer D is also multihomed and has a secondary connection to provider P. R and P use these secondary connections to send to B and D respectively; however, these secondary connections are not advertised to other providers. Give forwarding tables for P, Q and R.

    7.0. Consider the following network of providers P-S, all using BGP. The providers are the horizontal lines; each provider is its own AS.

    (a).♢ What routes to network NS will P receive, assuming each provider exports all its routes to its neighbors without filtering? For each route, list the AS-path.
    (b). What routes to network NQ will P receive? For each route, list the AS-path.
    (c). Suppose R now uses export filtering so as not to advertise any of its routes to P, though it does continue to advertise its routes to S. What routes to network NR will P receive, with AS-paths?

    8.0. Consider the following network of Autonomous Systems AS1 through AS6, which double as destinations. When AS1 advertises itself to AS2, for example, the AS-path it provides is ⟨AS1⟩.

     │                     :
     │                     :
     │                     :
    (a). If neither AS3 nor AS6 exports their AS3–AS6 link to their neighbors AS2 and AS5 to the left, what routes will AS2 receive to reach AS5? Specify routes by AS-path.
    (b). What routes will AS2 receive to reach AS6?
    (c). Suppose AS3 exports to AS2 its link to AS6, but AS6 continues not to export the AS3–AS6 link to AS5. How will AS5 now reach AS3? How will AS2 now reach AS6? Assume that there are no local preferences in use in BGP best-path selection, and that the shortest AS-path wins.

    9.0. Suppose that Internet routing in the US used geographical routing, and the first 12 bits of every IP address represent a geographical area similar in size to a telephone area code. Megacorp gets the prefix, based geographically in Chicago, and allocates subnets from this prefix to its offices in all 50 states. Megacorp routes all its internal traffic over its own network.

    (a). Assuming all Megacorp traffic must enter and exit in Chicago, what is the route of traffic to and from the San Diego office to a client also in San Diego?
    (b). Now suppose each office has its own link to a local ISP, but still uses its IP addresses. Now what is the route of traffic between the San Diego office and its neighbor?
    (c). Suppose Megacorp gives up and gets a separate geographical prefix for each office, eg for San Diego and for Boston. How must it configure its internal IP forwarding tables to ensure that its internal traffic is still routed entirely over its own network?

    10.0. Suppose we try to use BGP’s strategy of exchanging destinations plus paths as an interior routing-update strategy, perhaps replacing distance-vector routing. No costs or hop-counts are used, but routers attach to each destination a list of the routers used to reach that destination. Routers can also have route preferences, such as “prefer my link to B whenever possible”.

    (a). Consider the network of 9.2 Distance-Vector Slow-Convergence Problem:

    The D–A link breaks, and B offers A what it thinks is its own route to D. Explain how exchanging path information prevents a routing loop here.
    (b). Suppose the network is as below, and initially each router knows about itself and its immediately adjacent neighbors. What sequence of router announcements can lead to A reaching F via A→D→E→B→C→F, and what individual router preferences would be necessary? (Initially, for example, A would reach B directly; what preference might make it prefer A→D→E→B?)
    │        │        │
    │        │        │
    │        │        │

    (c). Explain why this method is equivalent to using the hopcount metric with either distance-vector or link-state routing, if routers are not allowed to have preferences and if the router-path length is used as a tie-breaker.

    11.0. In the following AS-path from AS0 to AS4, with customers lower than providers, how far can a customer route of AS0 be exported towards AS4? How far can a customer route of AS4 be exported towards AS0?

         /   \
        /     \
       /       AS2--peer--AS3
      /                      \
    AS0                       AS4

    12.0. Complete the proof of the no-valley theorem of 10.6.9 BGP Relationships to include peer-to-peer links.

    (a). Show that the existing argument also works if the Ai-to-Ai+1 link was peer-to-peer rather than provider-to-customer, establishing that an upwards link cannot appear to the right of a peer-to-peer link.

    (b). Show that the existing argument works if the Ak-1-to-Ak link was peer-to-peer rather than customer-to-provider, establishing that a downwards link cannot appear to the left of a peer-to-peer link.

    (c). Show that there cannot be two peer-to-peer links.

  • 10.7: Epilog and Exercises is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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