One document matched: draft-atlas-rtgwg-mrt-frr-architecture-00.xml
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<rfc category="info" docName="draft-atlas-rtgwg-mrt-frr-architecture-00" ipr="trust200902">
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<!-- ***** FRONT MATTER ***** -->
<front>
<!-- The abbreviated title is used in the page header - it is only necessary if the
full title is longer than 39 characters -->
<title abbrev="MRT FRR Architecture">An Architecture for IP/LDP Fast-Reroute Using Maximally Redundant Trees</title>
<!-- add 'role="editor"' below for the editors if appropriate -->
<!-- Another author who claims to be an editor -->
<author fullname="Alia Atlas" initials="A.K.A." role="editor" surname="Atlas">
<organization>Juniper Networks</organization>
<address>
<postal>
<street>10 Technology Park Drive</street>
<city>Westford</city>
<region>MA</region>
<code>01886</code>
<country>USA</country>
</postal>
<email>akatlas@juniper.net</email>
</address>
</author>
<author fullname="Maciek Konstantynowicz" initials="M.K." surname="Konstantynowicz">
<organization>Juniper Networks</organization>
<address>
<email>maciek@juniper.net</email>
</address>
</author>
<author fullname="Gábor Sándor Enyedi" initials="G.S.E." surname="Enyedi">
<organization>Ericsson</organization>
<address>
<postal>
<street>Irinyi utca 4-10</street>
<city>Budapest</city>
<country>Hungary</country>
<code>1117</code>
</postal>
<email>Gabor.Sandor.Enyedi@ericsson.com</email>
</address>
</author>
<author fullname="András Császár" initials="A.C." surname="Császár">
<organization>Ericsson</organization>
<address>
<postal>
<street>Irinyi J ut 4-10</street>
<city>Budapest</city>
<country>Hungary</country>
<code>1117</code>
</postal>
<email>Andras.Csaszar@ericsson.com</email>
</address>
</author>
<author fullname="Russ White" initials="R.W." surname="White">
<organization>Cisco Systems</organization>
<address>
<email>russwh@cisco.com</email>
</address>
</author>
<author fullname="Mike Shand" initials="M.S." surname="Shand">
<organization>Cisco Systems</organization>
<address>
<email>mshand@cisco.com</email>
</address>
</author>
<date year="2011" />
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<!-- Meta-data Declarations -->
<area>Routing</area>
<workgroup>Routing Area Working Group</workgroup>
<abstract>
<t>As IP and LDP Fast-Reroute are increasingly deployed, the
coverage limitations of Loop-Free Alternates are seen as a
problem that requires a straightforward and consistent solution
for IP and LDP, for unicast and multicast. This draft describes
an architecture based on redundant backup trees where a single
failure can cut a point-of-local-repair from the destination
only on one of the pair of redundant trees.</t>
<t>One innovative algorithm to compute such topologies is maximally
disjoint backup trees. Each router can compute its next-hops
for each pair of maximally disjoint trees rooted at each node in
the IGP area with computational complexity similar to that
required by Dijkstra.</t>
<t>The additional state, address and computation requirements are
believed to be significantly less than the Not-Via architecture
requires.</t>
</abstract>
</front>
<middle>
<section title="Introduction">
<t>There is still work required to completely provide IP and LDP
Fast-Reroute<xref target="RFC5714"/> for unicast and multicast traffic. This draft
proposes an architecture to provide 100% coverage.</t>
<t>Loop-free alternates (LFAs)<xref target="RFC5286"/> provide a
useful mechanism for link and node protection but getting
complete coverage is quite hard. <xref target="LFARevisited"/>
defines sufficient conditions to determine if a network provides
link-protecting LFAs and also proves that augmenting a network
to provide better coverage is NP-hard. <xref
target="I-D.ietf-rtgwg-lfa-applicability"/> discusses the
applicability of LFA to different topologies with a focus on
common PoP architectures.</t>
<t>While Not-Via <xref
target="I-D.ietf-rtgwg-ipfrr-notvia-addresses"/> is defined as
an architecture, in practice, it has proved too complicated and
stateful to spark substantial interest in implementation or
deployment. Academic implementations <xref
target="LightweightNotVia"/> exist and have found the address
management complexity high (but no standardization has been done
to reduce this).</t>
<t>A different approach is needed and that is what is described
here. It is based on the idea of using disjoint backup
topologies as realized by Maximally Redundant Trees (described in
<xref target="LightweightNotVia"/>); the general
architecture could also apply to future improved redundant tree
algorithms.</t>
<section title="Goals for Extending IP Fast-Reroute coverage beyond LFA">
<t>Any scheme proposed for extending IPFRR network topology coverage
beyond LFA, apart from attaining basic IPFRR properties, should also
aim to achieve the following usability goals:</t>
<t><list style="symbols">
<t>ensure maximum physically feasible link and node disjointness
regardless of topology,</t>
<t>automatically compute backup next-hops based on the topology
information distributed by link-state IGP,</t>
<t>do not require any signaling in the case of failure and use
pre-programmed backup next-hops for forwarding,</t>
<t>introduce minimal amount of additional addressing and state on
routers,</t>
<t>enable gradual introduction of the new scheme and backward
compatibility,</t>
<t>and do not impose requirements for external computation.</t>
</list></t>
</section>
</section>
<section title="Maximally Redundant Trees (MRT)">
<t>In the last few years, there's been substantial research on how to
compute and use redundant trees. Redundant trees are directed spanning
trees that provide disjoint paths towards their common root. These
redundant trees only exist and provide link protection if the network
is 2-edge-connected and node protection if the network is
2-vertex-connected. Such connectiveness may not be the case in real
networks, either due to architecture or due to a previous failure.
The work on maximally redundant trees has added three useful pieces
that make them ready for use in a real network.</t>
<t><list style="symbols">
<t>Computable when network isn't 2-edge or 2-vertex connected: The
maximally redundant trees are computed so that only the cut-edges or
cut-vertices are shared between the multiple trees.</t>
<t>Algorithm is based on a common network topology database. No
messaging as has been suggested in other work is necessary.</t>
<t>An algorithm <xref target="MRTLinear"/> is
given that allows a router to compute its next-hops on each pair of
maximally redundant trees to each node in the network in O( e ) time -
or O(e + n log n), if Dijkstra is used instead of BFS.</t>
</list></t>
<t>There is, of course, significantly more in the literature related to
redundant trees and even fast-reroute, but the formulation of the
Maximally Redundant Trees (MRT) algorithm makes it very well suited to
use in routers.</t>
<t>A known disadvantage of MRT, and redundant trees in general, is
that the trees do not necessarily provide shortest detour paths. The
use of SPF in tree-building and some heuristics can improve this, but
the length of the alternate paths is topology-dependent. Providing
shortest detour paths would require failure-specific detour paths such
as in <xref target="I-D.ietf-rtgwg-ipfrr-notvia-addresses"/>, but the
state-reduction advantage of MRT lies in the detour being established
per destination (root) instead of per destination AND per failure.</t>
<t>A simple but not optimal way of computing maximally redundant
trees is described in <xref target="MRT_Algorithm_Example"/>. </t>
<section title="Redundant Trees Overview">
<t>In graph theory, a pair of maximally redundant trees are a pair of
directed spanning trees of an directed graph with a common root node
(this root can be any node of the graph), such that the two paths
along the two trees to the root from any other node are as
edge-disjoint and as vertex-disjoint as it is possible. It is known
that such trees can be found in any connected networks for any
selected root. A pair of trees for the graph depicted in <xref
target="Non-2-connected_Network_Example"/> is shown in <xref
target="MRTs_rooted_at_r"/> considering "r" as the root. </t>
<figure anchor="Non-2-connected_Network_Example"
title="A non-2-connected network">
<artwork>
e---d i
/ / \ /|
r---c f--g |
\ \ / \|
a---b j
</artwork>
</figure>
<figure anchor="MRTs_rooted_at_r"
title='The two maximally redundant trees rooted at node "r".'>
<artwork>
e---d i e---d i
/ /| / \ |
r c f--g | r---c f--g |
\ \ / | \ \|
a---b j a---b j
</artwork>
</figure>
<t>The two paths along the two trees to a given root of a 2-connected
graph are node-disjoint, while in any non-2-connected graph, only the
cut-vertices and cut-edges can be contained by both of the paths. As
an example consider the trees depicted in
<xref target="MRTs_rooted_at_r"/>. Here, the two paths from e.g. node "b" to "r" are node-disjoint
(since there are such two paths), and the two paths from e.g. node "i"
to "r" have only node "f" and "g" and link "f-g" in common.</t>
</section>
</section>
<section title="Maximally Redundant Trees (MRT) and Fast-Reroute">
<t>In normal IGP routing, each router has its shortest-path-tree to
all destinations. From the perspective of a particular destination,
D, this looks like a reverse SPT (rSPT). To use maximally redundant
trees, in addition, each destination D has two maximally redundant
trees associated with it; by convention these will be called the red
and blue redundant trees.</t>
<t>Redundant trees are practical to maintain redundancy even after a
single link or node failure. If a pair of maximally redundant trees is
computed rooted at each node, all the nodes remain reachable along one
of the trees in the case of a single link or node failure.</t>
<t>When there is a link or node failure affecting the rSPT, each node
will still have a path via one of the redundant trees to reach the
destination D. Consider a simple 5-node ring (S--A--B--D--C--S), with
traffic sent from sources S and C to destination D. In this case, if
the link C->D fails, then C can forward traffic along the blue
redundant tree to reach D. Of course, if the link S->C fails, then S
can simply use its LFA of A.</t>
<t>In a failure free network, packets are forwarded along the shortest
path tree as done today. However, if forwarding the packet fails at a
node, the router detecting the failure locally reroutes the packet
along the blue MRT. If forwarding the packet along the blue MRT fails
again, the packet is forwarded along the red MRT. If there is only a
single link or node failure, the packet must get to the root along
either of the trees. Therefore if forwarding along the red MRT fails,
either multiple failures occurred, or the single failure split the
network into two, and packets must be dropped.</t>
<t>The above logic gives the following basic rules for unicast use of
maximally redundant trees and fast-reroute when failure of the primary
is detected are:</t>
<t><list style='numbers'>
<t>If there is an node-protecting LFA, use it.</t>
<t>Otherwise, if only link-protection is acceptable and there is a link-protecting LFA, use it.</t>
<t>Otherwise, if the blue MRT next-hop shouldn't fail with the
primary, send traffic along the blue MRT next-hop.</t>
<t>Otherwise, if the red MRT next-hop shouldn't fail with the
primary, send traffic along the red MRT next-hop.</t>
<t>If traffic is received on the blue redundant tree and the appropriate next-hop is not available, then send the traffic on the red redundant tree.</t>
<t>If traffic is received on the red redundant tree and the appropriate next-hop is not available, discard it.</t>
</list></t>
<section title="Multi-homed Prefixes">
<t>One advantage of LFAs that would be good to preserve is the ability
to protect multi-homed prefixes against ABR failure. For instance, if
a prefix from the backbone is available via both ABR A and ABR B, if A
fails, then the traffic should be redirected to B. This can also be
done for backups via MRT.</t>
<t>If there exist multiple multi-homed prefixes that share the same
connectivity and the difference in metrics to those routers, then a
single proxy-node can be used to represent the set. In addition to
computing the pair of MRTs associated with each router destination D
in the area, a pair of MRTs can be computed for each such proxy-node
to fully protect against ABR failure. </t>
</section>
<section title="Unicast Forwarding with MRT Fast-Reroute">
<t>With LFA, there is no need to tunnel unicast traffic, whether IP or
LDP. The traffic is simply sent to an alternate. The behavior with
MRT Fast-Reroute is different depending upon whether IP or LDP unicast
traffic is considered.</t>
<t>Logically, one could use the same IP address or LDP FEC and then
also use 2 bits to express the topology to use. The topology options
are (00) IGP/SPT, (01) blue MRT, (10) red MRT. Unfortunately, there
just aren't 2 spare bits available in the IPv4 or IPv6 header. This
has different consequences for IP and LDP because LDP can just add a
topology label on top or take 2 spare bits from the label space.</t>
<section title="IP Unicast Forwarding">
<t>For IP, there is no currently practical alternative except
tunneling. The tunnel egress can be the original destination in the
area, the next-next-hop, etc.. If the tunnel egress is the original
destination router, then the traffic remains on the redundant tree
with sub-optimal routing. If the tunnel egress is the
next-next-hop, then protection of multi-homed prefixes and
node-failure for ABRs is not available.</t>
<t>In either case, each router that supports MRT fast-reroute would
need to announce two additional loopback addresses and their
associated MRT color. Those addresses are used as destination
addresses for MRT-blue and MRT-red IP tunnels respectively. They allow
the transit nodes to identify the traffic as being forwarded along
either MRT-blue or MRT-red tree topology to reach the tunnel
destination. Announcements of these two additional loopback addresses
per router with their MRT color requires IGP extensions.</t>
<t>IP packets could be tunneled via LDP. This has the advantage that
more routers can do line-rate encapsulation and decapsulation. If
tunneled via LDP, naturally one of the LDP unicast forwarding options
would need to be used. It would be possible to use just a LDP
Topology-Identifier label on top of the IP packet; if done, this would
avoid any need to allocate or signal additional IP addreses and is
particularly interesting for multi-homed prefixes.</t>
<t>For proxy-nodes associated with one or more multi-homed prefixes,
the problem is harder because there is no router associated with the
proxy-node, so its loopbacks can't be known or used. In this case,
each router attached to the proxy-node could announce two common IP
addresses with their associated MRT colors. This would require
configuration as well as the previously mentioned IGP extensions.
Similarly, in the LDP case, two additional FEC bindings could be
announced.</t>
<section title="Protocol Extensions and Considerations: OSPF and ISIS">
<t>This captures an initial understanding of what may need to be specified.</t>
<t><list style="symbols">
<t>Capabilities: Does a router support MRT? Does the router do MRT tunneling with LDP or IP or GRE or...?</t>
<t>Topology Association: A router needs to advertise a loopback and associate it with an MRT whether blue or red. Additional flexibility for future uses would be good.</t>
<t>Proxy-nodes for Multi-homed Prefixes: We need a way to advertise common addresses with MRT for multi-homed prefixes' proxy-nodes. Currently, those proxy-nodes aren't named or considered.</t>
<t>Algorithm-specific Commonalities: In specifying the exact details for a common algorithm, there may be tie-breakers that are better done based on configuration than just using Router ID.</t>
</list></t>
<t>As with LFA, it is expected that OSPF Virtual Links will not be supported.</t>
</section>
</section>
<section title="LDP Unicast Forwarding">
<t>For LDP, it is very desirable to avoid tunneling because, for at least
node protection, this requires knowledge of remote LDP label mappings.
There are two different mechanisms that could be used.</t>
<t><list style="numbers">
<t>Create Topology-Identification Labels: Use the label-stacking
ability of MPLS and specify only two additional labels - one for
each associated MRT color - by a new FEC type. When sending a
packet onto an MTR, first swap the LDP label and then push the
topology-identification label for that MTR color. When receiving a
packet with a topology-identification label, pop it and use it to
guide the next-hop selection in combination with the next label in
the stack; then swap the remaining label, if appropriate, and push
the topology-identification label for the next-hop. This has
minimal usage of additional labels, memory and LDP communication.
It does increase the size of packets and the complexity of the
required label operations and look-ups.</t>
<t> Encode Topology in Labels: In addition to sending a single
label for a FEC, a router would provide two additional labels with
their associated MRT colors. This is simple, but reduces the label
space for other uses. It also increases the memory to store the
labels and the communication required by LDP.</t>
</list></t>
<t>Note that with LDP unicast forwarding, regardless of whether
topology-identification label or encoding topology in label is used,
no additional loopbacks per router are required as are required in the
IP unicast forwarding case. This is because LDP labels are used on a
hop-by-hop basis to identify MRT-blue and MRT-red forwarding
trees.</t>
<section title="Protocol Extensions and Considerations: LDP">
<t>This captures an initial understanding of what may need to be specified.</t>
<t><list style="numbers">
<t>Topology-Identification Labels: Define a new FEC type that
describes the topology for MRT and the associated MRT color.</t>
<t>Specify Topology in Label: When sending a Label Mapping, have the
ability to send a Label TLV and multiple Topology-Label TLVs. The
Topology-Label TLV would specify MRT and the associated MRT
color.</t>
</list></t>
</section>
</section>
</section>
<section title="Multicast Forwarding with MRT Fast-Reroute">
<t>There are several basic issues with doing Fast-Reroute for
multicast traffic, whether the alternates used are LFA or MRT. They
are given below:</t>
<t><list style="numbers">
<t>The Point-of-Local-Repair (PLR) does not know the set of
next-next-hops in the multicast tree.</t>
<t>For mLDP, the PLR does not know the appropriate labels to use for
the next-next-hops in the multicast tree.</t>
<t>The Merge Point (MP) does not know upon what interface to expect
backup traffic. For LFAs, this is a particular issue since the LFA
selected by a PLR is known only to that PLR.</t>
</list></t>
<t>There are also issues about how to manage traffic.</t>
<t><list style="letters">
<t>When should the PLR stop sending traffic on the alternate? Based
upon a configurable time-out is the most general answer. For PIM,
an explicit Withdraw or Backup Withdraw could be sent, but they
could always be lost and are not reliable. For mLDP, even if the
PLR is known, for node-protection, there is no targeted LDP session
and so no way for the MP to explicitly withdraw the label that was
implicitly learned by the PLR.</t>
<t>Can anything be done about traffic missed due to different
latencies along new primary and alternate/old primary trees? If a
router is willing and able to examine traffic from both the
alternate and new primary, perhaps the full set of packets could be
assured. This requires more investigation, but such an option would
be at most optional. A router could also continue to accept traffic
from both the old alternate and the new primary for a period longer
than the expected difference in latency, but this comes with a
possible doubling of traffic during that period.</t>
</list></t>
<section title="Tunneled? Yes">
<t>The disadvantages of tunneling unicast traffic do not fully
translate to those for multicast. With MRT fast-reroute, IP unicast
traffic is tunneled. With mLDP, in the suggested extensions (later),
along with learning the next-next-hops on the multicast tree, the
associated labels can be learned so there is no need for targeted
sessions.</t>
<t>If multicast traffic is not tunneled along the alternates, then
there is the question of what happens when unencapsulated backup
traffic intersects the normal multicast tree before reaching the MPs.
Resolving this is likely to introduce significant complexity and state
into the routers, with the only gain being the avoidance of a tunnel.</t>
<t>Therefore, tunneling for IP and mLDP multicast traffic along the
selected alternates is required. This means all replication is done
by the PLR.</t>
</section>
<section title="PIM Forwarding">
<t>For node-protection, the merge points would be the next-next-hops
in the tree. For a PLR to learn them, additional PIM Join Attributes
<xref target="I-D.ietf-pim-mtid"/> need to be defined to specify the
set of next-hops from which the sending node has received Joins. For
link-protection, of course a PLR knows the routers that have sent it
Joins.</t>
<t>An MP must know the interface that alternate traffic should be
accepted from. To do this, a new Upstream Backup Join would be added
to PIM. This Upstream Backup Join would be sent by the PLR to MPs.
If the PLR has selected an LFA for a MP, then the PLR tunnels the
Upstream Backup Join to the MP via the LFA. If the PLR will use MRT,
then the PLR must send two Upstream Backup Joins - one transmited via
the blue MRT and one transmited via the red MRT; these will also be
tunneled via LDP or IP as is configured in the network.</t>
<t>The Upstream Backup Join will specify the PLR, the MP, the (S, G),
and the alternate details (e.g. LFA with neighbor address, blue MRT,
red MRT). If desired, the alternate topology could be used to verify
the incoming interface appropriately via a tree-appropriate RPF check.
Upon receiving the Upstream Backup Join, the MP will accept specified
multicast traffic from the LFA backup neighbour, blue or red MRT
respectively.</t>
<section title="Protocol Extensions and Considerations: PIM">
<t>This captures an initial understanding of what may need to be
specified. This is focusing on PIM Sparse mode.</t>
<t><list style="symbols">
<t>Capabilities: New Hello Option Capabilities to indicate the ability
to understand the new Join Attributes and Upstream Backup Join.</t>
<t>Next-Hops: Need a new Join Attribute<xref
target="I-D.ietf-pim-mtid"/> to send the next-hops to the PLR. This
list could be updated and sent upstream every time it changes.</t>
<t>Upstream Backup Join</t>
</list></t>
</section>
</section>
<section title="mLDP Forwarding">
<t>As in PIM, in mLDP<xref target="I-D.ietf-mpls-ldp-p2mp"/> a
mechanism must be added so that the PLR can learn the next-next-hops.
The PLR also needs to learn the associated label-bindings. This can
be done via a new P2MP Child Data Object. This object would include
the primary loopback of an LSR that has provided labels for the FEC to
the sending LSR along with the label specified. Multiple P2MP Child
Data Objects could be included in a P2MP Label Mapping; only those
specified in the most recent P2MP Label Mapping should be stored and
used.</t>
<t>This will provide the PLR with the MPs and their associated labels.
The MPs will accept traffic received with that label from any
interface, so no signaling is required before the alternates are used.</t>
<t>Traffic sent out each alternate will be tunneled with a destination
of the MP.</t>
</section>
<section title="Live-Live Multicast">
<t>In <xref target="I-D.karan-mofrr">MoFRR</xref>, the idea of joining
both a primary and a secondary tree is introduced with the requirement
that the primary and secondary trees be link and node disjoint. This
works well for networks where there are dual-planes, as explained in
<xref target="I-D.karan-mofrr"/>. For other networks, it may still be
desirable to have two disjoint multicast trees and allow a receiver to
join both and make its own decision about what to do.</t>
<t>MRT allows this, but would require minor extensions to PIM or mLDP.
The pair of maximally redundant trees is rooted at the multicast group
source S. IF asymmetric link costs aren't a concern, then the same
set of next-hops (previous-hops in this case) could be used as is used
for MRT fast-reroute. The extension to PIM would be to specify which
MRT tree is being joined - so instead of specifying join(S,G), it
would specify join(S,G, MRT red) or join(S,G, MRT blue). Similarly, a
new P2MP FEC with Tree Identifier Element would need to be defined; it
would include the topology to be used which could be IGP, MRT red, or
MRT blue.</t>
<t>The receiver would still need to detect failures and handle traffic
discarding as is specified in <xref target="I-D.karan-mofrr"/>.</t>
</section>
</section>
<section title="MRT Algorithm Open Issues">
<t>The MTR algorithm as given in <xref target=
"MRTLinear"/> handles most of the issues that occur in real
networks, but there are a few aspects that need to be considered and
factored in.</t>
<t><list style="symbols">
<t>Broadcast Interfaces: While a broadcast interface can simply be
represented as a pseudo-node in the graph, the rules for handling it
given that there is a requirement to provide node-protection as well
as link-protection need to be defined.</t>
<t> Parallel Links: It is quite common to have parallel links in a
real network. In the case where node-disjoint paths are possible, the
parallel links just introduce the possibility of multiple next-hops
along the MTR. In the case where node-disjoint paths aren't possible,
having the ability to use parallel links is important. </t>
<t>Improved Paths in MTRs: In the tree-building, it should be
straightforward to use SPF instead of BFS. There are additional
heuristics in the Finding Multiple Maximally Redundant Trees in Linear
Time paper that should be evaluated for realistic benefits.</t>
<t>Asymmetric Link Costs: The tree-building must consider that links may have asymmetric costs.</t>
<t>Administratively Unavailable Links and Nodes: With the standard
need to avoid a flag day, not all routers may participate in MTR and
those that aren't must not be used in an MTR. Additionally, links can
be overloaded or administratively specified as not available just as
is considered with LFA. Such links may not be used in the MTR.</t>
<t>ECMP: Consider the ability to use multiple equal-cost paths in
building the MRT to get additional capacity along the MRT.</t>
</list></t>
<section title="SRLG Protection">
<t>As shown in <xref target="MRT_Algorithm_Example"/>, a
straightforward way to build two redundant trees involves taking a
link from a ready node to a non-ready node to provide one path and
then determining the shortest-path back to a ready node that doesn't
include that ready node. Creating similar redundancy with arbitrarily
placed Shared-Risk Link Groups is still a challenging open
problem.</t>
</section>
<section title="Common Computation">
<t>In the MTR algorithm, there are some places where decisions are made
as to which link to use next, which neighbor to consider, etc. The
exact rules to follow and a detailed algorithm with example need to be
provided. Ideally, there would be reference pseudo-code.</t>
</section>
</section>
</section>
<section anchor="Acknowledgements" title="Acknowledgements">
<t>The authors would like to thank Hannes Gredler, Robert Kebler,
Ted Qian, Kishore Tiruveedhula, Santosh Esale, Nitin Bahadur, Harish
Sitaraman and Raveendra Torvi for their suggestions and review.</t>
</section>
<!-- Possibly a 'Contributors' section ... -->
<section anchor="IANA" title="IANA Considerations">
<t>This doument includes no request to IANA.</t>
</section>
<section anchor="Security" title="Security Considerations">
<t>This architecture is not currently believed to introduce new security concerns.</t>
</section>
</middle>
<!-- *****BACK MATTER ***** -->
<back>
<!-- References split into informative and normative -->
<!-- There are 2 ways to insert reference entries from the citation libraries:
1. define an ENTITY at the top, and use "ampersand character"RFC2629; here (as shown)
2. simply use a PI "less than character"?rfc include="reference.RFC.2119.xml"?> here
(for I-Ds: include="reference.I-D.narten-iana-considerations-rfc2434bis.xml")
Both are cited textually in the same manner: by using xref elements.
If you use the PI option, xml2rfc will, by default, try to find included files in the same
directory as the including file. You can also define the XML_LIBRARY environment variable
with a value containing a set of directories to search. These can be either in the local
filing system or remote ones accessed by http (http://domain/dir/... ).-->
<references title="Normative References">
&RFC5714;
&RFC5286;
&I-D.karan-mofrr;
&I-D.ietf-mpls-ldp-p2mp;
&I-D.ietf-pim-mtid;
</references>
<references title="Informative References">
&I-D.ietf-rtgwg-ipfrr-notvia-addresses;
&I-D.ietf-rtgwg-lfa-applicability;
<reference anchor="MRTLinear"
target="http://opti.tmit.bme.hu/~enyedi/ipfrr/distMaxRedTree.pdf">
<front>
<title>On Finding Maximally Redundant Trees in Strictly Linear Time</title>
<author fullname="Gábor Sándor Enyedi" initials="G.S.E." surname="Enyedi"/>
<author fullname="Gabor Retvari" initials="G.R." surname="Retvari"/>
<author fullname="András Császár" initials="A.C." surname="Császár"/>
<date year="2009"/>
</front>
<seriesInfo name="IEEE Symposium on Computers and Comunications (ISCC)" value=""/>
<format type='PDF' target="http://opti.tmit.bme.hu/~enyedi/ipfrr/distMaxRedTree.pdf"/>
</reference>
<reference anchor="Maintaining Colored Trees"
target="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.138.6025&rep=rep1&type=pdf">
<front>
<title>Maintaining colored trees for disjoint multipath routing under node failures</title>
<author fullname="G. Jayavelu"/>
<author fullname="S. Ramasubramanian"/>
<author fullname="O. Younis"/>
<date year="2009"/>
</front>
<seriesInfo name="IEEE/AC Transactions on Networking" value="vol. 17, no. 1, pp. 346-359"/>
<format type='PDF' target="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.138.6025&rep=rep1&type=pdf"/>
</reference>
<reference anchor="LightweightNotVia"
target="http://mycite.omikk.bme.hu/doc/71691.pdf">
<front>
<title>IP Fast ReRoute: Lightweight Not-Via without Additional Addresses</title>
<author fullname="Gábor Sándor Enyedi" initials="G.S.E." surname="Enyedi"/>
<author fullname="Gabor Retvari" initials="G.R." surname="Retvari"/>
<author fullname="Peter Szilagyi" initials="P.S." surname="Szilagyi"/>
<author fullname="András Császár" initials="A.C." surname="Császár"/>
<date year="2009" />
</front>
<seriesInfo name="Proceedings of IEEE INFOCOM" value=""/>
<format type='PDF' target="http://mycite.omikk.bme.hu/doc/71691.pdf"/>
</reference>
<reference anchor="LFARevisited"
target="http://opti.tmit.bme.hu/~tapolcai/papers/retvari2011lfa_infocom.pdf">
<front>
<title>IP Fast ReRoute: Loop Free Alternates Revisited</title>
<author fullname="Gabor Retvari" initials="G.R." surname="Retvari"/>
<author fullname="Janos Tapolcai" initials="J.T." surname="Tapolcai"/>
<author fullname="Gábor Sándor Enyedi" initials="G.S.E." surname="Enyedi"/>
<author fullname="András Császár" initials="A.C." surname="Császár"/>
<date year="2011" />
</front>
<seriesInfo name="Proceedings of IEEE INFOCOM" value=""/>
<format type='PDF' target="http://opti.tmit.bme.hu/~tapolcai/papers/retvari2011lfa_infocom.pdf"/>
</reference>
</references>
<section anchor="MRT_Algorithm_Example" title="Computing Maximally Redundant Trees">
<t>This is possible but not optimal way to compute maximally redundant
trees. It is included to provide some intuition about how the
maximally redundant trees are built.</t>
<t>In <xref target="MRT Alg 2-connect"/>, we describe how to handle a
network that is 2-connected. Then that is assumption is relaxed and finally
how to handle distributed computation to obtain the same trees is given.</t>
<section anchor="MRT Alg 2-connect"
title="Simple pair of maximally redundant trees in 2-connected networks">
<t>Finding a simple pair of maximally redundant trees in a 2-connected
network is straightforward. We call a node "ready", if it was already
added to the trees. Initially, the only ready node is the common root
(node r in the sequel).</t>
<t> When we have at least one node x in the network, which is not ready,
find two node-disjoint paths from x either to r or to two distinct
ready nodes. Since the network is 2-connected, there are always two
node-disjoint paths from x to r. It is possible that one or both of
these paths reaches another ready node sooner than r, in which case
we have the two node-disjoint paths to distinct nodes. Combining the
directed links of these paths makes up an *ear*.</t>
<figure anchor="Ear Figure"
title="An *ear* connected to node x and y (x and y are ready).">
<artwork>
x---a
\
b
|
c
/
y---d
</artwork>
</figure>
<t> Let x and y be the two ready endpoints of an ear, and first suppose
that they are different nodes and none of them is r. Note that both x
and y are in the two trees (since they are "ready") and if x is an
ancestor of y in the first tree (x is on the path from y to r), then
x cannot be the ancestor of y along the second tree at the same time.
Thus, it is safe to connect the nodes of the freshly found ear to x
in the first tree and to y in the second tree, if either x is an
ancestor of y in the first tree, or y is an ancestor of x in the
second tree. Considering the example in <xref target="Ear Figure"/>, this means that
links d-c-b-a-x should be added to the first tree, and a-b-c-d-y
should be added to the second one.</t>
<t> In the case, when either x=r or y=r or when neither x is an ancestor
of y nor y is an ancestor of x in any of the trees, the endpoints are
not firmly bound to one of the trees, it is only important to put the
links to one endpoint in one of the trees and put the links towards
the other endpoint to the other tree. In our example this means that
either d-c-b-a-x or a-b-c-d-y could be added to the first tree.
Naturally, then the other endpoint must be selected for the second
tree.</t>
<t> In some cases, we need to construct such (maximally) redundant trees,
where there is only one edge entering to the root on one of the
trees. This makes the root a leaf in that tree. To achieve this, we
can add the ear to the second tree through r only if both endpoints
are r. Moreover, we need to select an ear with different endpoints
when it is possible (it is always possible except for the first ear,
if the network is 2-connected).</t>
<t> Finding an ear is relatively simple and can be done in different
ways. Probably the simplest way is to find a ready node q (q is not
the root) with a non-ready neighbor w, (virtually) remove q from the
topology, and to find a path from w to r; since the network is 2-
connected, such a path either reaches r, or reach another ready node.
Moreover, when only r is ready such a node q does not exist, so we
select one of r's neighbors as w, and remove not r but the link
between them.</t>
<figure anchor="Figure 2-connected"
title="A 2-connected network">
<artwork>
e---d
/ / \
r---c f
\ \ /
a---b
</artwork>
</figure>
<figure anchor="Figure MRTs for 2-connected"
title="The two maximally redundant trees found in the network depicted in previous figure.">
<artwork>
e---d e---d
/ / \
r c f r---c f
\ \ / \
a---b a---b
</artwork>
</figure>
<t> Now, a simple example is in order. Consider the network depicted
in <xref target="Figure 2-connected"/>, and suppose that the common
root is node r. We have only r in the trees, so we select one of its
neighbors, let it be a, remove the link between them, and select a
path (let it be the shortest one) from a to r; this path is a-b-c-r,
so the ear is r-a-b-c-r. Since both endpoints of the ear are r,
selecting the right tree is not important, e.g., we can add c-b-a-r to
the first tree, and a-b-c-r to the second one
<xref target="Figure MRTs for 2-connected"/>. This way, r, a, b and c form the set of
"ready" nodes. From the ready set, c and d are not the root and have
non-ready neighbors. Let us select, e.g., c. The shortest path from d
to r when c is removed is d-e-r, so we have ear c-d-e-r, we add d-e-r
to the first tree and e-d-c to the second one (recall that we do not
want to create a new neighbor for r in the second tree). Finally, the
last non-ready node is f, and the ear is b-f-d. Since neither is b an
ancestor of d nor is d an ancestor of b in any of the trees, we can
connect f to the trees in both ways. E.g., add f-b to the first tree,
and f-d to the second one.</t>
</section>
<section title="Non-2-connected networks">
<t>When, however, the network is not 2-connected, it is not always
possible to find a pair of node-disjoint paths from any node x to root
r, which makes our previous algorithm unable to find the trees.
However, while the network is connected, it is made up by 2-connected
components bordered by "cut-vertices" (naturally, some of these
components may contain only one node). A node is a cut-vertex, if
removing that node splits the network into two.</t>
<t>A simple algorithm to find the components and the cut-vertices can
be to (virtually) remove each vertex one by one, and check
connectivity with BFS or DFS. Moreover, nodes a and b are in the same
2-connected component, if a remains reachable from b after removing
any single node. Note that linear time algorithms do exist that find
both the 2-connected components and the cut-vertices.</t>
<t>Now, we can build up redundant trees in each component. In
components containing r, the root of such trees must be r. Otherwise,
in the remaining components the root must be the last node in the
component along a path to the root. Recall, that this must be a
cut-vertex, so it is the same for each path emanating from that
component.</t>
<t>At this point, we are ready, if there is no cut-edge in the
network. However, if some 2-connected components are connected by a
cut-edge, we must add that edge to both of the trees.</t>
<figure anchor="Figure Non-2-connected"
title="Non-2-connected network">
<artwork>
e---d i
/ / \ /|
r---c f--g |
\ \ / \|
a---b j
</artwork>
</figure>
<figure anchor="Figure MRTs in non-2-connected"
title="The two maximally redundant trees found in the network depicted previously.">
<artwork>
e---d i e---d i
/ /| / \ |
r c f--g | r---c f--g |
\ \ / | \ \|
a---b j a---b j
</artwork>
</figure>
<t>As an example consider the network depicted in
<xref target="Figure Non-2-connected"/>. Observe that now we have two 2-connected
components, one contains r, a, b, c, d, e, f and the other contains g,
i, j. Moreover, these components have no common node, they are
connected with a cut-edge.</t>
<t>Finding the trees in the component containing r is already described; these
trees are the same as previously. Moreover, the other component is a
cycle, so it will be covered by a single ear. Finally we must add
link f-g to both of the trees, to get the trees depicted in
<xref target="Figure MRTs in non-2-connected"/>.</t>
</section>
<section title="Finding maximally redundant trees in distributed environment">
<t>If we need to compute exactly the same maximally redundant trees at
each of the routers, consistency needs to be ensured by tie-breaking
mechanisms. Observe that the previous algorithm has multiple choices
when it selects how to connect nodes to the trees when only r is
ready, how to select ready node q and non-ready node w for a later
ear and when neither of the endpoints is an ancestor of the other
one.</t>
<t>All of the previous decision points can be handled in a consistent
fashion. E.g., the first ear should be connected in such a way, that
the neighbor of r with the lowest ID must be directly connected to r
in the first tree. Moreover, later we should choose ready router with
non-ready neighbor as q and its non-ready neighbor with the lowest ID
as w. Finally, when neither of the endpoint is an ancestor of the
other one, connect the ear to the endpoint with the lower ID in the
first tree.</t>
</section>
</section>
<!-- Change Log
v00 2011-06-28 AKA Initial version
-->
</back>
</rfc>
| PAFTECH AB 2003-2026 | 2026-04-24 01:42:19 |