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Internet Draft                               Alia Atlas, Ed (Avici Systems)
Expires: November 2004



             U-turn Alternates for IP/LDP Local Protection


               draft-atlas-ip-local-protect-uturn-00.txt


Status of this Memo


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Abstract



   This document extends the architecture and selection process for
   providing local protection for IP unicast and/or LDP traffic in the
   event of a single link or node failures until the router has
   converged.  When computing the primary next-hop for a prefix, a
   router S also determines an alternate next-hop which can be used if
   the primary next-hop fails.  The alternate can be either a loop-free
   alternate, as described elsewhere, or a U-turn alternate, which goes
   to a neighbor whose primary next-hop to the prefix is the router S,
   but that neighbor has a loop-free node-protecting alternate, which
   thus does not go through router S to reach the destination prefix.


   A router may indicate the capability to break U-turns on its links;
   only such links can be used as U-turn alternate next-hops.  To signal




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   this capability, a router must be capable of detecting when it
   receives traffic for a given destination from a primary neighbor for
   that destination and the router must forward that traffic to the
   selected alternate next-hop.


   To support U-Turn alternates and node-protection, a router must know
   what links its neighbor can consider for alternates, how a neighbor
   will select an alternate, and upon which interfaces a neighbor can
   break U-turns.  This document defines a common selection criteria
   which MUST be followed.  In addition, it is necessary to signal two
   capabilities per link.  First is whether U-turns can be broken on the
   link and second is whether the link should be used as an alternate,
   as determined administratively.







































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Contents


  1  Introduction  .................................................  3
  2  Terminology  ..................................................  5
  3  Finding an Alternate  .........................................  6
  3.1  U-Turn Alternates  ..........................................  7
  3.1.1 ECMP U-Turn Neighbors  ..................................... 11
  3.1.2 U-Turn Neighbor's Alternate  ............................... 12
  3.1.2.1  Computing Alternate So Primary Next-Hop Can Use
           Computing Router for U-Turn Alternate  .................. 14
  3.2  Selection of an Alternate  .................................. 15
  3.2.1  IP Local Protection Alternate Capability  ................. 15
  3.2.2  U-Turn Breaking Capability  ............................... 16
  3.2.3  Characterization of Neighbors  ............................ 16
  3.2.4  Selection Procedure  ...................................... 17
  3.2.4.1  Alternate Selection with One Primary Neighbor  .......... 17
  3.2.4.2  Alternate Selection with Multiple Potential
           Primary Neighbors  ...................................... 18
  4  Using an Alternate  ........................................... 19
  4.1  Breaking U-Turns  ........................................... 19
  4.1.1  Broadcast and NBMA Interfaces  ............................ 21
  4.2  Responding to a Local Failure  .............................. 22
  5  Requirements on LDP Mode  ..................................... 22
  6  Routing Aspects  .............................................. 22
  7  U-Turn Alternates Interactions with Tunnels  .................. 24
  8  Security Considerations  ...................................... 24
  9  Intellectual Property Considerations  ......................... 24
  10 Full Copyright Statement  ..................................... 24
  11 References  ................................................... 25
  12 Authors Information  .......................................... 26
  13 Editor's Information  ......................................... 27
  Appendix A  U-turn Alternate Proofs  ............................. 27



1. Introduction


   Applications such as VoIP and pseudo-wires can be very sensitive to
   traffic loss, such as occurs when a link or router in the network
   fails.  A router's convergence time is generally on the order of
   seconds; the application traffic may be sensitive to losses greater
   than 10s of milliseconds.


   This document extends the architecture defined in [LOOP-FREE], which
   allows a router whose local link has failed to forward traffic to a
   pre-computed alternate until the router installs the new primary
   next-hops based upon the changed network topology.


   The existence of suitable loop-free alternate next-hops is topology




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   dependent.  This document defines a second type of alternate next-
   hop, known as a u-turn alternate, and provides the common behavior
   and selection method necessary to allow u-turn alternates to
   function.


   The topology in Figure 1 is an example where there is no loop-free
   alternate from S to D, but there is a u-turn alternate.


                \
              @@@   /__
                /   \     +--+--+
               +----------| N_1 |
               |     5    +-----+
               |               |
           +---+-+             |
           |  S  |          @  |10
           +-----+          @  |
              |            \@/ |
           |  |5               |
          \|/ |                |
              |                |
           +-----+             |
           |  P  |          +-----+
           +-----+          | R_1 |
                |           +-----+
            |   |5             |
           \|/  |           |  |10
                |          \|/ |
               +-----+         |
               |  D  |---------+
               +-----+


                    Figure 1: Topology with U-turn Alternate


   In Figure 1, there is no loop-free alternate for S to use to reach D.
   This is because the costs are such that N_1 uses S as its primary
   neighbor; therefore if S were to send the traffic to N_1, it would
   loop back to S.  If both S and N_1 support the mechanisms defined in
   this document, then S could use N_1 as a u-turn alternate.  Traffic
   destined to D which was sent by S to N_1 would be forwarded by N_1 to
   R_1, N_1's loop-free node-protecting alternate.


   As with loop-free alternates, the existence of suitable u-turn
   alternates is topology dependent; it extends the coverage on topology
   above that seen with just loop-free alternates.



2. Terminology




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   SPT --- Shortest Path Tree


   D --- The destination router under discussion.


   S --- The source router under discussion. It is the viewpoint from
                which IP/LDP Local Protection is described.


   P --- The router which is the primary next-hop neighbor to get from S
          to D. Where there is an ECMP set for the shortest path from S
          to D, these will be referred to as P_1, P_2, etc.


   N_i --- The ith neighbor of S


   R_i_j --- The jth neighbor of N_i, the ith neighbor of S.


   Distance_!S(N_i, D) --- The distance of the shortest path from N_i to
          D which does not go through router S.


   Distance_opt(A, B) or D_opt(A,B) --- The distance of a shortest path
          from A to B.


   Reverse Distance of a node X --- This is the Distance_opt(X, S).


   Loop-Free Alternate --- This is a next-hop that is not a primary
          next-hop whose shortest path to the destination from the
          alternate neighbor does not go back through the router S.


   U-Turn Alternate --- This is an alternate next-hop of S that goes to
          a neighbor N_i, whose primary next-hop is S, and whose
          alternate neighbor does not go back trough the router S, which
          may therefore use the link to N_i as an alternate.


   Link(A->B) --- A link connecting router A to router B.


   ____\   This is an arrow indicating the primary next-hop towards D.
       /


   @@@@\   This is an arrow indicating the alternate next-hop towards D
       /


   Primary Neighbor --- One or more of the primary next-hops for S to
        reach the destination D goes directly to this neighbor.


   Loop-Free Neighbor --- A Neighbor N_i which is not the primary
        neighbor and whose shortest path to D does not go through S.


   U-Turn Neighbor --- A neighbor N_i is a U-Turn neighbor of router S
        with respect to a given destination D if and only if S is a




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        primary neighbor of  N_i to reach the destination D for all
        primary paths which go through S to reach D.


   ECMP U-Turn Neighbor --- A neighbor N_i which is a U-Turn neighbor
        and which has at least one equal cost path to reach D that does
        not go through S as well as the path(s) which do go through S to
        reach D.


   Looping Neighbor --- A neighbor N_i is a looping neighbor of router S
        with respect to a given destination D if and only if S is not
        the primary next-hop of N_i on at least one optimal path from S
        to D which also goes through S.


   Loop-Free Node-Protecting Alternate --- This is a path via a Loop-
        Free Neighbor N_i which does not go through the particular
        primary neighbor of S which is being protected to reach the
        destination D.


   Loop-Free Link-Protecting Alternate --- This is a path via a Loop-
        Free Neighbor N_i which does go through the particular primary
        neighbor of S which is being protected to reach the destination
        D.


   U-Turn Node-Protecting Alternate --- This is a path via a U-Turn
        Neighbor N_i which does not go through S or any of S's primary
        neighbors to reach the destination D.


   U-Turn Link-Protecting Alternate --- This is a path via a U-Turn
        Neighbor N_i which does not go through S but does go through one
        or more of S's primary neighbors to reach the destination D.



3. Finding an Alternate


   As with primary next-hops, an alternate next-hop is discussed in
   relation to a particular destination router D.  For this discussion,
   the following terminology, illustrated in Figure 2, will be used.
   The router on which the search for an alternate is proceeding is S.
   The primary next-hop neighbor to get from S to D is P.  Additionally,
   S has various neighbors which will be labeled N_1, N_2, etc.  Where
   an arbitrary neighbor of S is intended, N_i will be used.  Routers
   which are neighbors of neighbors will be labeled R_1, R_2, etc.
   Where an arbitrary neighbor of a neighbor N_i is intended, it will be
   referred to as R_i_j.



                                                 +-----+
                               \          /    _| R_2 |




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                    +-----+__    \|     |/    / +-----+
                    | N_3 |  \   -+     +- __/       \
                    +-----+   \____       /           \
                     \             \     /             \
                      \             +-----+             \
                       \           _| N_2 |              \
                        |       __/ +-----+               \
                         \     /         \                 |
                          \   /     /     \_               |
                        +-----+   |/        \              |
                        |  S  |   +-         \  +-----+    |
                        +-----+               \_| R_1 |    |
                    /    /   \                  +-----+    |
                  |/    /     \                  /         |
                  +-   /       \                /          |
                      /       +-----+          /   /       |
              +-----+/        | N_1 |         /  |/        |
              |  P  |         +-----+        /   +-        |
              +-----+            \          /             /
                 \             \  \__      /             /
              \   \             \|   \    /             /
               \|  \            -+    +-----+          /
               -+   \_________________|  D  |---------/
                                      +-----+


                      Figure 2:  Topology for Terminology


   As described in [LOOP-FREE], a neighbor can provide a loop-free
   alternate if Equation 1 is true.


      Distance_!S(N_i, D) < Distance_opt(N_i, S) + Distance_opt(S, D)


              Equation 1: Criteria for a Loop-Free Alternate



3.1 U-Turn Alternates


   In examining realistic networks, it was seen that loop-free
   alternates did not provide adequate coverage for the traffic between
   all the source-destination pairs.  This means that it is not
   sufficient to expand the set of points where S can cause its traffic
   to join the SPT to be only S's neighbors.


   The next possibility is to see whether S could expand its SPT join
   points to include router S's neighbors' neighbors.  This is only of
   interest if S had no loop-free node-protecting alternate available
   for the given destination D.  If there are no loop-free alternates,
   that implies that all of S's non-primary neighbors will send traffic




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   for D back to S.


                                    +-----+  \
                                    | N_4 |\  \|      /  +-----+
                                    +-----+ \ -+    |/  /| R_3 |
                                      /      \      +- / +-----+
                                     /     15 |      _/      |
                                    |         |   5 /        |
                                    | 50       \   /         |
                +-----+             |         +-----+        |
                | N_2 |            /   ______/| N_3 |        |
                +-----+ \         /   /       +-----+     70 |
                 |    \  \|      /   / 30   /                |
               10|     \ -+     /   /     |/                 |
                 |   15 \      +-----+    +-                 |
              @  |       \-----|  S  |                       |
              @  |     /       +-----+                       |
             \@/ |     @@@@        |                         |
                 |     \      |    |10                      /
                 |            |    |                       /
              +-----+        \_/   |                      /
              | R_2 |           +-----+                  /
              +-----+           |  P  |                 /
                 \              +-----+                /
              \   \ 40            /                   /
               \|  \          10 /  /                /
               -+   \           / |/                /
                    +-----+    /  +-               /
                    | R_1 |---/                   /
                    +-----+                      /
                        \     10            +-----+
                     \   \------------------|  D  |
                      \|                    +-----+
                      -+


                        P is primary next-hop of S
                   N_2 and N_3 are U-Turn Neighbors of S
                      N_4 is a Looping Neighbor of S


   Figure 3: Terminology of Looping Neighbors and Example U-Turn Alternate


   The topology shown in Figure 3 gives an example where router S has no
   loop-free alternate to reach D.  Router S uses P as its primary
   next-hop (distance of 30).  S has three other neighbors, but all of
   them will send traffic for D back through S.


   In order for S to be able to use a neighbor's neighbor as a point
   where S's traffic can rejoin the SPT, S must be able to direct




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   traffic to a neighbor N_i and that neighbor N_i must be able to
   direct traffic to one of its appropriate neighbors R_i_j instead of
   along the SPT.  In deciding to use its alternate, S has the ability
   to force traffic destined to D to go through the selected alternate
   neighbor N_i.  However, for S to reach the appropriate neighbor's
   neighbor R_i_j, the selected neighbor N_i  must be able to detect
   that the traffic should not be sent along its shortest path to D,
   which would lead back to S, and should instead be sent to its
   appropriate neighbor R_i_j.


   This detection and forwarding contrary to the SPT by N_i must occur
   without any communication from S upon the failure which would cause S
   to redirect the traffic to N_i.  There is already communication from
   S to N_i indicating when a link has failed, but such communication
   would cause the fail-over of traffic to take longer than the desired
   10s of milliseconds if N_i depended upon it to decide that it should
   forward contrary to the SPT.  In essence, the assumption being made
   is that the time budget to recover traffic in the event of a failure
   is being consumed by router S's detection of the failure and switch-
   over to its pre-computed alternate.


   With that assumption, it is clear that N_i's behavior to forward
   traffic contrary to the SPT on receiving traffic from S must be a
   default behavior.  This default behavior must not change how traffic
   is forwarded unless a forwarding loop is detected; basic IP
   forwarding must be preserved in the absence of a failure.  Router N_i
   can detect if it is receiving traffic from a neighbor to whom it
   would forward that traffic; this detection is done via a reverse
   forwarding check.  Such a reverse forwarding check should consider
   not only if traffic is received on the same interface as it would be
   forwarded out, but whether it was received from the same neighbor to
   whom it would be forwarded.  Normally, if traffic fails a reverse
   forwarding check (i.e. would be forwarded out to the same neighbor as
   received from), then that traffic is either discarded or forwarded
   into a loop.  In IP/LDP Local Protection, however, traffic that fails
   a reverse forwarding check is forwarded to the appropriate R_i_j, if
   available, rather than being discarded.


   First, this detection can be used by N_i to determine not to forward
   the traffic according to the SPT (or discard it), but to instead send
   the traffic to N_i's appropriate neighbor R_i_j.  N_i can only detect
   the traffic to be redirected if S sends it directly to N_i, which is
   under S's control, and if N_i would send that traffic back to S,
   according to the SPT.  This motivates the definition of a Looping
   Neighbor and a U-turn Neighbor.


        Looping Neighbor --- A neighbor N_i is a looping neighbor of
                             router S with respect to a given




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                             destination D if any of N_i's shortest
                             paths to D goes through S but S is not the
                             primary next-hop of  N_i for all those
                             paths through S.


        U-Turn Neighbor --- A neighbor N_i is a U-Turn Neighbor of
                            router S with respect to a given destination
                            D if and only if S is a primary next-hop of
                            N_i to reach the destination D for all
                            primary paths which go through S to reach D.



   A Looping Neighbor cannot provide any type of alternate.  A U-Turn
   neighbor may be able to provide an alternate.  In Figure 3, S has two
   U-Turn Neighbors N_2 and N_3 and one looping neighbor N_4.  For
   neighbor N_4, the path to D is N_3 to S to N_1 to R_1 to D; because
   there is a node between N4 and S on the path, N_4 is a looping
   neighbor.


   Mathematically, for a neighbor N_i to be a U-Turn neighbor, it is
   necessary that Equation 2, which is the exact opposite of Equation 1,
   be true.  If the equality is true, that means that there are multiple
   optimal paths, at least one of which goes through S and one does not.
   Such a neighbor may be an ECMP U-Turn neighbor or may be a looping
   neighbor.


     Distance_!S(N_i, D) >= Distance_opt(N_i, S) + Distance_opt(S, D)


                  Equation 2: U-Turn or Looping Neighbor


   Additionally, all optimal paths to reach D that go via S must be via
   a direct link between N_i and S.  If a neighbor N_i satisfies
   Equation 2 and all optimal paths to reach D that go via S are via a
   direct link between N_i and S, then it is a U-turn neighbor.


   The above clarifies what a U-Turn neighbor is and how such a neighbor
   can detect traffic from router S and redirect it.  It is still
   necessary to describe where the U-Turn neighbor N_i redirects the
   traffic.


   It is also necessary to describe on what interfaces a router N_i must
   consider that it could be a U-Turn neighbor.  A router N_i must
   detect traffic coming from its primary neighbor and redirect that
   traffic to the appropriate alternate.  This is termed breaking a U-
   turn because it redirects traffic to the alternate and avoids
   forwarding the traffic back into the U-turn loop.  If a router
   advertises that an interface is U-turn capable, meaning that the
   router can break U-turns on traffic entering that interface, then the




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   router must break U-turns for all traffic coming from a primary
   neighbor.  The router is not responsible for breaking U-turns for
   traffic from potential primary neighbors which were not selected.


3.1.1. ECMP U-Turn Neighbors


   The above definition for U-Turn Neighbor allows a neighbor, which has
   equal cost paths (an ECMP set) where one of those paths goes directly
   to S and others may not, to be a U-Turn Neighbor.   Consider the
   topology shown in Figure 4.  In this figure, N_1 has three equal-cost
   paths to reach D which are N_1 - S - P - D, N_1 - R_1 - D, and N_1 -
   R_2 - D.   Because the only path that goes through S goes directly
   through S, N_1 is a U-Turn neighbor of S.


                                +-----+------\
                             /--| N_1 |   5   \
                         /  /   +-----+\       \       +-----+
                       |/  / 10     \   \ 15    \------| R_3 |
                       +- /       10 \   \             +-----+
                         /            |   \  \             |
                      +-----+     |   |    \  \|           |
                      |  S  |    \|/  |     \ -+           |  |
                      +-----+         |      \             | \|/
                        /          +-----+    \            |
                   /   /  10       | R_1 |     \         15|
                 |/   /            +-----+      \          |
                 +-  /           /   /        +-----+      |
                    /          |/   / 20      | R_2 |      |
                 +-----+       +-  /          +-----+      |
                 |  P  |          |      /__  15 /         |
                 +-----+          |      \      /          |
                    \             |    /-------/        +-----+
                  \  \ 10         |   /                 |  X  |
                   \| \           |  /            /__   +-----+
                   -+  \       +-----+            \       / 15
                        \------|  D  |-------------------/
                               +-----+


                      Figure 4: ECMP U-Turn Neighbor


      Distance_!S(N_i, D) = Distance_opt(N_i, S) + Distance_opt(S, D)


                         Equation 3: ECMP Neighbor


   A neighbor is an ECMP neighbor if Equation 3 is true.  S does not
   know whether a neighbor N_i supports ECMP or how that neighbor
   selects among the equal cost paths.  Recall that a node will only
   break U-Turns on the interfaces connected to that node's primary




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   neighbors.


   Consider the topology in Figure 5, where N_2 has three equal cost
   primary neighbors which are S, N_1 and R_1.  If N_2 were to select
   only N_1 as its primary neighbor, then N_2 would break U-Turns only
   on traffic received from N_1 and not on traffic received from S.
   Therefore, S cannot consider N_2 as an ECMP U-Turn neighbor because S
   cannot rely upon N_2 to break U-turns for traffic destined to D which
   is received from S.


   If N_2 has multiple paths to reach D which go through S and not all
   such paths have a first hop which is a direct link between N_2 and S,
   then S cannot use N_2 as a U-Turn neighbor.


                                           10    +-----+
                              /   /--------------| N_2 |\  \
                            |/   /               +-----+ \  \|
                            +-  /             /----/ 5    \ -+
                               /             /      /      \
                              /      5  +-----+   |/        |
                             /     /----| N_1 |   +-        | 5
                          +-----+ /     +-----+             |
                          |  S  |/   /                   +-----+
                          +-----+  |/                    | R_1 |
                        /  /       +-                    +-----+
                      |/  / 5                                /
                      +- /                                  /  15
                  +-----+                         /--------/
                  |  P  |                        /
                  +-----+                       /    /
                      \                        /   |/
                   \   \ 5            +-----+ /    +-
                    \|  \-------------|  D  |/
                    -+                +-----+


       Figure 5: ECMP Neighbor Which is Not an ECMP U-Turn Neighbor


   If all paths from an ECMP neighbor N_i to destination D which go via
   S have S as the primary neighbor, then S can use N_2 as a ECMP U-Turn
   neighbor.


3.1.2. U-Turn Neighbor's Alternate


   The requirement for the neighbor's neighbor R_i_j to which a U-Turn
   Neighbor N_i will redirect traffic from S destined to D is that the
   traffic not come back to S.  Equation 4 gives this requirement that
   R_i_j must have a path to D that does not go through S which is
   shorter than the path to D going via S.  This can be expressed as




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   follows.


    Distance_!S(R_i_j, D) < Distance_opt(R_i_j, S) + Distance_opt(S, D)


                Equation 4: Loop-Free Neighbor's Neighbor


   Equation 4 means that a U-Turn neighbor's alternate cannot be an ECMP
   set which contains that U-Turn neighbor.


   If N_i is a U-Turn neighbor, then the optimal path to D from N_i is
   via S; the path is N_i - S - ... - D.  Therefore, if the optimal path
   from R_i_j goes through N_i, it must also go through S.  Thus, if
   Equation 4 holds for a R_i_j, that implies that the path from R_i_j
   does not go through N_i.   This may be made clearer by considering
   Figure 6 below.  If the shortest path from R_1 to D went through N_1,
   then it would go through S as well, because the shortest path from
   N_1 to D is through S.  Therefore, if the shortest path from R_1 does
   not go through S, it cannot have gone through N_1.


                                            5    +-----+      @
                              /   /--------------| N_2 |\     @
                            |/   /               +-----+ \    \@/
                            +-  / /@\                     \
                               /  @                        \
                              /  @                          |
                             /                              | 15
                          +-----+                           |
                          |  S  |                        +-----+
                          +-----+                        | R_1 |
                        /  /                             +-----+
                      |/  / 5                                /
                      +- /                                  /   5
                  +-----+                         /--------/
                  |  P  |                        /
                  +-----+                       /    /
                      \                        /   |/
                   \   \ 5            +-----+ /    +-
                    \|  \-------------|  D  |/
                    -+                +-----+


                    Figure 6: U-Turn Alternate Example



        This is a proof by contradiction showing that if a neighbor's
        neighbor Ri,j is loop-free with respect to S, then it is also
        loop-free with respect to Ni.


        If the optimal path from Ri,j to D goes through Ni, then




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             D_!S,N_i(R_i,j , D) = D_opt(R_i,j, N_i) + D_opt(Ni, D)


        Because N_i is a U-Turn neighbor, the shortest path to D is via
        S so:
                  D_opt(N_i, D) = D_opt(N_i, S) + D_opt(S, D)


        The previous two equations can be combined to form the
        following:
        D_!S,N_i(R_i,j , D) = D_opt(R_i,j, N_i) + D_opt(N_i, S) + D_opt(S, D)


        The following observation can be made because Distanceopt(Ri,j,
        S) is the minimum distance of a path to get from Ri,j to S, so
        the path to do so via Ni cannot have a lower distance.
              D_opt(R_i,j, S) = D_opt(R_i,j, N_i) + D_opt(N_i, S)


        This can be combined with the previous equation to yield
               D_!S,Ni(R_i,j , D) = D_opt(R_i,j, S) + D_opt(S, D)


        This equation is the opposite of Equation 4.  Thus, if Equation
        4 is true, then the optimal path from Ri,j to D does not go
        through Ni.


          Proof 1: Proof that a Loop-Free R_i_j (Neighbor's Neighbor)
                       Implies R_i_j Doesn't Loop to Neighbor N_i


   The proof given in Proof 1 means that if a U-Turn Neighbor N_i has
   itself a neighbor R_i_j that satisfies Equation 4, then that router
   R_i_j is itself a loop-free alternate with respect to N_i.
   Regrettably, the converse does not apply; just because R_i_j is
   loop-free with respect to N_i and D does not mean that R_i_j is
   loop-free with respect to S and D.


3.1.2.1. Computing Alternate So Primary Next-Hop Can Use Computing
         Router for U-Turn Alternate


   Each router independently computes the alternate that it will select.
   It is necessary to consider what alternate S could select so that S's
   primary next-hop P could use S as a U-Turn alternate.  In other
   words, consider the computation when S is in the role of a neighbor
   to the router doing the computation.


   To describe this using router S as the computing router, S would need
   to verify that both Equation 1 is true and that S's selected
   alternate N_i does not have a path that goes through P.


   This can be described as if N_i were doing the computation as
   follows.  The criteria described in Equation 4 requires that if a U-
   Turn neighbor N_i is to be used as a U-Turn alternate then N_i must




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   have a loop-free alternate which avoids N_i's primary neighbor S.
   Such an alternate will be referred to as a loop-free node-protecting
   alternate.  N_i can identify loop-free alternates by checking the
   validity of Equation 5.  Additionally, N_i will need to tell whether
   the path from a loop-free R_i_j to D goes through N_i's primary
   next-hop neighbor, S.


            D_!S(R_i_j, D) < D_opt(R_i_j, N_i) + D_opt(N_i, D)


                Equation 5: Neighbor's Loop-Free Alternate



3.2 Selection of an Alternate


   A router S may have multiple alternates that it must decide between.
   A common selection method is necessary to support U-Turn Alternates.
   This is because it is not sufficient for router S to know that its
   U-Turn neighbor N_i has itself a neighbor R_i,j that is loop-free
   with respect to S and D if S does not also know that N_i will select
   that R_i,j or another with the same properties.


   The same set of failure scenarios that can be protected against with
   a loop-free alternate is of interest with a u-turn alternate.
   Similarly, there is the same interaction with maximum costed links
   and broadcast interfaces as described in [LOOP-FREE].  In addition,
   if all links from a neighbor N_i to a neighbor's neighbor R_i_j have
   a reverse cost of LSInfinity, then router S cannot consider that N_i
   could provide a U-turn alternate via R_i_j.


3.2.1. IP Local Protection Alternate Capability


   There are a number of different reasons why an operator may not wish
   for a particular interface to be used as an alternate.  For instance,
   the interface may go to an edge router or the interface may not have
   sufficient bandwidth to contain the traffic which would be put on it
   in the event of failure.


   Because a router's neighbors may desire to use that router to provide
   a U-turn alternate, a router must flood to its neighbors which
   interfaces are not capable of providing alternates.  This information
   allows a router's neighbors to accurately determine whether or not
   the router has a loop-free node-protecting alternate.


   The extensions to signal this local-protection alternate capability
   are described in [OSPF-LOCAL-PROTECT] and [ISIS-LOCAL-PROTECT].


3.2.2. U-Turn Breaking Capability





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   A router S may only use its neighbor N_u as a U-Turn alternate if N_u
   indicates that it is capable of breaking U-Turns on a link between S
   and N_u.  The capability to break U-Turns must be signaled for a link
   in order for S to determine that it can use N_u as a U-Turn
   alternate.  By default, S MUST assume that a neighbor cannot provide
   a U-Turn alternate unless that neighbor indicates the U-Turn breaking
   capability on a link between S and N_u.  This U-Turn breaking
   capability need only be flooded to a node's neighbors.


   The extensions to signal the U-turn breaking capability are also
   described in [OSPF-LOCAL-PROTECT] and [ISIS-LOCAL-PROTECT].



3.2.3 Characterization of Neighbors


   Each neighbor N_i can be categorized as to the type of path it can
   provide to a particular destination D.  Once the primary paths have
   been determined and removed from consideration, each neighbor can be
   characterized as providing a path in one of the following categories
   for a particular destination D.  It is possible for a neighbor to
   provide both the primary path and a loop-free link-protecting
   alternate.  The path through the neighbor N_i is either a:



        (A) Loop-Free Node-Protecting Alternate --- not a primary path
        and the path avoids both S, the interfaces connecting S to its
        primary neighbors, and its primary neighbors on the path to D.


        (B) Loop-Free Link-Protecting Alternate --- not a primary path
        and the path avoids S and the interfaces connecting S to its
        primary neighbors, but goes through a primary neighbor on the
        path to D.


        (C) U-Turn Node-Protecting Alternate --- the neighbor is a U-
        Turn neighbor or a ECMP U-Turn neighbor and the alternate that
        the neighbor has selected does not go through a primary neighbor
        of S to reach D.


        (D) U-Turn Link-Protecting Alternate --- the neighbor is a U-
        Turn neighbor or a ECMP U-Turn neighbor and the alternate that
        the neighbor has selected goes through a primary neighbor of S
        to reach D.


        (E) Unavailable --- because the neighbor is looping or a U-Turn
        neighbor which didn't itself have a loop-free node-protecting
        path, or a U-Turn neighbor which couldn't break U-Turns or the
        links to the neighbor are configured to not be used as
        alternates.  The neighbor may also be disqualified because it is




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        connected to S solely via broadcast interfaces which also have
        primary next-hops.



3.2.4. Selection Procedure


   Once the neighbors have been categorized, a selection can be made.
   The selection should maximize the failures which can be protected
   against.  A node S can only be used to break U-turns by its primary
   neighbors if S has a loop-free node-protecting alternate.


   The selection procedure depends on whether S has a single potential
   primary neighbor or multiple potential primary neighbors.  A router S
   is defined to have a single potential primary neighbor only if there
   are no equal cost paths that go through any other neighbor; i.e., a
   router S cannot be considered to have a single potential primary
   neighbor just because S does not support ECMP or just because S
   selects as primary next-hops links to only one potential primary
   neighbor.


3.2.4.1. Alternate Selection with One Primary Neighbor


   Because a router S can only be used to break U-Turns by its primary
   neighbor if S selects a loop-free node-protecting alternate, the
   following rules MUST be followed when selecting an alternate. This
   describes a policy which reduces the computational complexity
   associated with identifying the u-turn alternates.


        then S MUST select one of those alternates. Let M be the set of
        neighbors which provide loop-free node-protecting alternates.
        If S has multiple loop-free node protecting alternates, then S
        MUST select the best alternate through a N_k such that:


               D_!S(N_k, D) - D_opt(N_k, P) = min_forall m in M
                               (D_!S(m, D) - D_opt(m, P))


                Equation 6: Selection Among Multiple Loop-Free
                             Node-Protecting Alternates


        where P is the primary neighbor of S.


        To rephrase the above to consider the S is the node looking for
        a U-Turn alternate, the way of selecting among loop-free node-
        protecting alternates above, ensures that N_i's primary neighbor
        S can determine which alternate was picked by N_i.  For S to
        know that S's U-Turn neighbor N_i can provide a loop-free node-
        protecting alternate, S must know if





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            min_forall j in J ( D_!S(R_i_j, D) - D_opt(R_i_j, S) )
                                 < D_opt(S, D)


                Equation 7: Determination if a U-Turn Neighbor
                            can provide a U-Turn Alternate


        If a router obeys Equation 6 when selecting among multiple
        loop-free node-protecting alternates, as it MUST for IP/LDP
        Local Protection, this allows S to determine exactly which
        alternate was selected by N_i without needing to know the each
        D_!S(R_i_j).  Equation 7 allows S to determine that N_i has a
        loop-free node-protecting alternate.  Equation 6 allows S to
        know exactly which alternate will be selected so that S can
        determine whether that alternate protects against S's primary
        neighbor as well.  If there are multiple neighbors which provide
        the minimum as expressed in Equation 6, then a router can select
        among them arbitrarily.


        2. If a router S has no loop-free node-protecting alternates,
        then S's alternate selection has no consequences for its
        neighbors because S cannot provide a U-Turn alternate.
        Therefore, S can select freely among the loop-free link-
        protecting alternates, u-turn node-protecting alternates and u-
        turn link protecting alternates which S has available.  Clearly
        selecting a u-turn node-protecting alternate, if one is
        available, will provide node-protection, while the other options
        will not.  Selection among these categories is a router-local
        decision.


        3.  If S has neither loop-free node-protecting alternates,
        loop-free link-protecting alternates, u-turn node-protecting
        alternates, nor u-turn link-protecting alternates, then S has no
        alternate available for traffic to the destination D from the
        source S.


3.2.4.2. Alternate Selection with Multiple Potential Primary Neighbors


   The selection among multiple equal cost paths is a router-local
   decision.  Therefore, a router N_i cannot know which of the potential
   primary neighbors that S will choose to use.


   As described in Section 3.1.2.1, N_i can only select S for its U-Turn
   alternate if any potential primary neighbor which S might select,
   except for N_i itself, will not go via N_i to reach the destination
   D.


   Since a router S has multiple potential primary neighbors, router S
   MUST select one or more alternates for breaking U-Turns from among




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   next-hops to its potential primary neighbors.  If router S does not
   have a potential primary neighbor that is node-protecting for a
   particular primary next-hop, that indicates that the particular
   primary neighbor will not use S as a U-turn alternate.


   Router S need not use the same alternate(s) for breaking U-Turns on
   traffic received from a primary next-hop as for when the primary
   next-hop fails.  The alternate(s) used when a primary next-hop fails
   are a router-local decision.


4. Using an Alternate


   If an alternate is available, it is used in two circumstances.  In
   the first circumstance, it is used to redirect traffic received from
   a primary next-hop neighbor.  In the second circumstance, it is used
   to redirect traffic when the primary next-hop has failed.  As
   mentioned in Section 3.2.4.2, for destinations with multiple
   potential primary neighbors, the alternates used for each purpose
   need not be the same.


4.1. Breaking U-Turns


   If one ignores potential security redirection, IP forwarding is a
   purely destination based algorithm.  Traffic is forwarded based upon
   the destination IP address, regardless of the incoming interface.


   As previously described in Section 3.1.2, IP/LDP Local Protection
   requires that a U-Turn neighbor be capable of detecting traffic
   coming from the primary next-hop neighbor and redirecting it to the
   alternate, if an alternate which is node-protecting is available.
   This becomes the new default behavior.  This behavior is described
   below.  A router which indicates that it is capable of breaking U-
   Turns on an interface MUST obey the following behavior on that
   interface.


     For an IP destination
         If packet received on interface connected to a primary neighbor {
             if the interface is U-Turn Breaking Capable {
                 if primary next-hop has a loop-free
                    node-protecting alternate
                        forward the packet to that alternate
                 else forward to a primary next-hop
             } else forward to a primary next-hop
         } else forward to a primary next-hop


                             New Forwarding Rule






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                             +--------------------------+
                             |          N_1             |
                             |                          |
                             |   primary    alternate   |  Router
                             | D:  S            R_1     |  Forwarding
                             | C:  R_1          R_2     |  Table
                             |                          |
                             |--------+--------+--------|
                             | D: R_1 | D: S   | D: S   |  Interfaces'
                             | C: R_1 | C: R_1 | C: R_2 |  Forwarding
                             +--------------------------+
                               /           |         \
                              / L_1        | L_2      \ L_3
                             /             |           \
                            /           +-----+         \
                         +-----+        | R_2 |          \
                         |  S  |        +-----+         +-----+
                         +-----+          /             | R_1 |
                          /              /              +-----+
                         /              /                   /
                        /              /                   /
                 +-----+              /          /--------/
                 |  P  |             /          /
                 +-----+         __ /  __      /
                     \          /  \  /  \    /
                      \        /    \/    \  /
                       \------ |           |
                                \ CLOUD   /
                               _/         |
                              /           |
                              \_   ___   /
                               /\_/   \_/
                              /          \
                             /            \
                            /            +-----+
                         +-----+         |  D  |
                         |  C  |         +-----+
                         +-----+


                     Figure 7: Example Forwarding Table


   If an interface is U-Turn capable and has a node-protecting
   alternate, traffic received on its primary next-hop will be forwarded
   to its alternate next-hop.  Otherwise, the current behavior will be
   preserved, which is forwarding traffic received to its primary next-
   hop.


   If a broadcast interface is U-turn capable, then it is acceptable to




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   forward traffic from all nodes on that interface via the alternate
   path.  This will work if all nodes on that interface have a common
   topology because they are in the same OSPF area or ISIS level.


   To clarify the above behavior, consider the example below in Figure
   7. In this case, router N_1 has a primary and an alternate for two
   destinations D and C. The primary next-hop for destination D is
   router S and the alternate next-hop is R_1.  Similarly, the primary
   next-hop for destination C is router R_1 and the alternate next-hop
   is R_2.   The three interfaces L_1, L_2, and L_3 shown on router N_1
   have different forwarding tables as shown in Figure 7; additional
   interfaces would have the same forwarding table as for interface L_2,
   which is not a primary next-hop for either destination.


4.1.1. Broadcast and NBMA Interfaces


   NBMA and broadcast interfaces can be treated identically for IP/LDP
   Local Protection; both involve the case of possibly receiving traffic
   from multiple neighbors.  With broadcast interfaces (i.e. Gigabit
   Ethernet), there can be multiple neighbors connected to the same
   interface.  If all the neighbors are not in the same area, then it is
   not desirable to treat the traffic received identically, because
   traffic may be incorrectly sent to the alternate.  It is extremely
   desirable to have at most one forwarding table per interface.
   Therefore, it must be considered whether all traffic received on an
   interface can be treated identically, regardless of the neighbor
   sourcing the traffic on that interface, as long as all the neighbors
   on the interface are in the same area.


   The cost for any node on the broadcast interface to reach S or P will
   be identical.  Because all link costs are positive, no neighbor on
   the broadcast interface will ever send traffic to S along that
   interface in order to reach P.  Therefore, S can assume that any
   traffic received on the broadcast interface which goes to a
   destination via a primary next-hop neighbor that is also on the
   broadcast interface is in fact sent by that primary next-hop neighbor
   and should be redirected to break the U-Turn.


   Thus, if router S has a primary next-hop neighbor for a given prefix
   on the broadcast interface, S should redirect all traffic received
   destined to that prefix on the broadcast interface to S's alternate
   next-hop.


   An interface can be either a primary next-hop or the alternate next-
   hop, but not both because there would be no protection if the
   interface failed.






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                 +-----------+-----------+------------+----------+
                 |           |           |            |          |
                 |           | /P\       | /P\        | /P\      | /P\
                 | 2        3|  |       3|  |        4|  |      5|  |
                 |           |           |            |          |
              +-----+      +-----+     +-----+     +-----+    +-----+
              |  P  |      |  S  |     | N_1 |     | N_2 |    | N_3 |
              +-----+      +-----+     +-----+     +-----+    +-----+
                 \            \  10
             \    \ 10      @  \________
              \|   \         @|         \
              -+    \        -+       +-----+
                     \        ________| N_4 |
                      \      /   10   +-----+
                    +-----+ /
                    |  D  |/
                    +-----+


                Figure 8: Topology With Broadcast Interface


4.2. Responding to a Local Failure


   When a local interface failure is detected, traffic that was destined
   to go out the failed interface must be redirected to the appropriate
   alternate next-hops.  The alternate next-hop is pre-computed to be
   reliable in the event of the failure scenario being protected against
   (i.e. link or node failure).


   Convergence on the part of the U-turn neighbor N_i will not
   invalidate the U-turn alternate.  The loop-free node-protecting
   alternate of N_i which goes via R_i,j will not be affected by the
   failure, because it was independent of the affected elements.  If
   N_i's new primary neighbor remains S, then the traffic will continue
   to be directed towards the appropriate R_i,j.  If N_i converges to a
   path which does not include S to reach D, then traffic received from
   S for D will be sent along the new path and no forwarding loop will
   ensue.


5. Requirements on LDP Mode


   U-turn alternates do not impose any additional sessions or signaling
   on LDP.  LDP can use the u-turn alternates to protect LDP traffic if
   the requirements specified in [LOOP-FREE] are met.


6. Routing Aspects


   As described in [LOOP-FREE], the additional complexity for inheriting
   alternate next-hops is for inter-region routes where there are ECMP




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   through different area border routers and yet a single primary
   neighbor.  This scenario is illustrated in Figure 9.


                           ...............  +--+--+    15
                     ......+----------------| ABRt|----------------+
                  ...      |  15            +-----+                |
                ..         |                    ...                |
              ..    5  +-----+   15    +--+--+     ..              |
             .  +------| A2  +---------| R1  |-----+ .             |
           ..   |      +-----+         +-----+ 20  | .             |
           .    |                                +-----+  10       |
          .     |                 +--------------| ABR2|---------+ |
          .     |                 |      15      +-----+         | |
         .  +-----+     5     +---+-+                .           | |
         .  |  S  |-----------|  P  |------------+   .         +-----+
          . +-----+           +-----+    5       |   .         |  D  |
          .     |                                |   .         +-----+
           .    |                                |  .             |
           ..   |     +-----+                  +-----+  20        |
             .  +-----| A1  |------------------| ABR1|------------+
              .   10  +-----+    15            +-----+
               ...                               ...
                  ...                         ...
                     ......              .....
                           ..............


                    Figure 9: Inter-Region Destination via
               Multiple Border Routers but One Primary Neighbor


        The main question when deciding whether an alternate can be
        inherited is whether or not that alternate will continue to
        provide the necessary protection.  I.e., will the alternate
        continue to be usable as an alternate and provide the same link
        or node protection with respect to the destination that was
        provided with respect to the border router.  The relationships
        shown in Figure 6 will be used for illustrative purposes,
        although the topology connecting them may be more general than
        that shown.  The proofs and explanations are provided in [LOOP-
        FREE] and below, but the answer is that the alternate will be
        usable as an alternate and provide at least the same link or
        node protection that was provided with respect to the border
        router.  The alternate next-hop inheritance procedure SHOULD
        select a loop-free node-protecting alternate, if one is
        available.


        [LOOP-FREE] proved this when only loop-free alternates were
        considered.  It is necessary to prove the same thing when U-turn
        alternates are considered.




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        The use of this for alternate next-hop inheritance applies to
        OSPF, ISIS and BGP as described in [LOOP-FREE].


7. U-Turn Alternates Interactions with Tunnels


   IP/LDP Local Protection treats IGP tunnels the same as any other
   link.  If router S is not the endpoint of the tunnel, then the
   alternate path is computed as normal.  If router S is the ingress
   into the tunnel, then all destinations which have the tunnel as a
   primary next-hop may be protected via a protection scheme associated
   with the tunnel.


   One issue with MPLS RSVP-TE tunnels is that an LSP may be created
   where the router uses penultimate-hop popping (PHP).  Traffic
   received via that tunnel is undistinguishable from traffic received
   over the interface.  If some of the traffic received via the LSP is
   destined back to the penultimate hop, then the egress router would
   consider that the traffic required U-Turn breaking and would redirect
   that traffic to its alternate, if available.  To avoid such a
   scenario, a router can simply not request PHP for those LSPs which
   are entering via an interface upon which the router has advertised
   that it can break U-Turns.  If a router must do PHP, then it can stop
   advertising the ability to break U-Turns upon the interface.


   For IP traffic, it is not possible to resolve the PHP issue.  For LDP
   traffic, it would be possible to advertise a different label for a
   FEC on targeted sessions from the label advertised for non-targeted
   sessions.  In this case, only traffic received with the label for
   non-targeted sessions would be subject to U-Turn breaking.


8. Security Considerations


   This document does not introduce any new security issues. The
   mechanisms described in this document depend upon the network
   topology distributed via an IGP, such as OSPF or ISIS.  It is
   dependent upon the security associated with those protocols.


9. Intellectual Property Considerations


   Avici Systems has intellectual property rights claimed in regard to
   the specification contained in this document.


10.  Full Copyright Statement


   Copyright (C) The Internet Society (2004).  This document is subject
   to the rights, licenses and restrictions contained in BCP 78, and
   except as set forth therein, the authors retain all their rights."





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   "This document and the information contained herein are provided on
   an "AS IS" basis and THE CONTRIBUTOR, THE ORGANIZATION HE/SHE
   REPRESENTS OR IS SPONSORED BY (IF ANY), THE INTERNET SOCIETY AND THE
   INTERNET ENGINEERING TASK FORCE DISCLAIM ALL WARRANTIES, EXPRESS OR
   IMPLIED, INCLUDING BUT NOT LIMITED TO ANY WARRANTY THAT THE USE OF
   THE INFORMATION HEREIN WILL NOT INFRINGE ANY RIGHTS OR ANY IMPLIED
   WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.


11. References


   [LOOP-FREE] A. Atlas, R. Torvi, G. Choudhury, B. Imhoff, C. Martin,
   D. Fedyk, "Loop-Free Alternates for IP/LDP Local Protection", draft-
   atlas-ip-local-protect-loopfree-00.txt, June 2004, work-in-progress


   [OSPF-LOCAL-PROTECT] A. Atlas, R. Torvi, G. Choudhury, B. Imhoff, C.
   Martin, D. Fedyk, "OSPFv2 Extensions for Link Capabilities and IP/LDP
   Local Protection", draft-atlas-ospf-local-protect-cap-00.txt,
   February 2004, work-in-progress


   [ISIS-LOCAL-PROTECT] A. Atlas, R. Torvi, C. Martin, "ISIS Extensions
   for Signaling Local Protection Capabilities", draft-martin-isis-
   local-protect-cap-00.txt, February 2004, work-in-progress


   [LDP] L. Anderson, P. Doolan, N. Feldman, A. Fredette, B. Thomas,
   "LDP Specification", RFC 3036, January 2001


   [RSVP-TE] D. Awduche, L. Berger, D. Gan, T. Li, V Srinivasan, G.
   Swallow, "RSVP-TE: Extensions to RSVP for LSP Tunnels", RFC 3209,
   December 2001


   [RSVP-TE FRR] P. Pan, D. Gan, G. Swallow, JP Vasseur, D. Cooper, A.
   Atlas, and M. Jork, "Fast Reroute Extensions to RSVP-TE for LSP
   Tunnels", work-in-progress draft-ietf-mpls-rsvp-lsp-fastreroute-
   06.txt, June 2004


   [RFC3137]  Retana, A., Nguyen, L., White, R., Zinin, A., and
   McPherson, D., "OSPF Stub Router Advertisement", RFC 3137, June 2001


   [RFC3277] D. McPherson, "Intermediate System to Intermediate System
   (IS-IS) Transient Blackhole Avoidance", RFC 3277, April 2002


   [ISIS] R. Callon, "Use of OSI IS-IS for Routing in TCP/IP and Dual
   Environments", RFC 1195, December 1990


   [RFC2966] T. Li, T. Przygienda, H. Smit, "Domain-wide Prefix
   Distribution with Two-Level IS-IS", RFC 2966, October 2000


   [OSPF] J. Moy, "OSPF Version 2", RFC 2328, April 1998




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   [RFC2370] R. Coltun, "The OSPF Opaque LSA Option", RFC 2370, July
   1998


12. Authors Information


   Raveendra Torvi
   Avici Systems
   101 Billerica Avenue
   N. Billerica, MA 01862
   USA
   email: rtorvi@avici.com
   phone: +1 978 964 2026


   Gagan Choudhury
   AT&T
   Room D5-3C21
   200 Laurel Avenue
   Middletown, NJ 07748
   USA
   email: gchoudhury@att.com
   phone: +1 732 420-3721


   Christian Martin
   Verizon
   1880 Campus Commons Drive
   Reston, VA 20191
   email: cmartin@verizon.com


   Brent Imhoff
   WilTel Communications
   3180 Rider Trail South
   Bridgeton, MO 63045
   USA
   email: brent.imhoff@wcg.com
   phone: +1 314 595 6853


   Don Fedyk
   Nortel Networks
   600 Technology Park
   Billerica, MA 01821
   email: dwfedyk@nortelnetworks.com
   phone: +1 978 288 3041


12. Editor's Information


   Alia Atlas
   Avici Systems
   101 Billerica Avenue




Atlas et al.                                                   [Page 26]


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   N. Billerica, MA 01862
   USA
   email: aatlas@avici.com
   phone: +1 978 964 2070


Appendix A: U-turn Alternate Proofs


                           ...............  +--+--+    15
                     ......+----------------| ABRt|----------------+
                  ...      |  15            +-----+                |
                ..         |                    ...                |
              ..    5  +-----+   15    +--+--+     ..              |
             .  +------| A2  +---------| R1  |-----+ .             |
           ..   |      +-----+         +-----+ 20  | .             |
           .    |                                +-----+  10       |
          .     |                 +--------------| ABR2|---------+ |
          .     |                 |      15      +-----+         | |
         .  +-----+     5     +---+-+                .           | |
         .  |  S  |-----------|  P  |------------+   .         +-----+
          . +-----+           +-----+    5       |   .         |  D  |
          .     |                                |   .         +-----+
           .    |                                |  .             |
           ..   |     +-----+                  +-----+  20        |
             .  +-----| A1  |------------------| ABR1|------------+
              .   10  +-----+    15            +-----+
               ...                               ...
                  ...                         ...
                     ......              .....
                           ..............


                    Figure 10: Inter-Region Destination via
               Multiple Border Routers but One Primary Neighbor



        Consider where A2 is a U-turn alternate for ABR2.   This case
        matters only if A2 is not a loop-free alternate for any ABR
        offering an optimal equal-cost path from S to D.


        There are two possibilities for the path from A2 to D.  First,
        A2's optimal path to D is via one of the set of ABRs giving
        optimal equal-cost paths from S to D.  Therefore, A2 is still a
        U-turn neighbor of S with respect to D.  Consider that R1 is the
        neighbor of A2 which provides the loop-free node-protecting
        alternate for ABR2.  In that case, either R1's optimal path to D
        is via one of the ABRs in the set, in which case that it is
        loop-free and avoids S be can be shown or R1 will go via a
        different ABR, ABRt, in which case it will also remain loop-free
        and avoid P (same proofs as in [LOOP-FREE] with R1 replacing




Atlas et al.                                                   [Page 27]


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        A2).


        The other possibility is that A2's optimal path to D is via a
        different ABR, ABRt.



                  Step i: D_opt(A2, ABRt) + D_opt(ABRt, D) <=
                 D_opt(A2, S) + D_opt(S, ABR2) + D_opt(ABR2, D)


                  Step ii: D_opt(S, ABR2) + D_opt(ABR2, D) <
                        D_opt(S, ABRt) + D_opt(ABRt, D)


          Step iii: D_opt(A2, S) + D_opt(S, ABR2) + D_opt(ABR2, D) <
                 D_opt(A2, S) + D_opt(S, ABRt) + D_opt(ABRt, D)


                  Step iv: D_opt(A2, ABRt) + D_opt(ABRt, D) <
                 D_opt(A2, S) + D_opt(S, ABRt) + D_opt(ABRt, D)


        Therefore, if Dopt(A2, D) is via ABRt, it does not go through S.



   The same proof can be done to show that the path would be loop-free
   with respect to P and D, simply by substituting P for S in the above
   proof.


   Thus, if A2 offered a U-Turn alternate for one of the ABRs offering
   an optimal equal-cost path from S to D, A2 will, at the worst, offer
   a U-turn alternate for D.


   If a U-Turn neighbor offered a node-protecting alternate to one of
   the ABRs offering an optimal equal-cost path from S to D, then the
   U-Turn neighbor will still offer a node-protecting alternate because
   it will fall into one of the following 3 categories:


     1) The U-turn neighbor is still a U-turn neighbor. Its neighbor Ri,
     which
        provides the loop-free node-protecting alternate, has the
     shortest path to D
        via one of the ABRs, in which case, if it was protecting against
     P before, it
        still will be.


     2) The U-turn neighbor is still a U-turn neighbor.  Its neighbor Ri
     has the
        shortest path to D via a different ABR, in which case it doesn't
     go through
        P.





Atlas et al.                                                   [Page 28]


Internet Draft                                             November 2004



     3) The U-turn neighbor offers a loop-free alternate to reach D, in
     which case it
        must go through a different ABR and therefore doesn't go through
     P.
















































Atlas et al.                                                   [Page 29]


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