--- 1/draft-ietf-rtgwg-mrt-frr-algorithm-07.txt 2016-01-10 10:16:07.590547278 -0800 +++ 2/draft-ietf-rtgwg-mrt-frr-algorithm-08.txt 2016-01-10 10:16:07.890554636 -0800 @@ -1,130 +1,131 @@ Routing Area Working Group G. Enyedi Internet-Draft A. Csaszar Intended status: Standards Track Ericsson -Expires: June 23, 2016 A. Atlas +Expires: July 13, 2016 A. Atlas C. Bowers Juniper Networks A. Gopalan University of Arizona - December 21, 2015 + January 10, 2016 - Algorithms for computing Maximally Redundant Trees for IP/LDP Fast- + An Algorithm for Computing Maximally Redundant Trees for IP/LDP Fast- Reroute - draft-ietf-rtgwg-mrt-frr-algorithm-07 + draft-ietf-rtgwg-mrt-frr-algorithm-08 Abstract A solution for IP and LDP Fast-Reroute using Maximally Redundant Trees is presented in draft-ietf-rtgwg-mrt-frr-architecture. This document defines the associated MRT Lowpoint algorithm that is used - in the default MRT profile to compute both the necessary Maximally + in the Default MRT profile to compute both the necessary Maximally Redundant Trees with their associated next-hops and the alternates to select for MRT-FRR. Status of This Memo This Internet-Draft is submitted in full conformance with the provisions of BCP 78 and BCP 79. Internet-Drafts are working documents of the Internet Engineering Task Force (IETF). Note that other groups may also distribute working documents as Internet-Drafts. The list of current Internet- Drafts is at http://datatracker.ietf.org/drafts/current/. Internet-Drafts are draft documents valid for a maximum of six months and may be updated, replaced, or obsoleted by other documents at any time. It is inappropriate to use Internet-Drafts as reference material or to cite them other than as "work in progress." - This Internet-Draft will expire on June 23, 2016. + This Internet-Draft will expire on July 13, 2016. Copyright Notice - Copyright (c) 2015 IETF Trust and the persons identified as the + Copyright (c) 2016 IETF Trust and the persons identified as the document authors. All rights reserved. This document is subject to BCP 78 and the IETF Trust's Legal Provisions Relating to IETF Documents (http://trustee.ietf.org/license-info) in effect on the date of publication of this document. Please review these documents carefully, as they describe your rights and restrictions with respect to this document. Code Components extracted from this document must include Simplified BSD License text as described in Section 4.e of the Trust Legal Provisions and are provided without warranty as described in the Simplified BSD License. Table of Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3 2. Requirements Language . . . . . . . . . . . . . . . . . . . . 5 3. Terminology and Definitions . . . . . . . . . . . . . . . . . 5 - 4. Algorithm Key Concepts . . . . . . . . . . . . . . . . . . . 7 + 4. Algorithm Key Concepts . . . . . . . . . . . . . . . . . . . 6 4.1. Partial Ordering for Disjoint Paths . . . . . . . . . . . 7 - 4.2. Finding an Ear and the Correct Direction . . . . . . . . 9 + 4.2. Finding an Ear and the Correct Direction . . . . . . . . 8 4.3. Low-Point Values and Their Uses . . . . . . . . . . . . . 11 - 4.4. Blocks in a Graph . . . . . . . . . . . . . . . . . . . . 15 - 4.5. Determining Local-Root and Assigning Block-ID . . . . . . 17 - 5. Algorithm Sections . . . . . . . . . . . . . . . . . . . . . 19 - 5.1. Interface Ordering . . . . . . . . . . . . . . . . . . . 19 - 5.2. MRT Island Identification . . . . . . . . . . . . . . . . 22 - 5.3. GADAG Root Selection . . . . . . . . . . . . . . . . . . 23 - 5.4. Initialization . . . . . . . . . . . . . . . . . . . . . 23 - 5.5. MRT Lowpoint Algorithm: Computing GADAG using lowpoint - inheritance . . . . . . . . . . . . . . . . . . . . . . . 24 - 5.6. Augmenting the GADAG by directing all links . . . . . . . 26 - 5.7. Compute MRT next-hops . . . . . . . . . . . . . . . . . . 30 + 4.4. Blocks in a Graph . . . . . . . . . . . . . . . . . . . . 14 + 4.5. Determining Local-Root and Assigning Block-ID . . . . . . 16 + 5. MRT Lowpoint Algorithm Specification . . . . . . . . . . . . 18 + 5.1. Interface Ordering . . . . . . . . . . . . . . . . . . . 18 + 5.2. MRT Island Identification . . . . . . . . . . . . . . . . 21 + 5.3. GADAG Root Selection . . . . . . . . . . . . . . . . . . 21 + 5.4. Initialization . . . . . . . . . . . . . . . . . . . . . 22 + 5.5. Constructing the GADAG using lowpoint inheritance . . . . 23 + 5.6. Augmenting the GADAG by directing all links . . . . . . . 25 + 5.7. Compute MRT next-hops . . . . . . . . . . . . . . . . . . 29 5.7.1. MRT next-hops to all nodes ordered with respect to - the computing node . . . . . . . . . . . . . . . . . 30 + the computing node . . . . . . . . . . . . . . . . . 29 5.7.2. MRT next-hops to all nodes not ordered with respect - to the computing node . . . . . . . . . . . . . . . . 31 + to the computing node . . . . . . . . . . . . . . . . 30 5.7.3. Computing Redundant Tree next-hops in a 2-connected - Graph . . . . . . . . . . . . . . . . . . . . . . . . 32 - 5.7.4. Generalizing for a graph that isn't 2-connected . . . 34 - 5.7.5. Complete Algorithm to Compute MRT Next-Hops . . . . . 35 - 5.8. Identify MRT alternates . . . . . . . . . . . . . . . . . 37 - 5.9. Named Proxy-Nodes . . . . . . . . . . . . . . . . . . . . 44 - 5.9.1. Determining Proxy-Node Attachment Routers . . . . . . 44 - 5.9.2. Computing if an Island Neighbor (IN) is loop-free . . 45 - 5.9.3. Computing MRT Next-Hops for Proxy-Nodes . . . . . . . 47 - 5.9.4. Computing MRT Alternates for Proxy-Nodes . . . . . . 53 - 6. MRT Lowpoint Algorithm: Next-hop conformance . . . . . . . . 61 - 7. Broadcast interfaces . . . . . . . . . . . . . . . . . . . . 61 - 7.1. Computing MRT next-hops on broadcast networks . . . . . . 62 + Graph . . . . . . . . . . . . . . . . . . . . . . . . 31 + 5.7.4. Generalizing for a graph that isn't 2-connected . . . 33 + 5.7.5. Complete Algorithm to Compute MRT Next-Hops . . . . . 34 + 5.8. Identify MRT alternates . . . . . . . . . . . . . . . . . 36 + 5.9. Named Proxy-Nodes . . . . . . . . . . . . . . . . . . . . 43 + 5.9.1. Determining Proxy-Node Attachment Routers . . . . . . 43 + 5.9.2. Computing if an Island Neighbor (IN) is loop-free . . 44 + 5.9.3. Computing MRT Next-Hops for Proxy-Nodes . . . . . . . 46 + 5.9.4. Computing MRT Alternates for Proxy-Nodes . . . . . . 52 + 6. MRT Lowpoint Algorithm: Next-hop conformance . . . . . . . . 60 + 7. Broadcast interfaces . . . . . . . . . . . . . . . . . . . . 60 + 7.1. Computing MRT next-hops on broadcast networks . . . . . . 61 7.2. Using MRT next-hops as alternates in the event of - failures on broadcast networks . . . . . . . . . . . . . 63 - 8. Python Implementation of MRT Lowpoint Algorithm . . . . . . . 64 - 9. Algorithm Alternatives and Evaluation . . . . . . . . . . . . 104 - 9.1. Algorithm Evaluation . . . . . . . . . . . . . . . . . . 105 - 10. Implementation Status . . . . . . . . . . . . . . . . . . . . 115 - 11. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . 115 - 12. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 115 - 13. Security Considerations . . . . . . . . . . . . . . . . . . . 115 - 14. References . . . . . . . . . . . . . . . . . . . . . . . . . 115 - 14.1. Normative References . . . . . . . . . . . . . . . . . . 115 - 14.2. Informative References . . . . . . . . . . . . . . . . . 115 - Appendix A. Option 2: Computing GADAG using SPFs . . . . . . . . 117 - Appendix B. Option 3: Computing GADAG using a hybrid method . . 122 - Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 124 + failures on broadcast networks . . . . . . . . . . . . . 62 + 8. Evaluation of Alternative Methods for Constructing GADAGs . . 63 + 9. Implementation Status . . . . . . . . . . . . . . . . . . . . 64 + 10. Operational Considerations . . . . . . . . . . . . . . . . . 65 + 10.1. GADAG Root Selection . . . . . . . . . . . . . . . . . . 65 + 10.2. Destination-rooted GADAGs . . . . . . . . . . . . . . . 65 + 11. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . 66 + 12. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 66 + 13. Security Considerations . . . . . . . . . . . . . . . . . . . 66 + 14. References . . . . . . . . . . . . . . . . . . . . . . . . . 66 + 14.1. Normative References . . . . . . . . . . . . . . . . . . 66 + 14.2. Informative References . . . . . . . . . . . . . . . . . 66 + Appendix A. Python Implementation of MRT Lowpoint Algorithm . . 67 + Appendix B. Constructing a GADAG using SPFs . . . . . . . . . . 108 + Appendix C. Constructing a GADAG using a hybrid method . . . . . 113 + Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 115 1. Introduction MRT Fast-Reroute requires that packets can be forwarded not only on the shortest-path tree, but also on two Maximally Redundant Trees (MRTs), referred to as the MRT-Blue and the MRT-Red. A router which experiences a local failure must also have pre-determined which alternate to use. This document defines how to compute these three things for use in MRT-FRR and describes the algorithm design decisions and rationale. The algorithm is based on those presented in [MRTLinear] and expanded in [EnyediThesis]. The MRT Lowpoint - algorithm is required for implementation when the default MRT profile + algorithm is required for implementation when the Default MRT profile is implemented. Just as packets routed on a hop-by-hop basis require that each router compute a shortest-path tree which is consistent, it is necessary for each router to compute the MRT-Blue next-hops and MRT-Red next-hops in a consistent fashion. This document defines the MRT Lowpoint algorithm to be used as a standard in the default MRT profile for MRT-FRR. As now, a router's FIB will contain primary next-hops for the current @@ -134,38 +135,40 @@ Red for forwarding received traffic on the MRT-Red. What alternate next-hops a point-of-local-repair (PLR) selects need not be consistent - but loops must be prevented. To reduce congestion, it is possible for multiple alternate next-hops to be selected; in the context of MRT alternates, each of those alternate next-hops would be equal-cost paths. This document defines an algorithm for selecting an appropriate MRT alternate for consideration. Other alternates, e.g. LFAs that are - downstream paths, may be preferred when available and that policy- - based alternate selection process [I-D.ietf-rtgwg-lfa-manageability] - is not captured in this document. + downstream paths, may be preferred when available. See the + Operational Considerations section of + [I-D.ietf-rtgwg-mrt-frr-architecture] for a more detailed discussion + of combining MRT alternates with those produced by other FRR + technologies. [E]---[D]---| [E]<--[D]<--| [E]-->[D] | | | | ^ | | | | | V | | V [R] [F] [C] [R] [F] [C] [R] [F] [C] | | | ^ ^ | | | | | | | V | [A]---[B]---| [A]-->[B] [A]---[B]<--| (a) (b) (c) a 2-connected graph MRT-Blue towards R MRT-Red towards R Figure 1 - Algorithms for computing MRTs can handle arbitrary network topologies + The MRT Lowpoint algorithm can handle arbitrary network topologies where the whole network graph is not 2-connected, as in Figure 2, as well as the easier case where the network graph is 2-connected (Figure 1). Each MRT is a spanning tree. The pair of MRTs provide two paths from every node X to the root of the MRTs. Those paths share the minimum number of nodes and the minimum number of links. Each such shared node is a cut-vertex. Any shared links are cut- links. [E]---[D]---| |---[J] | | | | | @@ -190,96 +193,38 @@ Figure 2 2. Requirements Language The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in [RFC2119]. 3. Terminology and Definitions - network graph: A graph that reflects the network topology where all - links connect exactly two nodes and broadcast links have been - transformed into a pseudonode representation (e.g. in OSPF, - viewing a Network LSA as representing a pseudonode). - - Redundant Trees (RT): A pair of trees where the path from any node X - to the root R on the first tree is node-disjoint with the path - from the same node X to the root along the second tree. These can - be computed in 2-connected graphs. - - Maximally Redundant Trees (MRT): A pair of trees where the path - from any node X to the root R along the first tree and the path - from the same node X to the root along the second tree share the - minimum number of nodes and the minimum number of links. Each - such shared node is a cut-vertex. Any shared links are cut-links. - Any RT is an MRT but many MRTs are not RTs. - - MRT Island: From the computing router, the set of routers that - support a particular MRT profile and are connected. - - MRT-Red: MRT-Red is used to describe one of the two MRTs; it is - used to describe the associated forwarding topology and MT-ID. - Specifically, MRT-Red is the decreasing MRT where links in the - GADAG are taken in the direction from a higher topologically - ordered node to a lower one. - - MRT-Blue: MRT-Blue is used to describe one of the two MRTs; it is - used to describe the associated forwarding topology and MT-ID. - Specifically, MRT-Blue is the increasing MRT where links in the - GADAG are taken in the direction from a lower topologically - ordered node to a higher one. - - cut-vertex: A vertex whose removal partitions the network. - - cut-link: A link whose removal partitions the network. A cut-link - by definition must be connected between two cut-vertices. If - there are multiple parallel links, then they are referred to as - cut-links in this document if removing the set of parallel links - would partition the network. - - 2-connected: A graph that has no cut-vertices. This is a graph - that requires two nodes to be removed before the network is - partitioned. + Please see the Terminology section of + [I-D.ietf-rtgwg-mrt-frr-architecture] for a complete list of + terminology relevant to this draft. The list below does not repeat + terminology introduced in that draft. spanning tree: A tree containing links that connects all nodes in the network graph. back-edge: In the context of a spanning tree computed via a depth- first search, a back-edge is a link that connects a descendant of a node x with an ancestor of x. - 2-connected cluster: A maximal set of nodes that are 2-connected. - In a network graph with at least one cut-vertex, there will be - multiple 2-connected clusters. - - block: Either a 2-connected cluster, a cut-link, or an isolated - vertex. - - DAG: Directed Acyclic Graph - a digraph containing no directed - cycle. - - ADAG: Almost Directed Acyclic Graph - a digraph that can be - transformed into a DAG with removing a single node (the root - node). - partial ADAG: A subset of an ADAG that doesn't yet contain all the nodes in the block. A partial ADAG is created during the MRT algorithm and then expanded until all nodes in the block are included and it is an ADAG. - GADAG: Generalized ADAG - a digraph, which has only ADAGs as all of - its blocks. The root of such a block is the node closest to the - global root (e.g. with uniform link costs). - DFS: Depth-First Search - DFS ancestor: A node n is a DFS ancestor of x if n is on the DFS- tree path from the DFS root to x. DFS descendant: A node n is a DFS descendant of x if x is on the DFS-tree path from the DFS root to n. ear: A path along not-yet-included-in-the-GADAG nodes that starts at a node that is already-included-in-the-GADAG and that ends at a node that is already-included-in-the-GADAG. The starting and ending nodes may be the same node if it is a cut-vertex. @@ -287,49 +232,47 @@ X >> Y or Y << X: Indicates the relationship between X and Y in a partial order, such as found in a GADAG. X >> Y means that X is higher in the partial order than Y. Y << X means that Y is lower in the partial order than X. X > Y or Y < X: Indicates the relationship between X and Y in the total order, such as found via a topological sort. X > Y means that X is higher in the total order than Y. Y < X means that Y is lower in the total order than X. - proxy-node: A node added to the network graph to represent a multi- - homed prefix or routers outside the local MRT-fast-reroute- - supporting island of routers. The key property of proxy-nodes is - that traffic cannot transit them. + X ?? Y: Indicates that X is unordered with respect to Y in the + partial order. UNDIRECTED: In the GADAG, each link is marked as OUTGOING, INCOMING or both. Until the directionality of the link is determined, the link is marked as UNDIRECTED to indicate that its direction hasn't been determined. OUTGOING: A link marked as OUTGOING has direction in the GADAG from the interface's router to the remote end. INCOMING: A link marked as INCOMING has direction in the GADAG from the remote end to the interface's router. 4. Algorithm Key Concepts There are five key concepts that are critical for understanding the - MRT Lowpoint algorithm and other algorithms for computing MRTs. The - first is the idea of partially ordering the nodes in a network graph - with regard to each other and to the GADAG root. The second is the - idea of finding an ear of nodes and adding them in the correct - direction. The third is the idea of a Low-Point value and how it can - be used to identify cut-vertices and to find a second path towards - the root. The fourth is the idea that a non-2-connected graph is - made up of blocks, where a block is a 2-connected cluster, a cut-link - or an isolated node. The fifth is the idea of a local-root for each - node; this is used to compute ADAGs in each block. + MRT Lowpoint algorithm. The first is the idea of partially ordering + the nodes in a network graph with regard to each other and to the + GADAG root. The second is the idea of finding an ear of nodes and + adding them in the correct direction. The third is the idea of a + Low-Point value and how it can be used to identify cut-vertices and + to find a second path towards the root. The fourth is the idea that + a non-2-connected graph is made up of blocks, where a block is a + 2-connected cluster, a cut-link or an isolated node. The fifth is + the idea of a local-root for each node; this is used to compute ADAGs + in each block. 4.1. Partial Ordering for Disjoint Paths Given any two nodes X and Y in a graph, a particular total order means that either X < Y or X > Y in that total order. An example would be a graph where the nodes are ranked based upon their unique IP loopback addresses. In a partial order, there may be some nodes for which it can't be determined whether X << Y or X >> Y. A partial order can be captured in a directed graph, as shown in Figure 3. In a graphical representation, a link directed from X to Y indicates @@ -480,27 +423,29 @@ while there exists connected nodes in graph that are not IN_GADAG Select a new ear. Let its endpoints be X and Y. if Y is root or (Y << X) add the ear towards X to the ADAG else // (a) X is root or (b)X << Y or (c) X, Y not ordered Add the ear towards Y to the ADAG Figure 6: Generic Algorithm to find ears and their direction in 2-connected graph - Algorithm Figure 6 merely requires that a cycle or ear be selected - without specifying how. Regardless of the way of selecting the path, - we will get an ADAG. The method used for finding and selecting the - ears is important; shorter ears result in shorter paths along the - MRTs. The MRT Lowpoint algorithm's method using Low-Point - Inheritance is defined in Section 5.5. Other methods are described - in the Appendices (Appendix A and Appendix B). + The algorithm in Figure 6 merely requires that a cycle or ear be + selected without specifying how. Regardless of the method for + selecting the path, we will get an ADAG. The method used for finding + and selecting the ears is important; shorter ears result in shorter + paths along the MRTs. The MRT Lowpoint algorithm uses the Low-Point + Inheritance method for constructing an ADAG (and ultimately a GADAG). + This method is defined in Section 5.5. Other methods for + constructing GADAGs are described in Appendix B and Appendix C. An + evaluation of these different methods is given in Section 8 As an example, consider Figure 5 again. First, we select the shortest cycle containing R, which can be R-A-B-F-D-E (uniform link costs were assumed), so we get to the situation depicted in Figure 5 (b). Finally, we find a node next to a ready node; that must be node C and assume we reached it from ready node B. We search a path from C to R without B in the original graph. The first ready node along this is node D, so the open ear is B-C-D. Since B<C and C->D to the ADAG. Since all the nodes are ready, we stop at this point. @@ -642,25 +587,25 @@ Third, as seen in Figure 9, even if L(x) < D(x), there may be a block that contains both the root and a DFS-child of a node while other DFS-children might be in different blocks. In this example, C's child D is in the same block as R while F is not. It is important to realize that the root of a block may also be the root of another block. 4.4. Blocks in a Graph - A key idea for an MRT algorithm is that any non-2-connected graph is - made up by blocks (e.g. 2-connected clusters, cut-links, and/or - isolated nodes). To compute GADAGs and thus MRTs, computation is - done in each block to compute ADAGs or Redundant Trees and then those - ADAGs or Redundant Trees are combined into a GADAG or MRT. + A key idea for the MRT Lowpoint algorithm is that any non-2-connected + graph is made up by blocks (e.g. 2-connected clusters, cut-links, + and/or isolated nodes). To compute GADAGs and thus MRTs, computation + is done in each block to compute ADAGs or Redundant Trees and then + those ADAGs or Redundant Trees are combined into a GADAG or MRT. [E]---| [J]-------[I] [P]---[O] | | | | | | | | | | | | [R] [D]---[C]--[F] [H]---[K] [N] | | | | | | | | | | | | [A]--------[B] [G]---| [L]---[M] (a) A graph with four blocks that are: @@ -678,21 +623,21 @@ (b) MRT-Blue for destination R [E]---| [J]-------->[I] [P]-->[O] | | | V V V [R] [D]-->[C]<---[F] [H]<---[K] [N] ^ | ^ | ^ | | V | | | V [A]<-------[B] [G]<--| [L]<--[M] - (c) MRT-Red for destionation R + (c) MRT-Red for destination R Figure 10 Consider the example depicted in Figure 10 (a). In this figure, a special graph is presented, showing us all the ways 2-connected clusters can be connected. It has four blocks: block 1 contains R, A, B, C, D, E, block 2 contains C, F, G, H, I, J, block 3 contains K, L, M, N, O, P, and block 4 is a cut-link containing H and K. As can be observed, the first two blocks have one common node (node C) and blocks 2 and 3 do not have any common node, but they are connected @@ -734,22 +679,22 @@ else mark x as cut-vertex Compute_Localroot(c, x) Compute_Localroot(gadag_root, gadag_root) Figure 11: A method for computing local-roots There are two different ways of computing the local-root for each node. The stand-alone method is given in Figure 11 and better - illustrates the concept; it is used by the MRT algorithms given in - the Appendices Appendix A and Appendix B. The MRT Lowpoint algorithm + illustrates the concept; it is used by the GADAG construction methods + given in Appendix B and Appendix C. The MRT Lowpoint algorithm computes the local-root for a block as part of computing the GADAG using lowpoint inheritance; the essence of this computation is given in Figure 12. Both methods for computing the local-root produce the same results. Get the current node, s. Compute an ear(either through lowpoint inheritance or by following dfs parents) from s to a ready node e. (Thus, s is not e, if there is such ear.) if s is e @@ -787,50 +732,53 @@ max_block_id += 1 Assign_Block_ID(c, max_block_id) else Assign_Block_ID(c, cur_block_id) max_block_id = 0 Assign_Block_ID(gadag_root, max_block_id) Figure 13: Assigning block id to identify blocks -5. Algorithm Sections +5. MRT Lowpoint Algorithm Specification - This algorithm computes one GADAG that is then used by a router to - determine its MRT-Blue and MRT-Red next-hops to all destinations. - Finally, based upon that information, alternates are selected for - each next-hop to each destination. The different parts of this - algorithm are described below. These work on a network graph after - its interfaces have been ordered as per Figure 14. + The MRT Lowpoint algorithm computes one GADAG that is then used by a + router to determine its MRT-Blue and MRT-Red next-hops to all + destinations. Finally, based upon that information, alternates are + selected for each next-hop to each destination. The different parts + of this algorithm are described below. - 1. Compute the local MRT Island for the particular MRT Profile. - [See Section 5.2.] + o Order the interfaces in the network graph. [See Section 5.1] - 2. Select the root to use for the GADAG. [See Section 5.3.] + o Compute the local MRT Island for the particular MRT Profile. [See + Section 5.2] - 3. Initialize all interfaces to UNDIRECTED. [See Section 5.4.] + o Select the root to use for the GADAG. [See Section 5.3] - 4. Compute the DFS value,e.g. D(x), and lowpoint value, L(x). [See - Figure 8.] + o Initialize all interfaces to UNDIRECTED. [See Section 5.4] - 5. Construct the GADAG. [See Section 5.5] + o Compute the DFS value,e.g. D(x), and lowpoint value, L(x). [See + Figure 8] - 6. Assign directions to all interfaces that are still UNDIRECTED. - [See Section 5.6.] + o Construct the GADAG. [See Section 5.5] - 7. From the computing router x, compute the next-hops for the MRT- - Blue and MRT-Red. [See Section 5.7.] + o Assign directions to all interfaces that are still UNDIRECTED. + [See Section 5.6] - 8. Identify alternates for each next-hop to each destination by + o From the computing router x, compute the next-hops for the MRT- + Blue and MRT-Red. [See Section 5.7] + + o Identify alternates for each next-hop to each destination by determining which one of the blue MRT and the red MRT the - computing router x should select. [See Section 5.8.] + computing router x should select. [See Section 5.8] + + A Python implementation of this algorithm is given in Appendix A. 5.1. Interface Ordering To ensure consistency in computation, all routers MUST order interfaces identically down to the set of links with the same metric to the same neighboring node. This is necessary for the DFS in Lowpoint_Visit in Section 4.3, where the selection order of the interfaces to explore results in different trees. Consistent interface ordering is also necessary for computing the GADAG, where the selection order of the interfaces to use to form ears can result @@ -867,25 +815,25 @@ parallel links will be added to the GADAG with the same direction assigned during the procedure for assigning direction to UNDIRECTED links described in Section 5.6. An implementation is free to apply some additional criteria to break ties in interface ordering in this situation, but that criteria is not specified here since it will not affect the final GADAG produced by the algorithm. The Interface_Compare function in Figure 14 relies on the interface.metric and the interface.neighbor.mrt_node_id values to order interfaces. The exact source of these values for different - IGPs (or flooding protocol in the case of ISIS-PCR - [I-D.ietf-isis-pcr]) and applications is specified in Figure 15. The - metric and mrt_node_id values for OSPFv2, OSPFv3, and IS-IS provided - here is normative. The metric and mrt_node_id values for ISIS-PCR - should be considered informational. + IGPs and applications is specified in Figure 15. The metric and + mrt_node_id values for OSPFv2, OSPFv3, and IS-IS provided here is + normative. The metric and mrt_node_id values for ISIS-PCR in this + table should be considered informational. The normative values are + specified in [IEEE8021Qca] . +--------------+-----------------------+-----------------------------+ | IGP/flooding | mrt_node_id | metric of | | protocol | of neighbor | interface | | and | on interface | | | application | | | +--------------+-----------------------+-----------------------------+ | OSPFv2 for | 4 octet Neighbor | 2 octet Metric field | | IP/LDP FRR | Router ID in | for corresponding | | | Link ID field for | point-to-point link | @@ -928,30 +876,20 @@ flooding protocols and applications The metrics are unsigned integers and MUST be compared as unsigned integers. The results of mrt_node_id comparisons MUST be the same as would be obtained by converting the mrt_node_ids to unsigned integers using network byte order and performing the comparison as unsigned integers. In the case of IS-IS for IP/LDP FRR with point-to-point links, the pseudonode number (the 7th octet) is zero. Broadcast interfaces will be discussed in Section 7. - In the case of IS-IS for IP/LDP FRR, this specification allows for - the use of Multi-Topology routing. [RFC5120] requires that - information related to the standard/default topology (MT-ID = 0) be - carried in the Extended IS Reachability TLV #22, while it requires - that the Multi-Topology IS Neighbor TLV #222 only be used to carry - topology information related to non-default topologies (with non-zero - MT-IDs). [RFC5120] enforces this by requiring an implementation to - ignore TLV#222 with MT-ID = 0. The current document also requires - that TLV#222 with MT-ID = 0 MUST be ignored. - 5.2. MRT Island Identification The local MRT Island for a particular MRT profile can be determined by starting from the computing router in the network graph and doing a breadth-first-search (BFS). The BFS explores only links that are in the same area/level, are not IGP-excluded, and are not MRT- ineligible. The BFS explores only nodes that are are not IGP- excluded, and that support the particular MRT profile. See section 7 of [I-D.ietf-rtgwg-mrt-frr-architecture] for more precise definitions of these criteria. @@ -972,78 +910,75 @@ intf.remote_node.IN_MRT_ISLAND = TRUE if (not intf.remote_node.IN_MRT_ISLAND)) intf.remote_node.IN_MRT_ISLAND = TRUE add_to_tail(explore_list, intf.remote_node) Figure 16: MRT Island Identification 5.3. GADAG Root Selection In Section 8.3 of [I-D.ietf-rtgwg-mrt-frr-architecture], the GADAG - Root Selection Policy is described for the MRT default profile. In - [I-D.ietf-ospf-mrt] and [I-D.ietf-isis-mrt], a mechanism is given for - routers to advertise the GADAG Root Selection Priority and - consistently select a GADAG Root inside the local MRT Island. The - MRT Lowpoint algorithm simply requires that all routers in the MRT - Island MUST select the same GADAG Root; the mechanism can vary based - upon the MRT profile description. Before beginning computation, the - network graph is reduced to contain only the set of routers that - support the specific MRT profile whose MRTs are being computed. + Root Selection Policy is described for the MRT default profile. This + selection policy allows routers to consistently select a common GADAG + Root inside the local MRT Island, based on advertised priority + values. The MRT Lowpoint algorithm simply requires that all routers + in the MRT Island MUST select the same GADAG Root; the mechanism can + vary based upon the MRT profile description. Before beginning + computation, the network graph is reduced to contain only the set of + routers that support the specific MRT profile whose MRTs are being + computed. As noted in Section 7, pseudonodes MUST NOT be considered for GADAG root selection. - Analysis has shown that the centrality of a router can have a - significant impact on the lengths of the alternate paths computed. - Therefore, it is RECOMMENDED that off-line analysis that considers - the centrality of a router be used to help determine how good a - choice a particular router is for the role of GADAG root. + It is expected that an operator will designate a set of routers as + good choices for selection as GADAG root by setting the GADAG Root + Selection Priority for that set of routers to lower (more preferred) + numerical values. For guidance on setting the GADAG Root Selection + Priority values, refer to Section 10.1. 5.4. Initialization Before running the algorithm, there is the standard type of initialization to be done, such as clearing any computed DFS-values, lowpoint-values, DFS-parents, lowpoint-parents, any MRT-computed next-hops, and flags associated with algorithm. It is assumed that a regular SPF computation has been run so that the primary next-hops from the computing router to each destination are known. This is required for determining alternates at the last step. Initially, all interfaces MUST be initialized to UNDIRECTED. Whether they are OUTGOING, INCOMING or both is determined when the GADAG is constructed and augmented. - It is possible that some links and nodes will be marked as unusable - using standard IGP mechanisms (see section 7 of - [I-D.ietf-rtgwg-mrt-frr-architecture]). Due to FRR manageability - considerations [I-D.ietf-rtgwg-lfa-manageability], it may also be - desirable to administratively configure some interfaces as ineligible - to carry MRT FRR traffic. This constraint MUST be consistently - flooded via the IGP [I-D.ietf-ospf-mrt] [I-D.ietf-isis-mrt] by the - owner of the interface, so that links are known to be MRT-ineligible - and not explored or used in the MRT algorithm. When a either - interface on a link is advertised as MRT-ineligible, the link MUST - NOT be included in the MRT Island, and will thus be excluded from the - GADAG. Computation of MRT next-hops will therefore not use any MRT- + It is possible that some links and nodes will be marked using + standard IGP mechanisms to discourage or prevent transit traffic. + Section 7.3.1 of [I-D.ietf-rtgwg-mrt-frr-architecture] describes how + those links and nodes are excluded from MRT Island formation. + + MRT-FRR also has the ability to advertise links MRT-Ineligible, as + described in Section 7.3.2 of [I-D.ietf-rtgwg-mrt-frr-architecture]. + These links are excluded from the MRT Island and the GADAG. + Computation of MRT next-hops will therefore not use any MRT- ineligible links. The MRT algorithm does still need to consider MRT- ineligible links when computing FRR alternates, because an MRT- ineligible link can still be the shortest-path next-hop to reach a destination. When a broadcast interface is advertised as MRT-ineligible, then the pseudo-node representing the entire broadcast network MUST NOT be included in the MRT Island. This is equivalent to excluding all of the broadcast interfaces on that broadcast network from the MRT Island. -5.5. MRT Lowpoint Algorithm: Computing GADAG using lowpoint inheritance +5.5. Constructing the GADAG using lowpoint inheritance As discussed in Section 4.2, it is necessary to find ears from a node x that is already in the GADAG (known as IN_GADAG). Two different methods are used to find ears in the algorithm. The first is by going to a not IN_GADAG DFS-child and then following the chain of low-point parents until an IN_GADAG node is found. The second is by going to a not IN_GADAG neighbor and then following the chain of DFS parents until an IN_GADAG node is found. As an ear is found, the associated interfaces are marked based on the direction taken. The nodes in the ear are marked as IN_GADAG. In the algorithm, first the @@ -1144,21 +1078,21 @@ if ((intf.remote_node.IN_GADAG == false) and (intf.remote_node.dfs_parent is not x)) Construct_Ear(x, Stack, intf, NEIGHBOR) Construct_GADAG_via_Lowpoint(topology, gadag_root) Figure 17: Low-point Inheritance GADAG algorithm 5.6. Augmenting the GADAG by directing all links - The GADAG, regardless of the algorithm used to construct it, at this + The GADAG, regardless of the method used to construct it, at this point could be used to find MRTs, but the topology does not include all links in the network graph. That has two impacts. First, there might be shorter paths that respect the GADAG partial ordering and so the alternate paths would not be as short as possible. Second, there may be additional paths between a router x and the root that are not included in the GADAG. Including those provides potentially more bandwidth to traffic flowing on the alternates and may reduce congestion compared to just using the GADAG as currently constructed. The goal is thus to assign direction to every remaining link marked @@ -2915,21 +2850,237 @@ alternates. For example, when the PLR observes that connectivity to an IP-layer node on a broadcast network has failed, the PLR may choose to still use the broadcast network to reach other IP-layer nodes which are still reachable. Or if the PLR observes that connectivity has failed to several IP-layer nodes on the same broadcast network, it may choose to treat the entire broadcast network as failed. The choice of MRT alternates by a PLR for a particular set of failure conditions is a local decision, since it does not require coordination with other nodes. -8. Python Implementation of MRT Lowpoint Algorithm +8. Evaluation of Alternative Methods for Constructing GADAGs + + This document specifies the MRT Lowpoint algorithm. One component of + the algorithm involves constructing a common GADAG based on the + network topology. The MRT Lowpoint algorithm computes the GADAG + using the method described in Section 5.5. This method aims to + minimize the amount of computation required to compute the GADAG. In + the process of developing the MRT Lowpoint algorithm, two alternative + methods for constructing GADAGs were also considered. These + alternative methods are described in Appendix B and Appendix C. In + general, these other two methods require more computation to compute + the GADAG. The analysis below was performed to determine if the + alternative GADAG construction methods produce shorter MRT alternate + paths in real network topologies, and if so, to what extent. + + Figure 30 compares results obtained using the three different methods + for constructing GADAGs on five different service provider network + topologies. MRT_LOWPOINT indicates the method specified in + Section 5.5, while MRT_SPF and MRT_HYBRID indicate the methods + specified in Appendix B and Appendix C, respectively. The columns on + the right present the distribution of alternate path lengths for each + GADAG construction method. Each MRT computation was performed using + a same GADAG root chosen based on centrality. + + For three of the topologies analyzed (T201, T206, and T211), the use + of MRT_SPF or MRT_HYBRID methods does not appear to provide a + significantly shorter alternate path lengths compared to the + MRT_LOWPOINT method. However, for two of the topologies (T216 and + T219), the use of the MRT_SPF method resulted in noticeably shorter + alternate path lengths than the use of the MRT_LOWPOINT or MRT_HYBRID + methods. + + It was decided to use the MRT_LOWPOINT method to construct the GADAG + in the algorithm specified in this draft, in order to initially offer + an algorithm with lower computational requirements. These results + indicate that in the future it may be useful to evaluate and + potentially specify other MRT algorithm variants that use different + GADAG construction methods. + + +-------------------------------------------------------------------+ + | Topology name | percentage of failure scenarios | + | | protected by an alternate N hops | + | GADAG construction | longer than the primary path | + | method +------------------------------------+ + | | | | | | | | | | no | + | | | | | | |10 |12 |14 | alt| + | |0-1|2-3|4-5|6-7|8-9|-11|-13|-15| <16| + +------------------------------+---+---+---+---+---+---+---+---+----+ + | T201(avg primary hops=3.5) | | | | | | | | | | + | MRT_HYBRID | 33| 26| 23| 6| 3| | | | | + | MRT_SPF | 33| 36| 23| 6| 3| | | | | + | MRT_LOWPOINT | 33| 36| 23| 6| 3| | | | | + +------------------------------+---+---+---+---+---+---+---+---+----+ + | T206(avg primary hops=3.7) | | | | | | | | | | + | MRT_HYBRID | 50| 35| 13| 2| | | | | | + | MRT_SPF | 50| 35| 13| 2| | | | | | + | MRT_LOWPOINT | 55| 32| 13| | | | | | | + +------------------------------+---+---+---+---+---+---+---+---+----+ + | T211(avg primary hops=3.3) | | | | | | | | | | + | MRT_HYBRID | 86| 14| | | | | | | | + | MRT_SPF | 86| 14| | | | | | | | + | MRT_LOWPOINT | 85| 15| 1| | | | | | | + +------------------------------+---+---+---+---+---+---+---+---+----+ + | T216(avg primary hops=5.2) | | | | | | | | | | + | MRT_HYBRID | 23| 22| 18| 13| 10| 7| 4| 2| 2| + | MRT_SPF | 35| 32| 19| 9| 3| 1| | | | + | MRT_LOWPOINT | 28| 25| 18| 11| 7| 6| 3| 2| 1| + +------------------------------+---+---+---+---+---+---+---+---+----+ + | T219(avg primary hops=7.7) | | | | | | | | | | + | MRT_HYBRID | 20| 16| 13| 10| 7| 5| 5| 5| 3| + | MRT_SPF | 31| 23| 19| 12| 7| 4| 2| 1| | + | MRT_LOWPOINT | 19| 14| 15| 12| 10| 8| 7| 6| 10| + +------------------------------+---+---+---+---+---+---+---+---+----+ + + Figure 30 + +9. Implementation Status + + [RFC Editor: please remove this section prior to publication.] + + Please see [I-D.ietf-rtgwg-mrt-frr-architecture] for details on + implementation status. + +10. Operational Considerations + + This sections discusses operational considerations related to the the + MRT Lowpoint algorithm and other potential MRT algorithm variants. + For a discussion of operational considerations related to MRT-FRR in + general, see the Operational Considerations section of + [I-D.ietf-rtgwg-mrt-frr-architecture]. + +10.1. GADAG Root Selection + + The Default MRT Profile uses the GADAG Root Selection Priority + advertised by routers as the primary criterion for selecting the + GADAG root. It is RECOMMENDED that an operator designate a set of + routers as good choices for selection as GADAG root by setting the + GADAG Root Selection Priority for that set of routers to lower (more + preferred) numerical values. Criteria for making this designation + are discussed below. + + Analysis has shown that the centrality of a router can have a + significant impact on the lengths of the alternate paths computed. + Therefore, it is RECOMMENDED that off-line analysis that considers + the centrality of a router be used to help determine how good a + choice a particular router is for the role of GADAG root. + + If the router currently selected as GADAG root becomes unreachable in + the IGP topology, then a new GADAG root will be selected. Changing + the GADAG root can change the overall structure of the GADAG as well + the paths of the red and blue MRT trees built using that GADAG. In + order to minimize change in the associated red and blue MRT + forwarding entries that can result from changing the GADAG root, it + is RECOMMENDED that operators prioritize for selection as GADAG root + those routers that are expected to consistently remain part of the + IGP topology. + +10.2. Destination-rooted GADAGs + + The MRT Lowpoint algorithm constructs a single GADAG rooted at a + single node selected as the GADAG root. It is also possible to + construct a different GADAG for each destination, with the GADAG + rooted at the destination. A router can compute the MRT-Red and MRT- + Blue next-hops for that destination based on the GADAG rooted at that + destination. Building a different GADAG for each destination is + computationally more expensive, but it may give somewhat shorter + alternate paths. Using destination-rooted GADAGs would require a new + MRT profile to be created with a new MRT algorithm specification, + since all routers in the MRT Island would need to use destination- + rooted GADAGs. + +11. Acknowledgements + + The authors would like to thank Shraddha Hegde, Eric Wu, Janos + Farkas, and Stewart Bryant for their suggestions and review. We + would also like to thank Anil Kumar SN for his assistance in + clarifying the algorithm description and pseudo-code. + +12. IANA Considerations + + This document includes no request to IANA. + +13. Security Considerations + + The algorithm described in this document does not introduce new + security concerns beyond those already discussed in the document + describing the MRT FRR architecture + [I-D.ietf-rtgwg-mrt-frr-architecture]. + +14. References + +14.1. Normative References + + [I-D.ietf-rtgwg-mrt-frr-architecture] + Atlas, A., Kebler, R., Bowers, C., Envedi, G., Csaszar, + A., Tantsura, J., and R. White, "An Architecture for IP/ + LDP Fast-Reroute Using Maximally Redundant Trees", draft- + ietf-rtgwg-mrt-frr-architecture-07 (work in progress), + October 2015. + + [RFC2119] Bradner, S., "Key words for use in RFCs to Indicate + Requirement Levels", BCP 14, RFC 2119, + DOI 10.17487/RFC2119, March 1997, + . + +14.2. Informative References + + [EnyediThesis] + Enyedi, G., "Novel Algorithms for IP Fast Reroute", + Department of Telecommunications and Media Informatics, + Budapest University of Technology and Economics Ph.D. + Thesis, February 2011, . + + [IEEE8021Qca] + IEEE 802.1, "IEEE 802.1Qca Bridges and Bridged Networks - + Amendment: Path Control and Reservation - Draft 2.1", + (work in progress), June 24, 2015, + . + + [ISO10589-Second-Edition] + International Organization for Standardization, + "Intermediate system to Intermediate system intra-domain + routeing information exchange protocol for use in + conjunction with the protocol for providing the + connectionless-mode Network Service (ISO 8473)", ISO/ + IEC 10589:2002, Second Edition, Nov. 2002. + + [Kahn_1962_topo_sort] + Kahn, A., "Topological sorting of large networks", + Communications of the ACM, Volume 5, Issue 11 , Nov 1962, + . + + [MRTLinear] + Enyedi, G., Retvari, G., and A. Csaszar, "On Finding + Maximally Redundant Trees in Strictly Linear Time", IEEE + Symposium on Computers and Comunications (ISCC) , 2009, + . + + [RFC2328] Moy, J., "OSPF Version 2", STD 54, RFC 2328, + DOI 10.17487/RFC2328, April 1998, + . + + [RFC5120] Przygienda, T., Shen, N., and N. Sheth, "M-ISIS: Multi + Topology (MT) Routing in Intermediate System to + Intermediate Systems (IS-ISs)", RFC 5120, + DOI 10.17487/RFC5120, February 2008, + . + + [RFC7490] Bryant, S., Filsfils, C., Previdi, S., Shand, M., and N. + So, "Remote Loop-Free Alternate (LFA) Fast Reroute (FRR)", + RFC 7490, DOI 10.17487/RFC7490, April 2015, + . + +Appendix A. Python Implementation of MRT Lowpoint Algorithm Below is Python code implementing the MRT Lowpoint algorithm specified in this document. In order to avoid the page breaks in the .txt version of the draft, one can cut and paste the Python code from the .xml version. The code is also posted on Github. While this Python code is believed to correctly implement the pseudo- code description of the algorithm, in the event of a difference, the pseudo-code description should be considered normative. @@ -4880,587 +5029,26 @@ Raise_GADAG_Root_Selection_Priority(topo,this_gadag_root) Run_MRT_for_All_Sources(topo) Write_Output_To_Files(topo, res_file_base) Generate_Basic_Topology_and_Run_MRT() Generate_Complex_Topology_and_Run_MRT() -9. Algorithm Alternatives and Evaluation - - This specification defines the MRT Lowpoint Algorithm, which is one - option among several possible MRT algorithms. Other alternatives are - described in the appendices. - - In addition, it is possible to calculate Destination-Rooted GADAG, - where for each destination, a GADAG rooted at that destination is - computed. Then a router can compute the blue MRT and red MRT next- - hops to that destination. Building GADAGs per destination is - computationally more expensive, but may give somewhat shorter - alternate paths. It may be useful for live-live multicast along - MRTs. - -9.1. Algorithm Evaluation - - The MRT Lowpoint algorithm is the lowest computation of the MRT - algorithms. Two other MRT algorithms are provided in Appendix A and - Appendix B. When analyzed on service provider network topologies, - they did not provide significant differences in the path lenghts for - the alternatives. This section does not focus on that analysis or - the decision to use the MRT Lowpoint algorithm as the default MRT - algorithm; it has the lowest computational and storage requirements - and gave comparable results. - - Since this document defines the MRT Lowpoint algorithm for use in - fast-reroute applications, it is useful to compare MRT and Remote LFA - [RFC7490]. This section compares MRT and remote LFA for IP Fast - Reroute in 19 service provider network topologies, focusing on - coverage and alternate path length. Figure 30 shows the node- - protecting coverage provided by local LFA (LLFA), remote LFA (RLFA), - and MRT against different failure scenarios in these topologies. The - coverage values are calculated as the percentage of source- - destination pairs protected by the given IPFRR method relative to - those protectable by optimal routing, against the same failure modes. - More details on alternate selection policies used for this analysis - are described later in this section. - - +------------+-----------------------------+ - | Topology | percentage of failure | - | | scenarios covered by | - | | IPFRR method | - | |-----------------------------+ - | | NP_LLFA | NP_RLFA | MRT | - +------------+---------+---------+---------+ - | T201 | 37 | 90 | 100 | - | T202 | 73 | 83 | 100 | - | T203 | 51 | 80 | 100 | - | T204 | 55 | 81 | 100 | - | T205 | 92 | 93 | 100 | - | T206 | 71 | 74 | 100 | - | T207 | 57 | 74 | 100 | - | T208 | 66 | 81 | 100 | - | T209 | 79 | 79 | 100 | - | T210 | 95 | 98 | 100 | - | T211 | 68 | 71 | 100 | - | T212 | 59 | 63 | 100 | - | T213 | 84 | 84 | 100 | - | T214 | 68 | 78 | 100 | - | T215 | 84 | 88 | 100 | - | T216 | 43 | 59 | 100 | - | T217 | 78 | 88 | 100 | - | T218 | 72 | 75 | 100 | - | T219 | 78 | 84 | 100 | - +------------+---------+---------+---------+ - - Figure 30 - - For the topologies analyzed here, LLFA is able to provide node- - protecting coverage ranging from 37% to 95% of the source-destination - pairs, as seen in the column labeled NP_LLFA. The use of RLFA in - addition to LLFA is generally able to increase the node-protecting - coverage. The percentage of node-protecting coverage with RLFA is - provided in the column labeled NP_RLFA, ranges from 59% to 98% for - these topologies. The node-protecting coverage provided by MRT is - 100% since MRT is able to provide protection for any source- - destination pair for which a path still exists after the failure. - - We would also like to measure the quality of the alternate paths - produced by these different IPFRR methods. An obvious approach is to - take an average of the alternate path costs over all source- - destination pairs and failure modes. However, this presents a - problem, which we will illustrate by presenting an example of results - for one topology using this approach ( Figure 31). In this table, - the average relative path length is the alternate path length for the - IPFRR method divided by the optimal alternate path length, averaged - over all source-destination pairs and failure modes. The first three - columns of data in the table give the path length calculated from the - sum of IGP metrics of the links in the path. The results for - topology T208 show that the metric-based path lengths for NP_LLFA and - NP_RLFA alternates are on average 78 and 66 times longer than the - path lengths for optimal alternates. The metric-based path lengths - for MRT alternates are on average 14 times longer than for optimal - alternates. - - +--------+------------------------------------------------+ - | | average relative alternate path length | - | |-----------------------+------------------------+ - |Topology| IGP metric | hopcount | - | |-----------------------+------------------------+ - | |NP_LLFA |NP_RLFA | MRT |NP_LLFA |NP_RLFA | MRT | - +--------+--------+--------+-----+--------+--------+------+ - | T208 | 78.2 | 66.0 | 13.6| 0.99 | 1.01 | 1.32 | - +--------+--------+--------+-----+--------+--------+------+ - - Figure 31 - - The network topology represented by T208 uses values of 10, 100, and - 1000 as IGP costs, so small deviations from the optimal alternate - path can result in large differences in relative path length. LLFA, - RLFA, and MRT all allow for at least one hop in the alterate path to - be chosen independent of the cost of the link. This can easily - result in an alternate using a link with cost 1000, which introduces - noise into the path length measurement. In the case of T208, the - adverse effects of using metric-based path lengths is obvious. - However, we have observed that the metric-based path length - introduces noise into alternate path length measurements in several - other topologies as well. For this reason, we have opted to measure - the alternate path length using hopcount. While IGP metrics may be - adjusted by the network operator for a number of reasons (e.g. - traffic engineering), the hopcount is a fairly stable measurement of - path length. As shown in the last three columns of Figure 31, the - hopcount-based alternate path lengths for topology T208 are fairly - well-behaved. - - Figure 32, Figure 33, Figure 34, and Figure 35 present the hopcount- - based path length results for the 19 topologies examined. The - topologies in the four tables are grouped based on the size of the - topologies, as measured by the number of nodes, with Figure 32 having - the smallest topologies and Figure 35 having the largest topologies. - Instead of trying to represent the path lengths of a large set of - alternates with a single number, we have chosen to present a - histogram of the path lengths for each IPFRR method and alternate - selection policy studied. The first eight colums of data represent - the percentage of failure scenarios protected by an alternate N hops - longer than the primary path, with the first column representing an - alternate 0 or 1 hops longer than the primary path, all the way up - through the eighth column respresenting an alternate 14 or 15 hops - longer than the primary path. The last column in the table gives the - percentage of failure scenarios for which there is no alternate less - than 16 hops longer than the primary path. In the case of LLFA and - RLFA, this category includes failure scenarios for which no alternate - was found. - - For each topology, the first row (labeled OPTIMAL) is the - distribution of the number of hops in excess of the primary path - hopcount for optimally routed alternates. (The optimal routing was - done with respect to IGP metrics, as opposed to hopcount.) The - second row(labeled NP_LLFA) is the distribution of the extra hops for - node-protecting LLFA. The third row (labeled NP_LLFA_THEN_NP_RLFA) - is the hopcount distribution when one adds node-protecting RLFA to - increase the coverage. The alternate selection policy used here - first tries to find a node-protecting LLFA. If that does not exist, - then it tries to find an RLFA, and checks if it is node-protecting. - Comparing the hopcount distribution for RLFA and LLFA across these - topologies, one can see how the coverage is increased at the expense - of using longer alternates. It is also worth noting that while - superficially LLFA and RLFA appear to have better hopcount - distributions than OPTIMAL, the presence of entries in the last - column (no alternate < 16) mainly represent failure scenarios that - are not protected, for which the hopcount is effectively infinite. - - The fourth and fifth rows of each topology show the hopcount - distributions for two alternate selection policies using MRT - alternates. The policy represented by the label - NP_LLFA_THEN_MRT_LOWPOINT will first use a node-protecting LLFA. If - a node-protecting LLFA does not exist, then it will use an MRT - alternate. The policy represented by the label MRT_LOWPOINT instead - will use the MRT alternate even if a node-protecting LLFA exists. - One can see from the data that combining node-protecting LLFA with - MRT results in a significant shortening of the alternate hopcount - distribution. - - +-------------------------------------------------------------------+ - | | percentage of failure scenarios | - | Topology name | protected by an alternate N hops | - | and | longer than the primary path | - | alternate selection +------------------------------------+ - | policy evaluated | | | | | | | | | no | - | | | | | | |10 |12 |14 | alt| - | |0-1|2-3|4-5|6-7|8-9|-11|-13|-15| <16| - +------------------------------+---+---+---+---+---+---+---+---+----+ - | T201(avg primary hops=3.5) | | | | | | | | | | - | OPTIMAL | 37| 37| 20| 3| 3| | | | | - | NP_LLFA | 37| | | | | | | | 63| - | NP_LLFA_THEN_NP_RLFA | 37| 34| 19| | | | | | 10| - | NP_LLFA_THEN_MRT_LOWPOINT | 37| 33| 21| 6| 3| | | | | - | MRT_LOWPOINT | 33| 36| 23| 6| 3| | | | | - +------------------------------+---+---+---+---+---+---+---+---+----+ - | T202(avg primary hops=4.8) | | | | | | | | | | - | OPTIMAL | 90| 9| | | | | | | | - | NP_LLFA | 71| 2| | | | | | | 27| - | NP_LLFA_THEN_NP_RLFA | 78| 5| | | | | | | 17| - | NP_LLFA_THEN_MRT_LOWPOINT | 80| 12| 5| 2| 1| | | | | - | MRT_LOWPOINT_ONLY | 48| 29| 13| 7| 2| 1| | | | - +------------------------------+---+---+---+---+---+---+---+---+----+ - | T203(avg primary hops=4.1) | | | | | | | | | | - | OPTIMAL | 36| 37| 21| 4| 2| | | | | - | NP_LLFA | 34| 15| 3| | | | | | 49| - | NP_LLFA_THEN_NP_RLFA | 35| 19| 22| 4| | | | | 20| - | NP_LLFA_THEN_MRT_LOWPOINT | 36| 35| 22| 5| 2| | | | | - | MRT_LOWPOINT_ONLY | 31| 35| 26| 7| 2| | | | | - +------------------------------+---+---+---+---+---+---+---+---+----+ - | T204(avg primary hops=3.7) | | | | | | | | | | - | OPTIMAL | 76| 20| 3| 1| | | | | | - | NP_LLFA | 54| 1| | | | | | | 45| - | NP_LLFA_THEN_NP_RLFA | 67| 10| 4| | | | | | 19| - | NP_LLFA_THEN_MRT_LOWPOINT | 70| 18| 8| 3| 1| | | | | - | MRT_LOWPOINT_ONLY | 58| 27| 11| 3| 1| | | | | - +------------------------------+---+---+---+---+---+---+---+---+----+ - | T205(avg primary hops=3.4) | | | | | | | | | | - | OPTIMAL | 92| 8| | | | | | | | - | NP_LLFA | 89| 3| | | | | | | 8| - | NP_LLFA_THEN_NP_RLFA | 90| 4| | | | | | | 7| - | NP_LLFA_THEN_MRT_LOWPOINT | 91| 9| | | | | | | | - | MRT_LOWPOINT_ONLY | 62| 33| 5| 1| | | | | | - +------------------------------+---+---+---+---+---+---+---+---+----+ - - Figure 32 - - +-------------------------------------------------------------------+ - | | percentage of failure scenarios | - | Topology name | protected by an alternate N hops | - | and | longer than the primary path | - | alternate selection +------------------------------------+ - | policy evaluated | | | | | | | | | no | - | | | | | | |10 |12 |14 | alt| - | |0-1|2-3|4-5|6-7|8-9|-11|-13|-15| <16| - +------------------------------+---+---+---+---+---+---+---+---+----+ - | T206(avg primary hops=3.7) | | | | | | | | | | - | OPTIMAL | 63| 30| 7| | | | | | | - | NP_LLFA | 60| 9| 1| | | | | | 29| - | NP_LLFA_THEN_NP_RLFA | 60| 13| 1| | | | | | 26| - | NP_LLFA_THEN_MRT_LOWPOINT | 64| 29| 7| | | | | | | - | MRT_LOWPOINT | 55| 32| 13| | | | | | | - +------------------------------+---+---+---+---+---+---+---+---+----+ - | T207(avg primary hops=3.9) | | | | | | | | | | - | OPTIMAL | 71| 24| 5| 1| | | | | | - | NP_LLFA | 55| 2| | | | | | | 43| - | NP_LLFA_THEN_NP_RLFA | 63| 10| | | | | | | 26| - | NP_LLFA_THEN_MRT_LOWPOINT | 70| 20| 7| 2| 1| | | | | - | MRT_LOWPOINT_ONLY | 57| 29| 11| 3| 1| | | | | - +------------------------------+---+---+---+---+---+---+---+---+----+ - | T208(avg primary hops=4.6) | | | | | | | | | | - | OPTIMAL | 58| 28| 12| 2| 1| | | | | - | NP_LLFA | 53| 11| 3| | | | | | 34| - | NP_LLFA_THEN_NP_RLFA | 56| 17| 7| 1| | | | | 19| - | NP_LLFA_THEN_MRT_LOWPOINT | 58| 19| 10| 7| 3| 1| | | | - | MRT_LOWPOINT_ONLY | 34| 24| 21| 13| 6| 2| 1| | | - +------------------------------+---+---+---+---+---+---+---+---+----+ - | T209(avg primary hops=3.6) | | | | | | | | | | - | OPTIMAL | 85| 14| 1| | | | | | | - | NP_LLFA | 79| | | | | | | | 21| - | NP_LLFA_THEN_NP_RLFA | 79| | | | | | | | 21| - | NP_LLFA_THEN_MRT_LOWPOINT | 82| 15| 2| | | | | | | - | MRT_LOWPOINT_ONLY | 63| 29| 8| | | | | | | - +------------------------------+---+---+---+---+---+---+---+---+----+ - | T210(avg primary hops=2.5) | | | | | | | | | | - | OPTIMAL | 95| 4| 1| | | | | | | - | NP_LLFA | 94| 1| | | | | | | 5| - | NP_LLFA_THEN_NP_RLFA | 94| 3| 1| | | | | | 2| - | NP_LLFA_THEN_MRT_LOWPOINT | 95| 4| 1| | | | | | | - | MRT_LOWPOINT_ONLY | 91| 6| 2| | | | | | | - +------------------------------+---+---+---+---+---+---+---+---+----+ - - Figure 33 - - +-------------------------------------------------------------------+ - | | percentage of failure scenarios | - | Topology name | protected by an alternate N hops | - | and | longer than the primary path | - | alternate selection +------------------------------------+ - | policy evaluated | | | | | | | | | no | - | | | | | | |10 |12 |14 | alt| - | |0-1|2-3|4-5|6-7|8-9|-11|-13|-15| <16| - +------------------------------+---+---+---+---+---+---+---+---+----+ - | T211(avg primary hops=3.3) | | | | | | | | | | - | OPTIMAL | 88| 11| | | | | | | | - | NP_LLFA | 66| 1| | | | | | | 32| - | NP_LLFA_THEN_NP_RLFA | 68| 3| | | | | | | 29| - | NP_LLFA_THEN_MRT_LOWPOINT | 88| 12| | | | | | | | - | MRT_LOWPOINT | 85| 15| 1| | | | | | | - +------------------------------+---+---+---+---+---+---+---+---+----+ - | T212(avg primary hops=3.5) | | | | | | | | | | - | OPTIMAL | 76| 23| 1| | | | | | | - | NP_LLFA | 59| | | | | | | | 41| - | NP_LLFA_THEN_NP_RLFA | 61| 1| 1| | | | | | 37| - | NP_LLFA_THEN_MRT_LOWPOINT | 75| 24| 1| | | | | | | - | MRT_LOWPOINT_ONLY | 66| 31| 3| | | | | | | - +------------------------------+---+---+---+---+---+---+---+---+----+ - | T213(avg primary hops=4.3) | | | | | | | | | | - | OPTIMAL | 91| 9| | | | | | | | - | NP_LLFA | 84| | | | | | | | 16| - | NP_LLFA_THEN_NP_RLFA | 84| | | | | | | | 16| - | NP_LLFA_THEN_MRT_LOWPOINT | 89| 10| 1| | | | | | | - | MRT_LOWPOINT_ONLY | 75| 24| 1| | | | | | | - +------------------------------+---+---+---+---+---+---+---+---+----+ - | T214(avg primary hops=5.8) | | | | | | | | | | - | OPTIMAL | 71| 22| 5| 2| | | | | | - | NP_LLFA | 58| 8| 1| 1| | | | | 32| - | NP_LLFA_THEN_NP_RLFA | 61| 13| 3| 1| | | | | 22| - | NP_LLFA_THEN_MRT_LOWPOINT | 66| 14| 7| 5| 3| 2| 1| 1| 1| - | MRT_LOWPOINT_ONLY | 30| 20| 18| 12| 8| 4| 3| 2| 3| - +------------------------------+---+---+---+---+---+---+---+---+----+ - | T215(avg primary hops=4.8) | | | | | | | | | | - | OPTIMAL | 73| 27| | | | | | | | - | NP_LLFA | 73| 11| | | | | | | 16| - | NP_LLFA_THEN_NP_RLFA | 73| 13| 2| | | | | | 12| - | NP_LLFA_THEN_MRT_LOWPOINT | 74| 19| 3| 2| 1| 1| 1| | | - | MRT_LOWPOINT_ONLY | 32| 31| 16| 12| 4| 3| 1| | | - +------------------------------+---+---+---+---+---+---+---+---+----+ - - Figure 34 - - +-------------------------------------------------------------------+ - | | percentage of failure scenarios | - | Topology name | protected by an alternate N hops | - | and | longer than the primary path | - | alternate selection +------------------------------------+ - | policy evaluated | | | | | | | | | no | - | | | | | | |10 |12 |14 | alt| - | |0-1|2-3|4-5|6-7|8-9|-11|-13|-15| <16| - +------------------------------+---+---+---+---+---+---+---+---+----+ - | T216(avg primary hops=5.2) | | | | | | | | | | - | OPTIMAL | 60| 32| 7| 1| | | | | | - | NP_LLFA | 39| 4| | | | | | | 57| - | NP_LLFA_THEN_NP_RLFA | 46| 12| 2| | | | | | 41| - | NP_LLFA_THEN_MRT_LOWPOINT | 48| 20| 12| 7| 5| 4| 2| 1| 1| - | MRT_LOWPOINT | 28| 25| 18| 11| 7| 6| 3| 2| 1| - +------------------------------+---+---+---+---+---+---+---+---+----+ - | T217(avg primary hops=8.0) | | | | | | | | | | - | OPTIMAL | 81| 13| 5| 1| | | | | | - | NP_LLFA | 74| 3| 1| | | | | | 22| - | NP_LLFA_THEN_NP_RLFA | 76| 8| 3| 1| | | | | 12| - | NP_LLFA_THEN_MRT_LOWPOINT | 77| 7| 5| 4| 3| 2| 1| 1| | - | MRT_LOWPOINT_ONLY | 25| 18| 18| 16| 12| 6| 3| 1| | - +------------------------------+---+---+---+---+---+---+---+---+----+ - | T218(avg primary hops=5.5) | | | | | | | | | | - | OPTIMAL | 85| 14| 1| | | | | | | - | NP_LLFA | 68| 3| | | | | | | 28| - | NP_LLFA_THEN_NP_RLFA | 71| 4| | | | | | | 25| - | NP_LLFA_THEN_MRT_LOWPOINT | 77| 12| 7| 4| 1| | | | | - | MRT_LOWPOINT_ONLY | 37| 29| 21| 10| 3| 1| | | | - +------------------------------+---+---+---+---+---+---+---+---+----+ - | T219(avg primary hops=7.7) | | | | | | | | | | - | OPTIMAL | 77| 15| 5| 1| 1| | | | | - | NP_LLFA | 72| 5| | | | | | | 22| - | NP_LLFA_THEN_NP_RLFA | 73| 8| 2| | | | | | 16| - | NP_LLFA_THEN_MRT_LOWPOINT | 74| 8| 3| 3| 2| 2| 2| 2| 4| - | MRT_LOWPOINT_ONLY | 19| 14| 15| 12| 10| 8| 7| 6| 10| - +------------------------------+---+---+---+---+---+---+---+---+----+ - - Figure 35 - - In the preceding analysis, the following procedure for selecting an - RLFA was used. Nodes were ordered with respect to distance from the - source and checked for membership in Q and P-space. The first node - to satisfy this condition was selected as the RLFA. More - sophisticated methods to select node-protecting RLFAs is an area of - active research. - - The analysis presented above uses the MRT Lowpoint Algorithm defined - in this specification with a common GADAG root. The particular - choice of a common GADAG root is expected to affect the quality of - the MRT alternate paths, with a more central common GADAG root - resulting in shorter MRT alternate path lengths. For the analysis - above, the GADAG root was chosen for each topology by calculating - node centrality as the sum of costs of all shortest paths to and from - a given node. The node with the lowest sum was chosen as the common - GADAG root. In actual deployments, the common GADAG root would be - chosen based on the GADAG Root Selection Priority advertised by each - router, the values of which would be determined off-line. - - In order to measure how sensitive the MRT alternate path lengths are - to the choice of common GADAG root, we performed the same analysis - using different choices of GADAG root. All of the nodes in the - network were ordered with respect to the node centrality as computed - above. Nodes were chosen at the 0th, 25th, and 50th percentile with - respect to the centrality ordering, with 0th percentile being the - most central node. The distribution of alternate path lengths for - those three choices of GADAG root are shown in Figure 36 for a subset - of the 19 topologies (chosen arbitrarily). The third row for each - topology (labeled MRT_LOWPOINT ( 0 percentile) ) reproduces the - results presented above for MRT_LOWPOINT_ONLY. The fourth and fifth - rows show the alternate path length distibution for the 25th and 50th - percentile choice for GADAG root. One can see some impact on the - path length distribution with the less central choice of GADAG root - resulting in longer path lenghths. - - We also looked at the impact of MRT algorithm variant on the - alternate path lengths. The first two rows for each topology present - results of the same alternate path length distribution analysis for - the SPF and Hybrid methods for computing the GADAG. These two - methods are described in Appendix A and Appendix B. For three of the - topologies in this subset (T201, T206, and T211), the use of SPF or - Hybrid methods does not appear to provide a significant advantage - over the Lowpoint method with respect to path length. Instead, the - choice of GADAG root appears to have more impact on the path length. - However, for two of the topologies in this subset(T216 and T219) and - for this particular choice of GAGAG root, the use of the SPF method - results in noticeably shorter alternate path lengths than the use of - the Lowpoint or Hybrid methods. It remains to be determined if this - effect applies generally across more topologies or is sensitive to - choice of GADAG root. - - +-------------------------------------------------------------------+ - | Topology name | percentage of failure scenarios | - | | protected by an alternate N hops | - | MRT algorithm variant | longer than the primary path | - | +------------------------------------+ - | (GADAG root | | | | | | | | | no | - | centrality percentile) | | | | | |10 |12 |14 | alt| - | |0-1|2-3|4-5|6-7|8-9|-11|-13|-15| <16| - +------------------------------+---+---+---+---+---+---+---+---+----+ - | T201(avg primary hops=3.5) | | | | | | | | | | - | MRT_HYBRID ( 0 percentile) | 33| 26| 23| 6| 3| | | | | - | MRT_SPF ( 0 percentile) | 33| 36| 23| 6| 3| | | | | - | MRT_LOWPOINT ( 0 percentile) | 33| 36| 23| 6| 3| | | | | - | MRT_LOWPOINT (25 percentile) | 27| 29| 23| 11| 10| | | | | - | MRT_LOWPOINT (50 percentile) | 27| 29| 23| 11| 10| | | | | - +------------------------------+---+---+---+---+---+---+---+---+----+ - | T206(avg primary hops=3.7) | | | | | | | | | | - | MRT_HYBRID ( 0 percentile) | 50| 35| 13| 2| | | | | | - | MRT_SPF ( 0 percentile) | 50| 35| 13| 2| | | | | | - | MRT_LOWPOINT ( 0 percentile) | 55| 32| 13| | | | | | | - | MRT_LOWPOINT (25 percentile) | 47| 25| 22| 6| | | | | | - | MRT_LOWPOINT (50 percentile) | 38| 38| 14| 11| | | | | | - +------------------------------+---+---+---+---+---+---+---+---+----+ - | T211(avg primary hops=3.3) | | | | | | | | | | - | MRT_HYBRID ( 0 percentile) | 86| 14| | | | | | | | - | MRT_SPF ( 0 percentile) | 86| 14| | | | | | | | - | MRT_LOWPOINT ( 0 percentile) | 85| 15| 1| | | | | | | - | MRT_LOWPOINT (25 percentile) | 70| 25| 5| 1| | | | | | - | MRT_LOWPOINT (50 percentile) | 80| 18| 2| | | | | | | - +------------------------------+---+---+---+---+---+---+---+---+----+ - | T216(avg primary hops=5.2) | | | | | | | | | | - | MRT_HYBRID ( 0 percentile) | 23| 22| 18| 13| 10| 7| 4| 2| 2| - | MRT_SPF ( 0 percentile) | 35| 32| 19| 9| 3| 1| | | | - | MRT_LOWPOINT ( 0 percentile) | 28| 25| 18| 11| 7| 6| 3| 2| 1| - | MRT_LOWPOINT (25 percentile) | 24| 20| 19| 16| 10| 6| 3| 1| | - | MRT_LOWPOINT (50 percentile) | 19| 14| 13| 10| 8| 6| 5| 5| 10| - +------------------------------+---+---+---+---+---+---+---+---+----+ - | T219(avg primary hops=7.7) | | | | | | | | | | - | MRT_HYBRID ( 0 percentile) | 20| 16| 13| 10| 7| 5| 5| 5| 3| - | MRT_SPF ( 0 percentile) | 31| 23| 19| 12| 7| 4| 2| 1| | - | MRT_LOWPOINT ( 0 percentile) | 19| 14| 15| 12| 10| 8| 7| 6| 10| - | MRT_LOWPOINT (25 percentile) | 19| 14| 15| 13| 12| 10| 6| 5| 7| - | MRT_LOWPOINT (50 percentile) | 19| 14| 14| 12| 11| 8| 6| 6| 10| - +------------------------------+---+---+---+---+---+---+---+---+----+ - - Figure 36 - -10. Implementation Status - - [RFC Editor: please remove this section prior to publication.] - - Please see [I-D.ietf-rtgwg-mrt-frr-architecture] for details on - implementation status. - -11. Acknowledgements - - The authors would like to thank Shraddha Hegde, Eric Wu, and Janos - Farkas for their suggestions and review. We would also like to thank - Anil Kumar SN for his assistance in clarifying the algorithm - description and pseudo-code. - -12. IANA Considerations - - This document includes no request to IANA. - -13. Security Considerations - - The algorithm described in this document does not introduce new - security concerns beyond those already discussed in the document - describing the MRT FRR architecture - [I-D.ietf-rtgwg-mrt-frr-architecture]. - -14. References - -14.1. Normative References - - [I-D.ietf-rtgwg-mrt-frr-architecture] - Atlas, A., Kebler, R., Bowers, C., Envedi, G., Csaszar, - A., Tantsura, J., and R. White, "An Architecture for IP/ - LDP Fast-Reroute Using Maximally Redundant Trees", draft- - ietf-rtgwg-mrt-frr-architecture-07 (work in progress), - October 2015. - - [RFC2119] Bradner, S., "Key words for use in RFCs to Indicate - Requirement Levels", BCP 14, RFC 2119, - DOI 10.17487/RFC2119, March 1997, - . - -14.2. Informative References - - [EnyediThesis] - Enyedi, G., "Novel Algorithms for IP Fast Reroute", - Department of Telecommunications and Media Informatics, - Budapest University of Technology and Economics Ph.D. - Thesis, February 2011, . - - [I-D.ietf-isis-mrt] - Li, Z., Wu, N., <>, Q., Atlas, A., Bowers, C., and J. - Tantsura, "Intermediate System to Intermediate System (IS- - IS) Extensions for Maximally Redundant Trees (MRT)", - draft-ietf-isis-mrt-01 (work in progress), October 2015. - - [I-D.ietf-isis-pcr] - Farkas, J., Bragg, N., Unbehagen, P., Parsons, G., - Ashwood-Smith, P., and C. Bowers, "IS-IS Path Computation - and Reservation", draft-ietf-isis-pcr-04 (work in - progress), December 2015. - - [I-D.ietf-ospf-mrt] - Atlas, A., Hegde, S., Bowers, C., Tantsura, J., and Z. Li, - "OSPF Extensions to Support Maximally Redundant Trees", - draft-ietf-ospf-mrt-01 (work in progress), October 2015. - - [I-D.ietf-rtgwg-lfa-manageability] - Litkowski, S., Decraene, B., Filsfils, C., Raza, K., - Horneffer, M., and P. Sarkar, "Operational management of - Loop Free Alternates", draft-ietf-rtgwg-lfa- - manageability-11 (work in progress), June 2015. - - [ISO10589-Second-Edition] - International Organization for Standardization, - "Intermediate system to Intermediate system intra-domain - routeing information exchange protocol for use in - conjunction with the protocol for providing the - connectionless-mode Network Service (ISO 8473)", ISO/ - IEC 10589:2002, Second Edition, Nov. 2002. - - [Kahn_1962_topo_sort] - Kahn, A., "Topological sorting of large networks", - Communications of the ACM, Volume 5, Issue 11 , Nov 1962, - . - - [MRTLinear] - Enyedi, G., Retvari, G., and A. Csaszar, "On Finding - Maximally Redundant Trees in Strictly Linear Time", IEEE - Symposium on Computers and Comunications (ISCC) , 2009, - . - - [RFC2328] Moy, J., "OSPF Version 2", STD 54, RFC 2328, - DOI 10.17487/RFC2328, April 1998, - . - - [RFC5120] Przygienda, T., Shen, N., and N. Sheth, "M-ISIS: Multi - Topology (MT) Routing in Intermediate System to - Intermediate Systems (IS-ISs)", RFC 5120, - DOI 10.17487/RFC5120, February 2008, - . - - [RFC7490] Bryant, S., Filsfils, C., Previdi, S., Shand, M., and N. - So, "Remote Loop-Free Alternate (LFA) Fast Reroute (FRR)", - RFC 7490, DOI 10.17487/RFC7490, April 2015, - . - -Appendix A. Option 2: Computing GADAG using SPFs +Appendix B. Constructing a GADAG using SPFs - The basic idea in this option is to use slightly-modified SPF - computations to find ears. In every block, an SPF computation is - first done to find a cycle from the local root and then SPF - computations in that block find ears until there are no more + The basic idea in this method for constructing a GADAG is to use + slightly-modified SPF computations to find ears. In every block, an + SPF computation is first done to find a cycle from the local root and + then SPF computations in that block find ears until there are no more interfaces to be explored. The used result from the SPF computation is the path of interfaces indicated by following the previous hops from the mininized IN_GADAG node back to the SPF root. To do this, first all cut-vertices must be identified and local-roots assigned as specified in Figure 12. The slight modifications to the SPF are as follows. The root of the block is referred to as the block-root; it is either the GADAG root or a cut-vertex. @@ -5513,48 +5101,49 @@ and cand_intf.local_node as TEMP_UNUSABLE if cand_intf.local_node is not block_root Mark cand_intf.local_node as TEMP_UNUSABLE Initialize ear_list to empty end_ear = Mod_SPF(spf_root, block_root) y = end_ear.spf_prev_hop while y.local_node is not spf_root add_to_list_start(ear_list, y) y.local_node.IN_GADAG = true y = y.local_node.spf_prev_intf - if(method is not hybrid) Set_Ear_Direction(ear_list, cand_intf.local_node, end_ear,block_root) Clear TEMP_UNUSABLE from all interfaces between cand_intf.remote_node and cand_intf.local_node + Clear TEMP_UNUSABLE from cand_intf.local_node return end_ear - Figure 37: Modified SPF for GADAG computation + Figure 31: Modified SPF for GADAG construction Assume that an ear is found by going from y to x and then running an SPF that terminates by minimizing z (e.g. y<->x...q<->z). Now it is necessary to determine the direction of the ear; if y << z, then the path should be y->x...q->z but if y >> z, then the path should be y<- x...q<-z. In Section 5.5, the same problem was handled by finding all ears that started at a node before looking at ears starting at - nodes higher in the partial order. In this algorithm, using that - approach could mean that new ears aren't added in order of their - total cost since all ears connected to a node would need to be found - before additional nodes could be found. + nodes higher in the partial order. In this GADAG construction + method, using that approach could mean that new ears aren't added in + order of their total cost since all ears connected to a node would + need to be found before additional nodes could be found. The alternative is to track the order relationship of each node with respect to every other node. This can be accomplished by maintaining two sets of nodes at each node. The first set, Higher_Nodes, contains all nodes that are known to be ordered above the node. The second set, Lower_Nodes, contains all nodes that are known to be - ordered below the node. This is the approach used in this algorithm. + ordered below the node. This is the approach used in this GADAG + construction method. Set_Ear_Direction(ear_list, end_a, end_b, block_root) // Default of A_TO_B for the following cases: // (a) end_a and end_b are the same (root) // or (b) end_a is in end_b's Lower Nodes // or (c) end_a and end_b were unordered with respect to each // other direction = A_TO_B if (end_b is block_root) and (end_a is not end_b) direction = B_TO_A @@ -5585,41 +5174,43 @@ add i.local_node to x.Higher_Nodes else foreach node x where x.localroot is block_root if end_b is in x.Lower_Nodes foreach interface i in ear_list add i.local_node to x.Lower_Nodes if end_a is in x.Higher_Nodes foreach interface i in ear_list add i.remote_node to x.Higher_Nodes - Figure 38: Algorithm to assign links of an ear direction + Figure 32: Algorithm to assign links of an ear direction - A goal of the algorithm is to find the shortest cycles and ears. An - ear is started by going to a neighbor x of an IN_GADAG node y. The - path from x to an IN_GADAG node is minimal, since it is computed via - SPF. Since a shortest path is made of shortest paths, to find the - shortest ears requires reaching from the set of IN_GADAG nodes to the - closest node that isn't IN_GADAG. Therefore, an ordered tree is - maintained of interfaces that could be explored from the IN_GADAG - nodes. The interfaces are ordered by their characteristics of - metric, local loopback address, remote loopback address, and ifindex, - as in the algorithm previously described in Figure 14. + A goal of this GADAG construction method is to find the shortest + cycles and ears. An ear is started by going to a neighbor x of an + IN_GADAG node y. The path from x to an IN_GADAG node is minimal, + since it is computed via SPF. Since a shortest path is made of + shortest paths, to find the shortest ears requires reaching from the + set of IN_GADAG nodes to the closest node that isn't IN_GADAG. + Therefore, an ordered tree is maintained of interfaces that could be + explored from the IN_GADAG nodes. The interfaces are ordered by + their characteristics of metric, local loopback address, remote + loopback address, and ifindex, based on the Interface_Compare + function defined in Figure 14. - The algorithm ignores interfaces picked from the ordered tree that - belong to the block root if the block in which the interface is - present already has an ear that has been computed. This is necessary - since we allow at most one incoming interface to a block root in each - block. This requirement stems from the way next-hops are computed as - was seen in Section 5.7. After any ear gets computed, we traverse - the newly added nodes to the GADAG and insert interfaces whose far - end is not yet on the GADAG to the ordered tree for later processing. + This GADAG construction method ignores interfaces picked from the + ordered list that belong to the block root if the block in which the + interface is present already has an ear that has been computed. This + is necessary since we allow at most one incoming interface to a block + root in each block. This requirement stems from the way next-hops + are computed as was seen in Section 5.7. After any ear gets + computed, we traverse the newly added nodes to the GADAG and insert + interfaces whose far end is not yet on the GADAG to the ordered tree + for later processing. Finally, cut-links are a special case because there is no point in doing an SPF on a block of 2 nodes. The algorithm identifies cut- links simply as links where both ends of the link are cut-vertices. Cut-links can simply be added to the GADAG with both OUTGOING and INCOMING specified on their interfaces. add_eligible_interfaces_of_node(ordered_intfs_tree,node) for each interface of node if intf.remote_node.IN_GADAG is false @@ -5664,25 +5255,25 @@ ear_end = SPF_for_Ear(cand_intf.local_node, cand_intf.remote_node, cand_intf.remote_node.localroot, SPF method) y = ear_end.spf_prev_hop while y.local_node is not cand_intf.local_node add_eligible_interfaces_of_node( ordered_intfs_tree, y.local_node) y = y.local_node.spf_prev_intf - Figure 39: SPF-based GADAG algorithm + Figure 33: SPF-based method for GADAG construction -Appendix B. Option 3: Computing GADAG using a hybrid method +Appendix C. Constructing a GADAG using a hybrid method - In this option, the idea is to combine the salient features of the + The idea of this method is to combine the salient features of the lowpoint inheritance and SPF methods. To this end, we process nodes as they get added to the GADAG just like in the lowpoint inheritance by maintaining a stack of nodes. This ensures that we do not need to maintain lower and higher sets at each node to ascertain ear directions since the ears will always be directed from the node being processed towards the end of the ear. To compute the ear however, we resort to an SPF to have the possibility of better ears (path lentghs) thus giving more flexibility than the restricted use of lowpoint/dfs parents. @@ -5693,21 +5284,21 @@ of an ear is pre-determined. Thus, whenever the block already has an ear computed, and we are processing an interface of the block root, we mark the block root as unusable before the SPF run that computes the ear. This ensures that the SPF terminates at some node other than the block-root. This in turn guarantees that the block-root has only one incoming interface in each block, which is necessary for correctly computing the next-hops on the GADAG. As in the SPF gadag, bridge ears are handled as a special case. - The entire algorithm is shown below in Figure 40 + The entire algorithm is shown below in Figure 34 find_spf_stack_ear(stack, x, y, xy_intf, block_root) if L(y) == D(y) // Special case for cut-links xy_intf.UNDIRECTED = false xy_intf.remote_intf.UNDIRECTED = false xy_intf.OUTGOING = true xy_intf.INCOMING = true xy_intf.remote_intf.OUTGOING = true xy_intf.remote_intf.INCOMING = true @@ -5743,21 +5334,21 @@ root.IN_GADAG = true Initialize Stack to empty push root onto Stack while (Stack is not empty) x = pop(Stack) for each interface intf of x y = intf.remote_node if y.IN_GADAG is false find_spf_stack_ear(stack, x, y, intf, y.block_root) - Figure 40: Hybrid GADAG algorithm + Figure 34: Hybrid GADAG construction method Authors' Addresses Gabor Sandor Enyedi Ericsson Konyves Kalman krt 11 Budapest 1097 Hungary Email: Gabor.Sandor.Enyedi@ericsson.com