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rfc:rfc5439

Network Working Group S. Yasukawa Request for Comments: 5439 NTT Category: Informational A. Farrel

                                                    Old Dog Consulting
                                                           O. Komolafe
                                                         Cisco Systems
                                                         February 2009
       An Analysis of Scaling Issues in MPLS-TE Core Networks

Status of This Memo

 This memo provides information for the Internet community.  It does
 not specify an Internet standard of any kind.  Distribution of this
 memo is unlimited.

Copyright Notice

 Copyright (c) 2009 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.

Abstract

 Traffic engineered Multiprotocol Label Switching (MPLS-TE) is
 deployed in providers' core networks.  As providers plan to grow
 these networks, they need to understand whether existing protocols
 and implementations can support the network sizes that they are
 planning.
 This document presents an analysis of some of the scaling concerns
 for the number of Label Switching Paths (LSPs) in MPLS-TE core
 networks, and examines the value of two techniques (LSP hierarchies
 and multipoint-to-point LSPs) for improving scaling.  The intention
 is to motivate the development of appropriate deployment techniques
 and protocol extensions to enable the application of MPLS-TE in large
 networks.
 This document only considers the question of achieving scalability
 for the support of point-to-point MPLS-TE LSPs.  Point-to-multipoint
 MPLS-TE LSPs are for future study.

Yasukawa, et al. Informational [Page 1] RFC 5439 Scaling in MPLS-TE February 2009

Table of Contents

 1. Introduction ....................................................3
    1.1. Overview ...................................................3
    1.2. Glossary of Notation .......................................5
 2. Issues of Concern for Scaling ...................................5
    2.1. LSP State ..................................................5
    2.2. Processing Overhead ........................................6
    2.3. RSVP-TE Implications .......................................6
    2.4. Management .................................................7
 3. Network Topologies ..............................................8
    3.1. The Snowflake Network Topology .............................9
    3.2. The Ladder Network Topology ...............................11
    3.3. Commercial Drivers for Selected Configurations ............14
    3.4. Other Network Topologies ..................................15
 4. Required Network Sizes .........................................16
    4.1. Practical Numbers .........................................16
 5. Scaling in Flat Networks .......................................16
    5.1. Snowflake Networks ........................................17
    5.2. Ladder Networks ...........................................18
 6. Scaling Snowflake Networks with Forwarding Adjacencies .........22
    6.1. Two-Layer Hierarchy .......................................22
         6.1.1. Tuning the Network Topology to Suit the
                Two-Layer Hierarchy ................................23
    6.2. Alternative Two-Layer Hierarchy ...........................24
    6.3. Three-Layer Hierarchy .....................................25
    6.4. Issues with Hierarchical LSPs .............................26
 7. Scaling Ladder Networks with Forwarding Adjacencies ............27
    7.1. Two-Layer Hierarchy .......................................27
    7.2. Three-Layer Hierarchy .....................................28
    7.3. Issues with Hierarchical LSPs .............................29
 8. Scaling Improvements through Multipoint-to-Point LSPs ..........30
    8.1. Overview of MP2P LSPs .....................................30
    8.2. LSP State: A Better Measure of Scalability ................31
    8.3. Scaling Improvements for Snowflake Networks ...............32
         8.3.1. Comparison with Other Scenarios ....................33
    8.4. Scaling Improvements for Ladder Networks ..................34
         8.4.1. Comparison with Other Scenarios ....................36
         8.4.2. LSP State Compared with LSP Numbers ................37
    8.5. Issues with MP2P LSPs .....................................37
 9. Combined Models ................................................39
 10. An Alternate Solution .........................................39
    10.1. Pros and Cons of the Alternate Solution ..................40
 11. Management Considerations .....................................42
 12. Security Considerations .......................................42
 13. Recommendations ...............................................42

Yasukawa, et al. Informational [Page 2] RFC 5439 Scaling in MPLS-TE February 2009

 14. Acknowledgements ..............................................43
 15. Normative References ..........................................43
 16. Informative References ........................................43

1. Introduction

 Network operators and service providers are examining scaling issues
 as they look to deploy ever-larger traffic engineered Multiprotocol
 Label Switching (MPLS-TE) networks.  Concerns have been raised about
 the number of Label Switched Paths (LSPs) that need to be supported
 at the edge and at the core of the network.  The impact on control
 plane and management plane resources threatens to outweigh the
 benefits and popularity of MPLS-TE, while the physical limitations of
 the routers may constrain the deployment options.
 Historically, it has been assumed that all MPLS-TE scaling issues can
 be addressed using hierarchical LSP [RFC4206].  However, analysis
 shows that the improvement gained by LSP hierarchies is not as
 significant in all topologies and at all points in the network as
 might have been presumed.  Further, additional management issues are
 introduced to determine the end-points of the hierarchical LSPs and
 to operate them.  Although this does not invalidate the benefits of
 LSP hierarchies, it does indicate that additional techniques may be
 desirable in order to fully scale MPLS-TE networks.
 This document examines the scaling properties of two generic MPLS-TE
 network topologies and investigates the benefits of two scaling
 techniques.

1.1. Overview

 Physical topology scaling concerns are addressed by building networks
 that are not fully meshed.  Network topologies tend to be meshed in
 the core but tree-shaped at the edges, giving rise to a snowflake
 design.  Alternatively, the core may be more of a ladder shape with
 tree-shaped edges.
 MPLS-TE, however, establishes a logical full mesh between all edge
 points in the network, and this is where the scaling problems arise
 since the structure of the network tends to focus a large number of
 LSPs within the core of the network.
 This document presents two generic network topologies (the snowflake
 and the ladder) and attempts to parameterize the networks by making
 some generalities.  It introduces terminology for the different
 scaling parameters and examines how many LSPs might be required to be
 carried within the core of a network.

Yasukawa, et al. Informational [Page 3] RFC 5439 Scaling in MPLS-TE February 2009

 Two techniques (hierarchical LSPs and multipoint-to-point LSPs) are
 introduced and an examination is made of the scaling benefits that
 they offer as well as of some of the concerns with using these
 techniques.
 Of necessity, this document makes many generalizations.  Not least
 among these is a set of assumptions about the symmetry and
 connectivity of the physical network.  It is hoped that these
 generalizations will not impinge on the usefulness of the overview of
 the scaling properties that this document attempts to give.  Indeed,
 the symmetry of the example topologies tends to highlight the scaling
 issues of the different solution models, and this may be useful in
 exposing the worst case scenarios.
 Although protection mechanisms like Fast Reroute (FRR) [RFC4090] are
 briefly discussed, the main body of this document considers stable
 network cases.  It should be noted that make-before-break
 re-optimisation after link failure may result in a significant number
 of 'duplicate' LSPs.  This issue is not addressed in this document.
 It should also be understood that certain deployment models where
 separate traffic engineered LSPs are used to provide different
 services (such as layer 3 Virtual Private Networks (VPNs) [RFC4110]
 or pseudowires [RFC3985]) or different classes of service [RFC3270]
 may result in 'duplicate' or 'parallel' LSPs running between any pair
 of provider edge nodes (PEs).  This scaling factor is also not
 considered in this document, but may be easily applied as a linear
 factor by the reader.
 The operation of security mechanisms in MPLS-TE networks [MPLS-SEC]
 may have an impact on the ability of the network to scale.  For
 example, they may increase both the size and number of control plane
 messages.  Additionally, they may increase the processing overhead as
 control plane messages are subject to processing algorithms (such as
 encryption), and security keys need to be managed.  Deployers will
 need to consider the trade-offs between scaling objectives and
 security objectives in their networks, and should resist the
 temptation to respond to a degradation of scaling performance by
 turning off security techniques that have previously been deemed as
 necessary.  Further analysis of the effects of security measures on
 scalability are not considered further in this document.
 This document is designed to help service providers discover whether
 existing protocols and implementations can support the network sizes
 that they are planning.  To do this, it presents an analysis of some
 of the scaling concerns for MPLS-TE core networks and examines the

Yasukawa, et al. Informational [Page 4] RFC 5439 Scaling in MPLS-TE February 2009

 value of two techniques for improving scaling.  This should motivate
 the development of appropriate deployment techniques and protocol
 extensions to enable the application of MPLS-TE in large networks.
 This document only considers the question of achieving scalability
 for the support of point-to-point MPLS-TE LSPs.  Point-to-multipoint
 MPLS-TE LSPs are for future study.

1.2. Glossary of Notation

 This document applies consistent notation to define various
 parameters of the networks that are analyzed.  These terms are
 defined as they are introduced throughout the document, but are
 grouped together here for quick reference.  Refer to the full
 definitions in the text for detailed explanations.
 n      A network level.  n = 1 is the core of the network.
        See Section 3 for more details on the definition of a level.
 P(n)   A node at level n in the network.
 S(n)   The number of nodes at level n.  That is, the number of P(n)
        nodes.
 L(n)   The number of LSPs seen by a P(n) node.
 X(n)   The number of LSP segment states held by a P(n) node.
 M(n)   The number of P(n+1) nodes subtended to a P(n) node.
 R      The number of rungs in a ladder network.
 E      The number of edge nodes (PEs) subtended below (directly or
        indirectly) a spar-node in a ladder network.
 K      The cost-effectiveness of the network expressed in terms of
        the ratio of the number of PEs to the number of network nodes.

2. Issues of Concern for Scaling

 This section presents some of the issues associated with the support
 of LSPs at a Label Switching Router (LSR) or within the network.
 These issues may mean that there is a limit to the number of LSPs
 that can be supported.

2.1. LSP State

 LSP state is the data (information) that must be stored at an LSR in
 order to maintain an LSP.  Here, we refer to the information that is
 necessary to maintain forwarding plane state and the additional
 information required when LSPs are established through control plane
 protocols.  While the size of the LSP state is implementation-
 dependent, it is clear that any implementation will require some data
 in order to maintain LSP state.

Yasukawa, et al. Informational [Page 5] RFC 5439 Scaling in MPLS-TE February 2009

 Thus, LSP state becomes a scaling concern because as the number of
 LSPs at an LSR increases, so the amount of memory required to
 maintain the LSPs increases in direct proportion.  Since the memory
 capacity of an LSR is limited, there is a related limit placed on the
 number LSPs that can be supported.
 Note that techniques to reduce the memory requirements (such as data
 compression) may serve to increase the number of LSPs that can be
 supported, but this will only achieve a moderate multiplier and may
 significantly decrease the ability to process the state rapidly.
 In this document, we define X(n) as "the number of LSP segment states
 held by a P(n) node."  This definition observes that an LSR at the
 end of an LSP only has to maintain state in one direction (i.e., into
 the network), while a transit LSR must maintain state in both
 directions (i.e., toward both ends of the LSP).  Furthermore, in
 multipoint-to-point (MP2P) LSPs (see Section 8), a transit LSR may
 need to maintain LSP state for one downstream segment (toward the
 destination) and multiple upstream segments (from multiple sources).
 That is, we define LSP segment state as the state necessary to
 maintain an LSP in one direction to one adjacent node.

2.2. Processing Overhead

 Depending largely on implementation issues, the number of LSPs
 passing through an LSR may impact the processing speed for each LSP.
 For example, control block search times can increase with the number
 of control blocks to be searched, and even excellent implementations
 cannot completely mitigate this fact.  Thus, since CPU power is
 constrained in any LSR, there may be a practical limit to the number
 of LSPs that can be supported.
 Further processing overhead considerations depend on issues specific
 to the control plane protocols, and are discussed in the next
 section.

2.3. RSVP-TE Implications

 Like many connection-oriented signaling protocols, RSVP-TE (Resource
 Reservation Protocol - Traffic Engineering) requires that state is
 held within the network in order to maintain LSPs.  The impact of
 this is described in Section 2.1.  Note that RSVP-TE requires that
 separate information is maintained for upstream and downstream
 relationships, but does not require any specific implementation of
 that state.

Yasukawa, et al. Informational [Page 6] RFC 5439 Scaling in MPLS-TE February 2009

 RSVP-TE is a soft-state protocol, which means that protocol messages
 (refresh messages) must be regularly exchanged between signaling
 neighbors in order to maintain the state for each LSP that runs
 between the neighbors.  A common period for the transmission (and
 receipt) of refresh messages is 30 seconds, meaning that each LSR
 must send and receive one message in each direction (upstream and
 downstream) every 30 seconds for every LSP it supports.  This has the
 potential to be a significant constraint on the scaling of the
 network, but various improvements [RFC2961] mean that this refresh
 processing can be significantly reduced, allowing an implementation
 to be optimized to remove nearly all concerns about soft-state
 scaling in a stable network.
 Observations of existing implementations indicate that there may be a
 threshold of around 50,000 LSPs above which an LSR struggles to
 achieve sufficient processing to maintain LSP state.  Although
 refresh reduction [RFC2961] may substantially improve this situation,
 it has also been observed that under these circumstances the size of
 the Srefresh may become very large, and the processing required may
 still cause significant disruption to an LSR.
 Another approach is to increase the refresh time.  There is a
 correlation between the percentage increase in refresh time and the
 improvement in performance for the LSR.  However, it should be noted
 that RSVP-TE's soft-state nature depends on regular refresh messages;
 thus, a degree of functionality is lost by increasing the refresh
 time.  This loss may be partially mitigated by the use of the RSVP-TE
 Hello message, and can also be reduced by the use of various GMPLS
 extensions [RFC3473], such as the use of [RFC2961] message
 acknowledgements on all messages.
 RSVP-TE also requires that signaling adjacencies be maintained
 through the use of Hello message exchanges.  Although [RFC3209]
 suggests that Hello messages should be retransmitted every 5 ms, in
 practice, values of around 3 seconds are more common.  Nevertheless,
 the support of Hello messages can represent a scaling limitation on
 an RSVP-TE implementation since one message must be sent and received
 to/from each signaling adjacency every time period.  This can impose
 limits on the number of neighbors (physical or logical) that an LSR
 supports, but does not impact the number of LSPs that the LSR can
 handle.

2.4. Management

 Another practical concern for the scalability of large MPLS-TE
 networks is the ability to manage the network.  This may be
 constrained by the available tools, the practicality of managing
 large numbers of LSPs, and the management protocols in use.

Yasukawa, et al. Informational [Page 7] RFC 5439 Scaling in MPLS-TE February 2009

 Management tools are software implementations.  Although such
 implementations should not constrain the control plane protocols, it
 is realistic to appreciate that network deployments will be limited
 by the scalability of the available tools.  In practice, most
 existing tools have a limit to the number of LSPs that they can
 support.  While a Network Management System (NMS) may be able to
 support a large number of LSPs, the number that can be supported by
 an Element Management System (EMS) (or the number supported by an NMS
 per-LSR) is more likely to be limited.
 Similarly, practical constraints may be imposed by the operation of
 management protocols.  For example, an LSR may be swamped by
 management protocol requests to read information about the LSPs that
 it supports, and this might impact its ability to sustain those LSPs
 in the control plane.  OAM (Operations, Administration, and
 Management), alarms, and notifications can further add to the burden
 placed on an LSR and limit the number of LSPs it can support.
 All of these considerations encourage a reduction in the number of
 LSPs supported within the network and at any particular LSR.

3. Network Topologies

 In order to provide some generic analysis of the potential scaling
 issues for MPLS-TE networks, this document explores two network
 topology models.  These topologies are selected partly because of
 their symmetry, which makes them more tractable to a formulaic
 approach, and partly because they represent generalizations of real
 deployment models.  Section 3.3 provides a discussion of the
 commercial drivers for deployed topologies and gives more analysis of
 why it is reasonable to consider these two topologies.
 The first topology is the snowflake model.  In this type of network,
 only the very core of the network is meshed.  The edges of the
 network are formed as trees rooted in the core.
 The second network topology considered is the ladder model.  In this
 type of network, the core of the network is shaped and meshed in the
 form of a ladder and trees are attached rooted to the edge of the
 ladder.
 The sections that follow examine these topologies in detail in order
 to parameterize them.

Yasukawa, et al. Informational [Page 8] RFC 5439 Scaling in MPLS-TE February 2009

3.1. The Snowflake Network Topology

 The snowflake topologies considered in this document are based on a
 hierarchy of connectivity within the core network.  PE nodes have
 connectivity to P-nodes as shown in Figure 1.  There is no direct
 connectivity between the PEs.  Dual homing of PEs to multiple P-nodes
 is not considered in this document, although it may be a valuable
 addition to a network configuration.
          P
         /|\
        / | \
       /  |  \
      /   |   \
    PE    PE   PE
    Figure 1 : PE to P-Node Connectivity
 The relationship between P-nodes is also structured in a hierarchical
 way.  Thus, as shown in Figure 2, multiple P-nodes at one level are
 connected to a P-node at a higher level.  We number the levels such
 that level 1 is the top level (top in our figure, and nearest to the
 core of the network) and level (n) is immediately above level (n+1);
 we denote a P-node at level n as a P(n).
 As with PEs, there is no direct connectivity between P(n+1) nodes.
 Again, dual homing of P(n+1) nodes to multiple P(n) nodes is not
 considered in this document, although it may be a valuable addition
 to a network configuration.
            P(n)
            /|\
           / | \
          /  |  \
         /   |   \
    P(n+1) P(n+1) P(n+1)
    Figure 2 : Relationship between P-Nodes
 At the top level, P(1) nodes are connected in a full mesh.  In
 reality, the level 1 part of the network may be slightly less well-
 connected than this, but assuming a full mesh provides for
 generality.  Thus, the snowflake topology comprises a clique with
 topologically equivalent trees subtended from each node in the
 clique.

Yasukawa, et al. Informational [Page 9] RFC 5439 Scaling in MPLS-TE February 2009

 The key multipliers for scalability are the number of P(1) nodes and
 the multiplier relationship between P(n) and P(n+1) at each level,
 down to and including PEs.
 We define the multiplier M(n) as the number of P(n+1) nodes at level
 (n+1) attached to any one P(n).  Assume that M(n) is constant for all
 nodes at level n.  Since nodes at the same level are not
 interconnected (except at the top level), and since each P(n+1) node
 is connected to precisely one P(n) node, M(n) is one less than the
 degree of the node at level n (that is, the P(n) node is attached to
 M(n) nodes at level (n+1) and to 1 node at level (n-1)).
 We define S(n) as the number of nodes at level (n).
 Thus:
    S(n) = S(1)*M(1)*M(2)*...*M(n-1)
 So the number of PEs can be expressed as:
    S(PE) = S(1)*M(1)*M(2)*...*M(n)
 where the network has (n) layers of P-nodes.
 Thus, we may depict an example snowflake network as shown in Figure
 3.  In this case:
    S(1) = 3
    M(1) = 3
    S(2) = S(1)*M(1) = 9
    M(2) = 2
    S(PE) = S(1)*M(1)*M(2) = 18

Yasukawa, et al. Informational [Page 10] RFC 5439 Scaling in MPLS-TE February 2009

      PE      PE  PE     PE  PE      PE
         \      \/         \/       /
      PE--P(2)  P(2)      P(2)  P(2)--PE
              \ |            | /
               \|            |/
     PE--P(2)---P(1)------P(1)---P(2)--PE
        /           \    /           \
      PE             \  /             PE
                      \/
                      P(1)
                      /|\
                     / | \
                    /  |  \
            PE--P(2)  P(2) P(2)--PE
                /      /\      \
              PE     PE  PE     PE
    Figure 3 : An Example Snowflake Network

3.2. The Ladder Network Topology

 The ladder networks considered in this section are based on an
 arrangement of routers in the core network that resembles a ladder.
 Ladder networks typically have long and thin cores that are arranged
 as conventional ladders.  That is, they have one or more spars
 connected by rungs.  Each node on a spar may have:
  1. connection to one or more other spars,
  2. connection to a tree of other core nodes,
  3. connection to customer nodes.
 Figure 4 shows a simplified example of a ladder network.  A core of
 twelve nodes makes up two spars connected by six rungs.

Yasukawa, et al. Informational [Page 11] RFC 5439 Scaling in MPLS-TE February 2009

              PE    PE           PE   PE
     PE PE PE | PE  | PE  PE  PE |  PE | PE
       \|    \|/    |/    |     \|    \|/
     PE-P-----P-----P-----P------P-----P--PE
        |     |     |     |      |     |\
        |     |     |     |      |     | PE
        |     |     |     |      |     |
     PE-P-----P-----P-----P------P-----P
       /|    /|\    |\    |\     |\     \
     PE PE PE | PE  | PE  | PE   | PE    PE
              PE    PE    PE     PE
    Figure 4 : A Simplified Ladder Network
 In practice, not all nodes on a spar (call them spar-nodes) need to
 have subtended PEs.  That is, they can exist simply to give
 connectivity along the spar to other spar-nodes, or across a rung to
 another spar.  Similarly, the connectivity between spars can be more
 complex with multiple connections from one spar-node to another spar.
 Lastly, the network may be complicated by the inclusion of more than
 two spars (or simplified by reduction to a single spar).
 These variables make the ladder network non-trivial to model.  For
 the sake of simplicity, we will make the following restrictions:
  1. There are precisely two spars in the core network.
  1. Every spar-node connects to precisely one spar-node on the other

spar. That is, each spar-node is attached to precisely one rung.

  1. Each spar-node connects to either one (end-spar) or two (core-spar)

other spar-nodes on the same spar.

  1. Every spar-node has the same number of PEs subtended. This does

not mean that there are no P-nodes subtended to the spar-nodes, but

   does mean that the edge tree subtended to each spar-node is
   identical.
 From these restrictions, we are able to quantify a ladder network as
 follows:
    R    - The number of rungs.  That is, the number of spar-nodes on
           each spar.
    S(1) - The number of spar-nodes in the network.  S(1)=2*R.
    E    - The number of subtended edge nodes (PEs) to each spar-node.

Yasukawa, et al. Informational [Page 12] RFC 5439 Scaling in MPLS-TE February 2009

 The number of rungs may vary considerably.  A number less than 3 is
 unlikely (since that would not be a significantly connected network),
 and a number greater than 100 seems improbable (because that would
 represent a very long, thin network).
 E can be treated as for the snowflake network.  That is, we can
 consider a number of levels of attachment from P(1) nodes, which are
 the spar-nodes, through P(i) down to P(n), which are the PEs.
 Practically, we need to only consider n=2 (PEs attached direct to the
 spar-nodes) and n=3 (one level of P-nodes between the PEs and the
 spar-nodes).
 Let M(i) be the ratio of P(i) nodes to P(i-1) nodes, i.e., the
 connectivity between levels of P-node as defined for the snowflake
 topology.  Hence, the number of nodes at any level (n) is:
    S(n) = S(1)*M(1)*M(2)*...*M(n-1)
 So the number of PEs subtended to a spar-node is:
    E = M(1)*M(2)*...*M(n)
 And the number of PEs can be expressed as:
    S(PE) = S(1)*M(1)*M(2)*...*M(n)
          = S(1)*E
 Thus, we may depict an example ladder network as shown in Figure 5.
 In this case:
   R = 5
   S(1) = 10
   M(1) = 2
   S(2) = S(1)*M(1) = 20
   M(2) = 2
   E = M(1)*M(2) = 4
   S(PE) = S(1)*E = 40

Yasukawa, et al. Informational [Page 13] RFC 5439 Scaling in MPLS-TE February 2009

    PE PE  PE PE PE PE PE PE PE PE PE PE PE PE  PE PE
      \|     \|    \|    \|   |/    |/    |/     |/
       P(2)   P(2) P(2) P(2) P(2) P(2) P(2)     P(2)
           \      \  |   \    /    |  /        /
    PE      \      \ |    \  /     | /        /       PE
      \      \      \|     \/      |/        /       /
    PE-P(2)---P(1)---P(1)---P(1)---P(1)---P(1)---P(2)-PE
              |      |      |      |      |
              |      |      |      |      |
              |      |      |      |      |
    PE-P(2)---P(1)---P(1)---P(1)---P(1)---P(1)---P(2)-PE
      /      /     / |     /\      |\        \       \
    PE      /     /  |    /  \     | \        \       PE
           /     /   |   /    \    |  \        \
       P(2)   P(2) P(2) P(2) P(2) P(2) P(2)     P(2)
      /|     /|    /|    /|   |\    |\    |\     |\
    PE PE  PE PE PE PE PE PE PE PE PE PE PE PE  PE PE
    Figure 5 : An Example Ladder Network

3.3. Commercial Drivers for Selected Configurations

 It is reasonable to ask why these two particular network topologies
 have been chosen.
 The most important consideration is physical scalability.  Each node
 (Label Switching Router - LSR) is only able to support a limited
 number of physical interfaces.  This necessarily reduces the ability
 to fully mesh a network and leads to the tree-like structure of the
 network toward the PEs.
 A realistic commercial consideration for an operator is the fact that
 the only revenue-generating nodes in the network are the PEs.  Other
 nodes are needed only to support connectivity and scalability.
 Therefore, there is a desire to maximize S(PE) while minimizing the
 sum of S(n) for all values of (n).  This could be achieved by
 minimizing the number of levels and maximizing the connectivity at
 each layer, M(n).  Ultimately, however, this would produce a network
 of just interconnected PEs, which is clearly in conflict with the
 physical scaling situation.
 Therefore, the solution calls for a "few" levels with "relatively
 large" connectivity at each level.  We might say that the cost-
 effectiveness of the network can be stated as:
 K = S(PE)/(S(1)+S(2) + ... + S(n)) where n is the level above the PEs

Yasukawa, et al. Informational [Page 14] RFC 5439 Scaling in MPLS-TE February 2009

 We should observe, however, that this equation may be naive in that
 the cost of a network is not actually a function of the number of
 routers (since a router chassis is often free or low cost), but is
 really a function of the cost of the line cards, which is, itself, a
 product of the capacity of the line cards.  Thus, the relatively high
 connectivity decreases the cost-effectiveness, while a topology that
 tends to channel data through a network core tends to demand higher
 capacity (and so, more expensive) line cards.
 A further consideration is the availability of connectivity (usually
 fibers) between LSR sites.  Although it is always possible to lay new
 fiber, this may not be cost-effective or timely.  The physical shape
 and topography of the country in which the network is laid is likely
 to be as much of a problem.  If the country is 'long and thin', then
 a ladder network is likely to be used.
 This document examines the implications for control plane and data
 plane scalability of this type of network when MPLS-TE LSPs are used
 to provide full connectivity between all PEs.

3.4. Other Network Topologies

 As explained in Section 1, this document is using two symmetrical and
 generalized network topologies for simplicity of modelling.  In
 practice, there are two other topological considerations.
 a. Multihoming
    It is relatively common for a node at level (n) to be attached to
    more than one node at level (n-1).  This is particularly common at
    PEs that may be connected to more than one P(n).
 b. Meshing within a level
    A level in the network will often include links between P-nodes at
    the same level, including the possibility of links between PEs.
    This may result in a network that looks like a series of
    concentric circles with spokes.
 Both of these features are likely to have some impact on the scaling
 of the networks.  However, for the purposes of establishing the
 ground rules for scaling, this document restricts itself to the
 consideration of the symmetrical networks described in Sections 2.1
 and 2.2.  Discussion of other network formats is for future study.

Yasukawa, et al. Informational [Page 15] RFC 5439 Scaling in MPLS-TE February 2009

4. Required Network Sizes

 An important question for this evaluation and analysis is the size of
 the network that operators require.  How many PEs are required?  What
 ratio of P to PE is acceptable?  How many ports do devices have for
 physical connectivity?  What type of MPLS-TE connectivity between PEs
 is required?
 Although presentation of figures for desired network sizes must be
 treated with caution because history shows that networks grow beyond
 all projections, it is useful to set some acceptable lower bounds.
 That is, we can state that we are interested in networks of at least
 a certain size.
 The most important features are:
  1. The network should have at least 1000 PEs.
  2. Each pair of PEs should be connected by at least one LSP in each

direction.

4.1. Practical Numbers

 In practice, reasonable target numbers are as follows.
 S(PE) >= 1000
 Number of levels is 3.  That is: 1, 2, and PE.
 M(2) <= 20
 M(1) <= 20
 S(1) <= 100

5. Scaling in Flat Networks

 Before proceeding to examine potential scaling improvements, we need
 to examine how well the flat networks described in the previous
 sections scale.
 Consider the requirement for a full mesh of LSPs linking all PEs.
 That is, each PE has an LSP to and from every other LSP.  Thus, if
 there are S(PE) PEs in the network, there are S(PE)*(S(PE) - 1) LSPs.
 Define L(n) as the number of LSPs handled by a level (n) LSR.
 L(PE) = 2*(S(PE) - 1)

Yasukawa, et al. Informational [Page 16] RFC 5439 Scaling in MPLS-TE February 2009

5.1. Snowflake Networks

 There are a total of S(PE) PEs in the network and, since each PE
 establishes an LSP with every other PE, it would be expected that
 there are S(PE) - 1 LSPs incoming to each PE and the same number of
 LSPs outgoing from the same PE, giving a total of 2(S(PE) - 1) on the
 incident link.  Hence, in a snowflake topology (see Figure 3), since
 there are M(2) PEs attached to each P(2) node, it may tempting to
 think that L(2) (the number of LSPs traversing each P(2) node) is
 simply 2*(S(PE) - 1)*M(2).  However, it should be noted that of the
 S(PE) - 1 LSPs incoming to each PE, M(2) - 1 originated from nodes
 attached to the same P(2) node, and so this value would count the
 LSPs between the M(2) PEs attached to each P(2) node twice: once when
 outgoing from the M(2) - 1 other nodes and once when incoming into a
 particular PE.
 There are a total of M(2)*(M(2) - 1) LSPs between these M(2) PEs and,
 since this value is erroneously included twice in 2*(S(PE) - 1)*M(2),
 the correct value is:
 L(2) = 2*M(2)*(S(PE) - 1) - M(2)*(M(2) - 1)
      = M(2)*(2*S(PE) - M(2) - 1)
 An alternative way of looking at this, that proves extensible for the
 calculation of L(1), is to observe that each PE subtended to a P(2)
 node has an LSP in each direction to all S(PE) - M(2) PEs in the rest
 of the system, and there are M(2) such locally subtended PEs; thus,
 2*M(2)*(S(PE) - M(2)).  Additionally, there are M(2)*(M(2) - 1) LSPs
 between the locally subtended PEs.  So:
 L(2) = 2*M(2)*(S(PE) - M(2)) + M(2)*(M(2) - 1)
      = M(2)*(2*S(PE) - M(2) - 1)
 L(1) can be computed in the same way as this second evaluation of
 L(2).  Each PE subtended below a P(1) node has an LSP in each
 direction to all PEs not below the P(1) node.  There are M(1)*M(2)
 PEs below the P(1) node, so this accounts for 2*M(1)*M(2)*(S(PE) -
 M(1)*M(2)) LSPs.  To this, we need to add the number of LSPs that
 pass through the P(1) node and that run between the PEs subtended
 below the P(1).  Consider each P(2): it has M(2) PEs, each of which
 has an LSP going to all of the PEs subtended to the other P(2) nodes
 subtended to the P(1).  There are M(1) - 1 such other P(2) nodes, and
 so M(2)*(M(1) - 1) other such PEs.  So the number of LSPs from the
 PEs below a P(2) node is M(2)*M(2)*(M(1) - 1).  And there are M(1)
 P(2) nodes below the P(1), giving rise to a total of
 M(2)*M(2)*M(1)*(M(1) - 1) LSPs.  Thus:

Yasukawa, et al. Informational [Page 17] RFC 5439 Scaling in MPLS-TE February 2009

 L(1) = 2*M(1)*M(2)*(S(PE) - M(1)*M(2)) + M(2)*M(2)*M(1)*(M(1) - 1)
      = M(1)*M(2)*(2*S(PE) - M(2)*(M(1) + 1))
 So, for example, with S(1) = 5, M(1) = 10, and M(2) = 20, we see:
    S(PE) = 1000
    L(PE) = 1998
    L(2)  = 39580
    L(1)  = 356000
 Alternatively, with S(1) = 10, M(1) = 10, and M(2) = 20, we see:
    S(PE) = 2000
    L(PE) = 3998
    L(2)  = 79580
    L(1)  = 756000
 In both examples, the number of LSPs at the core (P(1)) nodes is
 probably unacceptably large, even though there are only a relatively
 modest number of PEs.  In fact, L(2) may even be too large in the
 second example.

5.2. Ladder Networks

 In ladder networks, L(PE) remains the same at 2*(S(PE) - 1).
 L(2) can be computed using the same mechanism as for the snowflake
 topology because the subtended tree is the same format.  Hence,
 L(2) = 2*M(2)*(S(PE) - 1) - M(2)*(M(2) - 1)
 But L(1) requires a different computation because each P(1) not only
 sees LSPs for the subtended PEs, but is also a transit node for some
 of the LSPs that cross the core (the core is not fully meshed).
 Each P(1) sees:
 o  all of the LSPs between locally attached PEs,
 o  less those LSPs between locally attached PEs that can be served
    exclusively by the attached P(2) nodes,
 o  all LSPs between locally attached PEs and remote PEs, and
 o  LSPs in transit that pass through the P(1).
 The first three numbers are easily determined and match what we have
 seen from the snowflake network.  They are:

Yasukawa, et al. Informational [Page 18] RFC 5439 Scaling in MPLS-TE February 2009

 o  E*(E-1)
 o  M(1)*M(2)*(M(2)-1) = E*(M(2) - 1)
 o  2*E*E*(S(1) - 1)
 The number of LSPs in transit is more complicated to compute.  It is
 simplified by not considering the ends of the ladders but by
 examining an arbitrary segment of the middle of the ladder, such as
 shown in Figure 6.  We look to compute and generalize the number of
 LSPs traversing each core link (labeled a and b in Figure 6) and so
 determine the number of transit LSPs seen by each P(1).
       :    :    :    :    :    :
       :    :    :    :    :    :
     P(2) P(2) P(2) P(2) P(2) P(2)
         \  |   \    /    |  /
          \ |    \  /     | /
           \|     \/      |/
      ......P(1)---P(1)---P(1)......
            |   a  |      |
            |      |b     |
            |      |      |
      ......P(1)---P(1)---P(1)......
           /|     /\      |\
          / |    /  \     | \
         /  |   /    \    |  \
     P(2) P(2) P(2) P(2) P(2) P(2)
       :    :    :    :    :    :
       :    :    :    :    :    :
    Figure 6 : An Arbitrary Section of a Ladder Network
 Of course, the number of LSPs carried on links a and b in Figure 6
 depends on how LSPs are routed through the core network.  But if we
 assume a symmetrical routing policy and an even distribution of LSPs
 across all shortest paths, the result is the same.
 Now we can see that each P(1) sees half of 2a+b LSPs (since each LSP
 would otherwise be counted twice as it passed through the P(1)),
 except that some of the LSPs are locally terminated and so are only
 included once in the sum 2a+b.
 So L(1) = a + b/2 -
           (locally terminated transit LSPs)/2 +
           (locally contained LSPs)

Yasukawa, et al. Informational [Page 19] RFC 5439 Scaling in MPLS-TE February 2009

 Thus:
 L(1) = a + b/2 -
        2*E*E*(S(1) - 1)/2 +
        E*(E-1) - E*(M(2) - 1)
      = a + b/2 +
        E*E*(2 - S(1)) - E*M(2)
 So all we have to do is work out a and b.
 Recall that the ladder length R = S(1)/2, and define X = E*E.
 Consider the contribution made by all of the LSPs that make n hops on
 the ladder to the totals of each of a and b.  If the ladder was
 unbounded, then we could say that in the case of a, there are n*2X
 LSPs along the spar only, and n(n-1)*2X/n = 2X(n-1) LSPs use a rung
 and the spar.  Thus, the LSPs that make n hops on the ladder
 contribute (4n-2)X LSPs to a.  Note that the edge cases are special
 because LSPs that make only one hop on the ladder cannot transit a
 P(1) but only start or end there.
 So with a ladder of length R = S(1)/2, we could say:
       R
 a = SUM[(4i-2)*X] + 2RX
     i=2
   = 2*X*R*(R+1)
 And similarly, considering b in an unbounded ladder, the LSPs that
 only travel one hop on the LSP are a special case, contributing 2X
 LSPs, and every other LSP that traverses n hops on the ladder
 contributes 2n*2X/n = 4X LSPs.  So:
          R+1
 b = 2X + SUM[4X]
          i=2
   = 2*X + 4*X*R
 In fact, the ladders are bounded, and so the number of LSPs is
 reduced because of the effect of the ends of the ladders.  The links
 that see the most LSPs are in the middle of the ladder.  Consider a
 ladder of length R; a node in the middle of the ladder is R/2 hops
 away from the end of the ladder.  So we see that the formula for the
 contribution to the count of spar-only LSPs for a is only valid up to
 n=R/2, and for spar-and-rung LSPs, up to n=1+R/2.  Above these
 limits, the contribution made by spar-only LSPs decays as (n-R/2)*2X.

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 However, for a first-order approximation, we will use the values of a
 and b as computed above.  This gives us an upper bound of the number
 of LSPs without using a more complex formula for the reduction made
 by the effect of the ends of the ladder.
 From this:
 L(1) = a + b/2 +
        E*E*(2 - S(1)) - E*M(2)
      = 2*X*R*(R+1) +
        X + 2*X*R +
        E*E*(2 - S(1)) - E*M(2)
      = E*E*S(1)*(1 + S(1)/2) +
        E*E + E*E*S(1) +
        2*E+E - E*E*S(1) - E*M(2)
      = E*E*S(1)*(1 + S(1)/2) + 3*E+E - E*M(2)
      = E*E*S(1)*S(1)/2 + E*E*S(1) + 3*E*E - E*M(2)
 So, for example, with S(1) = 6, M(1) = 10, and M(2) = 17, we see:
    E     = 170
    S(PE) = 1020
    L(PE) = 2038
    L(2)  = 34374
    L(1)  = 777410
 Alternatively, with S(1) = 10, M(1) = 10, and M(2) = 20, we see:
    E     = 200
    S(PE) = 2000
    L(PE) = 3998
    L(2)  = 79580
    L(1)  = 2516000
 In both examples, the number of LSPs at the core (P(1)) nodes is
 probably unacceptably large, even though there are only a relatively
 modest number of PEs.  In fact, L(2) may even be too large in the
 second example.
 Compare the L(1) values with the total number of LSPs in the system
 S(PE)*(S(PE) - 1), which is 1039380 and 3998000, respectively.

Yasukawa, et al. Informational [Page 21] RFC 5439 Scaling in MPLS-TE February 2009

6. Scaling Snowflake Networks with Forwarding Adjacencies

 One of the purposes of LSP hierarchies [RFC4206] is to improve the
 scaling properties of MPLS-TE networks.  LSP tunnels (sometimes known
 as Forwarding Adjacencies (FAs)) may be established to provide
 connectivity over the core of the network, and multiple edge-to-edge
 LSPs may be tunneled down a single FA LSP.
 In our network we consider a mesh of FA LSPs between all core nodes
 at the same level.  We consider two possibilities here.  In the
 first, all P(2) nodes are connected to all other P(2) nodes by LSP
 tunnels, and the PE-to-PE LSPs are tunneled across the core of the
 network.  In the second, an extra layer of LSP hierarchy is
 introduced by connecting all P(1) nodes in an LSP mesh and tunneling
 the P(2)-to-P(2) tunnels through these.

6.1. Two-Layer Hierarchy

 In this hierarchy model, the P(2) nodes are connected by a mesh of
 tunnels.  This means that the P(1) nodes do not see the PE-to-PE
 LSPs.
 It remains the case that:
    L(PE) = 2*(S(PE) - 1)
 L(2) is slightly increased.  It can be computed as the sum of all
 LSPs for all attached PEs, including the LSPs between the attached PE
 (this figure is unchanged from Section 5.1, i.e., M(2)*(2*S(PE) -
 M(2) - 1)), plus the number of FA LSPs providing a mesh to the other
 P(2) nodes.  Since the number of P(2) nodes is S(2), each P(2) node
 sees 2*(S(2) - 1) FA LSPs.  Thus:
    L(2) = M(2)*(2*S(PE) - M(2) - 1) + 2*(S(2) - 1)
 L(1), however, is significantly reduced and can be computed as the
 sum of the number of FA LSPs to and from each attached P(2) to each
 other P(2) in the network, including (but counting only once) the FA
 LSPs between attached P(2) nodes.  In fact, the problem is identical
 to the L(2) computation in Section 5.1.  So:
 L(1) = M(1)*(2*S(2) - M(1) - 1)

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 So, for example, with S(1) = 5, M(1) = 10, and M(2) = 20, we see:
    S(PE) = 1000
    S(2)  = 50
    L(PE) = 1998
    L(2)  = 39678
    L(1)  = 890
 Alternatively, with S(1) = 10, M(1) = 10, and M(2) = 20, we see:
    S(PE) = 2000
    S(2)  = 100
    L(PE) = 3998
    L(2)  = 79778
    L(1)  = 1890
 So, in both examples, potential problems at the core (P(1)) nodes
 caused by an excessive number of LSPs can be avoided, but any problem
 with L(2) is made slightly worse, as can be seen from the table
 below.
 Example| Count | Unmodified    | 2-Layer
        |       | (Section 5.1) | Hierarchy
 -------+-------+---------------+----------
 A      | L(2)  |      39580    |   39678
        | L(1)  |     356000    |     890
 -------+-------+---------------+----------
 B      | L(2)  |      79580    |   79778
        | L(1)  |     756000    |    1890

6.1.1. Tuning the Network Topology to Suit the Two-Layer Hierarchy

 Clearly, we can reduce L(2) by selecting appropriate values of S(1),
 M(1), and M(2).  We can do this without negative consequences, since
 no change will affect L(PE) and since a large percentage increase in
 L(1) is sustainable now that L(1) is so small.
 Observe that:
    L(2) = M(2)*(2*S(PE) - M(2) - 1) + 2*(S(2) - 1)
 where S(PE) = S(1)*M(1)*M(2) and S(2) = S(1)*M(1).  So L(2) scales
 with M(2)^2 and we can have the most impact by reducing M(2) while
 keeping S(PE) constant.

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 For example, with S(1) = 10, M(1) = 10, and M(2) = 10, we see:
    S(PE) = 1000
    S(2)  = 100
    L(PE) = 1998
    L(2)  = 20088
    L(1)  = 1890
 And similarly, with S(1) = 20, M(1) = 20, and M(2) = 5, we see:
    S(PE) = 2000
    S(2)  = 400
    L(PE) = 3998
    L(2)  = 20768
    L(1)  = 15580
 These considerable scaling benefits must be offset against the cost-
 effectiveness of the network.  Recall from Section 3.3 that:
    K = S(PE)/(S(1)+S(2) ... + S(n))
 where n is the level above the PEs, so that for our network:
    K = S(PE) / (S(1) + S(2))
 Thus, in the first example the cost-effectiveness has been halved
 from 1000/55 to 1000/110.  In the second example, it has been reduced
 to roughly one quarter, changing from 2000/110 to 2000/420.
 So, although the tuning changes may be necessary to reach the desired
 network size, they come at a considerable cost to the operator.

6.2. Alternative Two-Layer Hierarchy

 An alternative to the two-layer hierarchy presented in Section 6.1 is
 to provide a full mesh of FA LSPs between P(1) nodes.  This technique
 is only of benefit to any nodes in the core of the level 1 network.
 It makes no difference to the PE and P(2) nodes since they continue
 to see only the PE-to-PE LSPs.  Furthermore, this approach increases
 the burden at the P(1) nodes since they have to support all of the
 PE-to-PE LSPs as in the flat model plus the additional 2*(S(1) - 1)
 P(1)-to-P(1) FA LSPs.  Thus, this approach should only be considered
 where there is a mesh of P-nodes within the ring of P(1) nodes, and
 is not considered further in this document.

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6.3. Three-Layer Hierarchy

 As demonstrated by Section 6.2, introducing a mesh of FA LSPs at the
 top level (P(1)) has no benefit, but if we introduce an additional
 level in the network (P(3) between P(2) and PE) to make a four-level
 snowflake, we can introduce a new layer of FA LSPs so that we have a
 full mesh of FA LSPs between all P(3) nodes to carry the PE-to-PE
 LSPs, and a full mesh of FA LSPs between all P(2) nodes to carry the
 P(3)-to-P(3) LSPs.
 The number of PEs is S(PE) = S(1)*M(1)*M(2)*M(3), and the number of
 PE-to-PE LSPs at a PE remains L(PE) = 2*(S(PE) - 1).
 The number of LSPs at a P(3) can be deduced from Section 6.1.  It is
 the sum of all LSPs for all attached PEs, including the LSPs between
 the attached PE, plus the number of FA LSPs providing a mesh to the
 other P(3) nodes.
 L(3) = M(3)*(2*S(PE) - M(3) - 1) + 2*(S(3) - 1)
 The number of LSPs at P(2) can also be deduced from Section 6.1 since
 it is the sum of all LSPs for all attached P(3) nodes, including the
 LSPs between the attached PE plus the number of FA LSPs providing a
 mesh to the other P(2) nodes.
 L(2) = M(2)*(2*S(3) - M(2) - 1) + 2*(S(2) - 1)
 Finally, L(1) can be copied straight from 6.1.
 L(1) = M(1)*(2*S(2) - M(1) - 1)
 For example, with S(1) = 5, M(1) = 5, M(2) = 5, and M(3) = 8, we see:
    S(PE) = 1000
    S(3)  = 125
    S(2)  = 25
    L(PE) = 1998
    L(3)  = 16176
    L(2)  = 1268
    L(1)  = 220

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 Similarly, with S(1) = 5, M(1) = 5, M(2) = 8, and M(3) = 10, we see:
    S(PE) = 2000
    S(3)  = 200
    S(2)  = 25
    L(PE) = 3998
    L(3)  = 40038
    L(2)  = 3184
    L(1)  = 220
 Clearly, there are considerable scaling improvements with this three-
 layer hierarchy, and all of the numbers (even L(3) in the second
 example) are manageable.
 Of course, the extra level in the network tends to reduce the cost-
 effectiveness of the networks with values of K = 1000/155 and K =
 2000/230 (from 1000/55 and 2000/110) for the examples above.  That is
 a reduction by a factor of 3 in the first case and 2 in the second
 case.  Such a change in cost-effectiveness has to be weighed against
 the desire to deploy such a large network.  If LSP hierarchies are
 the only scaling tool available, and networks this size are required,
 the cost-effectiveness may need to be sacrificed.

6.4. Issues with Hierarchical LSPs

 A basic observation for hierarchical scaling techniques is that it is
 hard to have any impact on the number of LSPs that must be supported
 by the level of P(n) nodes adjacent to the PEs (for example, it is
 hard to reduce L(3) in Section 6.3).  In fact, the only way we can
 change the number of LSPs supported by these nodes is to change the
 scaling ratio M(n) in the network -- in other words, to change the
 number of PEs subtended to any P(n).  But such a change has a direct
 effect on the number of PEs in the network and so the cost-
 effectiveness is impacted.
 Another concern with the hierarchical approach is that it must be
 configured and managed.  This may not seem like a large burden, but
 it must be recalled that the P(n) nodes are not at the edge of the
 network -- they are a set of nodes that must be identified so that
 the FA LSPs can be configured and provisioned.  Effectively, the
 operator must plan and construct a layered network with a ring of
 P(n) nodes giving access to the level (n) network.  This design
 activity is open to considerable risk as failing to close the ring
 (i.e., allowing a node to be at both level (n+1) and at level (n))
 may cause operational confusion.

Yasukawa, et al. Informational [Page 26] RFC 5439 Scaling in MPLS-TE February 2009

 Protocol techniques (such as IGP automesh [RFC4972]) have been
 developed to reduce the configuration necessary to build this type of
 multi-level network.  In the case of automesh, the routing protocol
 is used to advertise the membership of a 'mesh group', and all
 members of the mesh group can discover each other and connect with
 LSP tunnels.  Thus, the P(n) nodes giving access to level (n) can
 advertise their existence to each other, and it is not necessary to
 configure each with information about all of the others.  Although
 this process can help to reduce the configuration overhead, it does
 not eliminate it, as each member of the mesh group must still be
 planned and configured for membership.
 An important consideration for the use of hierarchical LSPs is how
 they can be protected using MPLS Fast Reroute (FRR) [RFC4090].  FRR
 may provide link protection either by protecting the tunnels as they
 traverse a broken link or by treating each level (n) tunnel LSP as a
 link in level (n+1) and providing protection for the level (n+1) LSPs
 (although in this model, fault detection and propagation time may be
 an issue).  Node protection may be performed in a similar way, but
 protection of the first and last nodes of a hierarchical LSP is
 particularly difficult.  Additionally, the whole notion of scaling
 with regard to FRR gives rise to separate concerns that are outside
 the scope of this document as currently formulated.
 Finally, observe that we have been explaining these techniques using
 conveniently symmetrical networks.  Consider how we would arrange the
 hierarchical LSPs in a network where some PEs are connected closer to
 the center of the network than others.

7. Scaling Ladder Networks with Forwarding Adjacencies

7.1. Two-Layer Hierarchy

 In Section 6.2, we observed that there is no value to placing FA LSPs
 between the P(1) nodes of our example snowflake topologies.  This is
 because those LSPs would be just one hop long and would, in fact,
 only serve to increase the burden at the P(1) nodes.  However, in the
 ladder model, there is value to this approach.  The P(1) nodes are
 the spar-nodes of the ladder, and they are not all mutually adjacent.
 That is, the P(1)-to-P(1) hierarchical LSPs can create a full mesh of
 P(1) nodes where one does not exist in the physical topology.
 The number of LSPs seen by a P(1) node is then:
 o all of the tunnels terminating at the P(1) node,
 o any transit tunnels, and
 o all of the LSPs due to subtended PEs.

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 This is a substantial reduction; all of the transit LSPs are reduced
 to just one per remote P(1) that causes any transit LSP.  So:
 L(1) = 2*(S(1) - 1) +
        O(S(1)*S(1)/2) +
        2*E*E*(S(1) - 1) + E*(E-1) - E*(M(2) - 1)
 where O(S(1)*S(1)/2) gives an upper bound order of magnitude.  So:
 L(1) = S(1)*S(1)/2 + 2*S(1) + 2*E*E*(S(1) - 1) - E*M(2) - 2
 So, in our two examples:
 With S(1) = 6, M(1) = 10, and M(2) = 17, we see:
    E     = 170
    S(PE) = 1020
    L(PE) = 2038
    L(2)  = 34374
    L(1)  = 286138
 Alternatively, with S(1) = 10, M(1) = 10, and M(2) = 20, we see:
    E     = 200
    S(PE) = 2000
    L(PE) = 3998
    L(2)  = 79580
    L(1)  = 716060
 Both of these show significant improvements over the previous L(1)
 figures of 777410 and 2516000.  But the numbers are still too large
 to manage, and there is no improvement in the L(2) figures.

7.2. Three-Layer Hierarchy

 We can also apply the three-layer hierarchy to the ladder model.  In
 this case, the number of LSPs between P(1) nodes is not reduced, but
 tunnels are also set up between all P(2) nodes.  Thus, the number of
 LSPs seen by a P(1) node is:
 o all of the tunnels terminating at the P(1) node,
 o any transit tunnels between P(1) nodes, and
 o all of the LSPs due to subtended P(2) nodes.
 No PE-to-PE LSPs are seen at the P(1) nodes.

Yasukawa, et al. Informational [Page 28] RFC 5439 Scaling in MPLS-TE February 2009

 L(1) = 2*(S(1) - 1) +
        O(S(1)*S(1)/2) +
        2*(S(1) - 1)*M(1)*M(1) + M(1)*(M(1) - 1)
 where O(S(1)*S(1)/2) gives an upper bound order of magnitude.  So:
 L(1) = S(1)*S(1)/2 + 2*S(1) + 2*M(1)*M(1)*S(1) - M(1)(M(1) + 1) - 2
 Unfortunately, there is a small increase in the number of LSPs seen
 by the P(2) nodes.  Each P(2) now sees all of the PE-to-PE LSPs that
 it saw before and is also an end-point for a set of P(2)-to-P(2)
 tunnels.  Thus, L(2) increases to:
 L(2) = 2*M(2)*(S(PE) - 1) - M(2)*(M(2) - 1) + 2*(S(1)*M(1) - 1)
 So, in our two examples:
 With S(1) = 6, M(1) = 10, and M(2) = 17, we see:
    E     = 170
    S(PE) = 1020
    L(PE) = 2038
    L(2)  = 34492
    L(1)  = 1118
 Alternatively, with S(1) = 10, M(1) = 10, and M(2) = 20, we see:
    E     = 200
    S(PE) = 2000
    L(PE) = 3998
    L(2)  = 79778
    L(1)  = 1958
 This represents a very dramatic decrease in LSPs across the core.

7.3. Issues with Hierarchical LSPs

 The same issues exist for hierarchical LSPs as described in Section
 6.4.  Although dramatic improvements can be made to the scaling
 numbers for the number of LSPs at core nodes, this can only be done
 at the cost of configuring P(2) to P(2) tunnels.  The mesh of P(1)
 tunnels is not enough.
 But the sheer number of P(2) to P(2) tunnels that must be configured
 is a significant management burden that can only be eased by using a
 technique like automesh [RFC4972].

Yasukawa, et al. Informational [Page 29] RFC 5439 Scaling in MPLS-TE February 2009

 It is significant, however, that the scaling problem at the P(2)
 nodes cannot be improved by using tunnels and that the only solution
 to ease this in the hierarchical approach would be to institute
 another layer of hierarchy (that is, P(3) nodes) between the P(2)
 nodes and the PEs.  This is, of course, a significant expense.

8. Scaling Improvements through Multipoint-to-Point LSPs

 An alternative (or complementary) scaling technique has been proposed
 using multipoint-to-point (MP2P) LSPs.  The fundamental improvement
 in this case is achieved by reducing the number of LSPs toward the
 destination as LSPs toward the same destination are merged.
 This section presents an overview of MP2P LSPs and describes their
 applicability and scaling benefits.

8.1. Overview of MP2P LSPs

 Note that the MP2P LSPs discussed here are for MPLS-TE and are not
 the same concept familiar in the Label Distribution Protocol (LDP)
 described in [RFC5036].
 Traffic flows generally converge toward their destination and this
 can be utilized by MPLS in constructing an MP2P LSP.  With such an
 LSP, the Label Forwarding Information Base (LFIB) mappings at each
 LSR are many-to-one so that multiple pairs {incoming interface,
 incoming label} are mapped to a single pair {outgoing interface,
 outgoing label}.  Obviously, if per-platform labels are used, this
 mapping may be optimized within an implementation.
 It is important to note that with MP2P MPLS-TE LSPs, the traffic
 flows are merged.  That is, some additional form of identifier is
 required if de-merging is required.  For example, if the payload is
 IP traffic belonging to the same client network, no additional de-
 merging information is required since the IP packet contains
 sufficient data.  On the other hand, if the data comes, for example,
 from a variety of VPN client networks, then the flows will need to be
 labeled in their own right as point-to-point (P2P) flows, so that
 traffic can be disambiguated at the egress of the MP2P LSPs.
 Techniques for establishing MP2P MPLS-TE LSPs and for assigning the
 correct bandwidth downstream of LSP merge points are out of the scope
 of this document.

Yasukawa, et al. Informational [Page 30] RFC 5439 Scaling in MPLS-TE February 2009

8.2. LSP State: A Better Measure of Scalability

 Consider the network topology shown in Figure 3.  Suppose that we
 establish MP2P LSP tunnels such that there is one tunnel terminating
 at each PE, and that that tunnel has every other PE as an ingress.
 Thus, a PE-to-PE MP2P LSP tunnel would have S(PE)-1 ingresses and one
 egress, and there would be S(PE) such tunnels.
 Note that there still remain 2*(S(PE) - 1) PE-to-PE P2P LSPs that are
 carried through these tunnels.
 Let's consider the number of LSPs handled at each node in the
 network.
 The PEs continue to handle the same number of PE-to-PE P2P LSPs, and
 must also handle the MP2P LSPs.  So:
 L(PE) = 2*(S(PE) - 1) + S(PE)
 But all P(n) nodes in the network only handle the MP2P LSP tunnels.
 Nominally, this means that L(n) = S(PE) for all values of n.  This
 would appear to be a great success with the number of LSPs cut to
 completely manageable levels.
 However, the number of LSPs is not the only issue (although it may
 have some impact for some of the scaling concerns listed in Section
 4).  We are more interested in the amount of LSP state that is
 maintained by an LSR.  This reflects the amount of storage required
 at the LSR, the amount of protocol processing, and the amount of
 information that needs to be managed.
 In fact, we were also interested in this measure of scalability in
 the earlier sections of this document, but in those cases we could
 see a direct correlation between the number of LSPs and the amount of
 LSP state since transit LSPs had two pieces of state information (one
 on the incoming and one on the outgoing interface), and ingress or
 egress LSPs had just one piece of state.
 We can quantify the amount of LSP state according to the number of
 LSP segments managed by an LSR.  So (as above), in the case of a P2P
 LSP, an ingress or egress has one segment to maintain, while a
 transit has two segments.  Similarly, for an MP2P LSP, an LSR must
 maintain one set of state information for each upstream segment
 (which, we can assume, is in a one-to-one relationship with the
 number of upstream neighbors) and exactly one downstream segment --
 ingresses obviously have no upstream neighbors, and egresses have no
 downstream segments.

Yasukawa, et al. Informational [Page 31] RFC 5439 Scaling in MPLS-TE February 2009

 So we can start again on our examination of the scaling properties of
 MP2P LSPs using X(n) to represent the amount of LSP state held at
 each P(n) node.

8.3. Scaling Improvements for Snowflake Networks

 At the PEs, there is only connectivity to one other network node: the
 P(2) node.  But note that if P2P LSPs need to be used to allow
 disambiguation of data at the MP2P LSP egresses, then these P2P LSPs
 are tunneled within the MP2P LSPs.  So X(PE) is:
 X(PE) = 2*(S(PE) - 1) if no disambiguation is required,
 and
 X(PE) = 4*(S(PE) - 1) if disambiguation is required.
 Each P(2) node has M(2) downstream PEs.  The P(2) sees a single MP2P
 LSP targeted at each downstream PE with one downstream segment (to
 that PE) and M(2) - 1 upstream segments from the other subtended PEs.
 Additionally, each of these LSPs has an upstream segment from the one
 upstream P(1).  This gives a total of M(2)*(1 + M(2)) LSP segments.
 There are also LSPs running from the subtended PEs to every other PE
 in the network.  There are S(PE) - M(2) such PEs, and the P(2) sees
 one upstream segment for each of these from each subtended PE.  It
 also has one downstream segment for each of these LSPs.  This gives
 (M(2) + 1)*(S(PE) - M(2)) LSP segments.
 Thus:
 X(2) = M(2)*(1 + M(2)) + (M(2) + 1)*(S(PE) - M(2))
      = S(PE)*(M(2) + 1)
 Similarly, at each P(1) node there are M(1) downstream P(2) nodes and
 so a total of M(1)*M(2) downstream PEs.  Each P(1) is connected in a
 full mesh with the other P(1) nodes and so has (S(1) - 1) neighbors.
 The P(1) sees a single MP2P LSP targeted at each downstream PE.  This
 has one downstream segment (to the P(2) to which the PE is connected)
 and M(1) - 1 upstream segments from the other subtended P(2) nodes.
 Additionally, each of these LSPs has an upstream segment from each of
 the P(1) neighbors.  This gives a total number of LSP segments of
 M(1)*M(2)*(M(1) + S(1) - 1).
 There are also LSPs running from each of the subtended PEs to every
 other PE in the network.  There are S(PE) - M(1)M(2) such PEs, and
 the P(1) sees one upstream segment for each of these from each

Yasukawa, et al. Informational [Page 32] RFC 5439 Scaling in MPLS-TE February 2009

 subtended P(2) (since the aggregation from the subtended PEs has
 already happened at the P(2) nodes).  It also has one downstream
 segment to the appropriate next hop P(1) neighbor for each of these
 LSPs.  This gives (M(1) + 1)*(S(PE) - M(1)*M(2)) LSP segments.
 Thus:
 X(1) = M(1)*M(2)*(M(1) + S(1) - 1) +
        (M(1) + 1)*(S(PE) - M(1)*M(2))
      = M(1)*M(2)*(S(1) - 2) + S(PE)*(M(1) + 1)
 So, for example, with S(1) = 10, M(1) = 10, and M(2) = 10, we see:
    S(PE) = 1000
    S(2)  = 100
    X(PE) = 3996   (or 1998)
    X(2)  = 11000
    X(1)  = 11800
 And similarly, with S(1) = 20, M(1) = 20, and M(2) = 5, we see:
    S(PE) = 2000
    S(2)  = 400
    X(PE) = 5996   (or 2998)
    X(2)  = 12000
    X(1)  = 39800

8.3.1. Comparison with Other Scenarios

 For comparison with the examples in Sections 5 and 6, we need to
 convert those LSP-based figures to our new measure of LSP state.
 Observe that each LSP in Sections 5 and 6 generates two state units
 at a transit LSR and one at an ingress or egress.  So we can provide
 conversions as follows:
 Section 5 (flat snowflake network)
   L(PE) = 2*(S(PE) - 1)
   L(2)  = M(2)*(2*S(PE) - M(2) - 1)
   L(1)  = M(1)*M(2)*(2*S(PE) - M(2)*(M(1) + 1))
   X(PE) = 2*(S(PE) - 1)
   X(2)  = 2*M(2)*(2*S(PE) - M(2) - 1)
   X(1)  = 2*M(1)*M(2)*(2*S(PE) - M(2)*(M(1) + 1))
   For the example with S(1) = 10, M(1) = 10, and M(2) = 10, this
   gives a comparison table as follows:

Yasukawa, et al. Informational [Page 33] RFC 5439 Scaling in MPLS-TE February 2009

      Count | Unmodified  |  MP2P
      ------+-------------+----------
      X(PE) |     1998    |   3996
      X(2)  |    39780    |  11000
      X(1)  |   378000    |  11800
   Clearly, this technique is a significant improvement over the flat
   network within the core of the network, although the PEs are more
   heavily stressed if disambiguation is required.
 Section 6.1 (two-layer hierarchy snowflake network)
   L(PE) = 2*(S(PE) - 1)
   L(2)  = M(2)*(2*S(PE) - M(2) - 1) + 2*(S(2) - 1)
   L(1)  = M(1)*(2*S(2) - M(1) - 1)
   X(PE) = 2*(S(PE) - 1)
   X(2)  = 2*M(2)*(2*S(PE) - M(2) - 1) + 2*(S(2) - 1)
   X(1)  = 2*M(1)*(2*S(2) - M(1) - 1)
   Note that in the computation of X(2) the hierarchical LSPs only add
   one state at each P(2) node.
   For the same example with S(1) = 10, M(1) = 10, and M(2) = 10, this
   gives a comparison table as follows:
      Count |   2-Layer   |  MP2P
            |  Hierarchy  |
      ------+-------------+----------
      X(PE) |     1998    |   3996
      X(2)  |    39978    |  11000
      X(1)  |     3780    |  11800
   We can observe that the MP2P model is better at P(2), but the
   hierarchical model is better at P(1).
 In fact, this comparison can be generalized to observe that the MP2P
 model produces its best effects toward the edge of the network, while
 the hierarchical model makes most impression at the core.  However,
 the requirement for disambiguation of P2P LSPs tunneled within the
 MP2P LSPs does cause a double burden at the PEs.

8.4. Scaling Improvements for Ladder Networks

 MP2P LSPs applied just within the ladder will not make a significant
 difference, but applying MP2P for all LSPs and at all nodes makes a
 very big difference without requiring any further configuration.

Yasukawa, et al. Informational [Page 34] RFC 5439 Scaling in MPLS-TE February 2009

 LSP state at a spar-node may be divided into those LSPs' segments
 that enter or leave the spar-node due to subtended PEs (local LSP
 segments), and those that enter or leave the spar-node due to remote
 PEs (remote segments).
 The local segments may be counted as:
 o  E LSPs targeting local PEs
 o  (S(1)-1)*E*M(1) LSPs targeting remote PEs
 The remote segments may be counted as:
 o  (S(1)-1)*E outgoing LSPs targeting remote PEs
 o  <= 3*S(1)*E incoming LSPs targeting any PE (there are precisely
    P(1) nodes attached to any other P(1) node)
 Hence, using X(1) as a measure of LSP state rather than a count of
 LSPs, we get:
 X(1) <= E + (S(1)-1)*E*M(1) + (S(1)-1)*E + 3*S(1)*E
      <= (4 + M(1))*S(1)*E - M(1)*E
 The number of LSPs at the P(2) nodes is also improved.  We may also
 count the LSP state in the same way so that there are:
 o  M(2) LSPs targeting local PEs,
 o  M(2)*(S(1)*E) LSPs from local PEs to all other PEs, and
 o  S(1)*E - M(2) LSPs to remote PEs.
 So using X(2) as a measure of LSP state and not a count of LSPs, we
 have:
 X(2) = M(2) + M(2)*(S(1)*E) + S(1)*E - M(2)
      = (M(2) + 1)*S(1)*E
 Our examples from Section 5.2 give us the following numbers:
 With S(1) = 6, M(1) = 10, and M(2) = 17, we see:
    E     = 170
    S(PE) = 1020
    X(PE) = 2038
    X(2)  = 18360
    X(1) <= 12580

Yasukawa, et al. Informational [Page 35] RFC 5439 Scaling in MPLS-TE February 2009

 Alternatively, with S(1) = 10, M(1) = 10, and M(2) = 20, we see:
    E     = 200
    S(PE) = 2000
    X(PE) = 3998
    X(2)  = 42000
    X(1) <= 26000

8.4.1. Comparison with Other Scenarios

 The use of MP2P compares very favorably with all scaling scenarios.
 It is the only technique able to reduce the value of X(2), and it
 does this by a factor of almost two.  The impact on X(1) is better
 than everything except the three-level hierarchy.
 The following table provides a quick cross-reference for the figures
 for the example ladder networks.  Note that the previous figures are
 modified to provide counts of LSP state rather than LSP numbers.
 Again, each LSP contributes one state at its end points and two
 states at transit nodes.
 Thus, for the all cases we have:
   X(PE) = 2*(S(PE) - 1) or
   X(PE) = 4*(S(PE) - 1) if disambiguation is required.
 In the unmodified (flat) case, we have:
   X(2) = 2*(M(2)*(2*S(PE) - M(2) - 1))
   X(1) = 2*(M(1)*M(2)*(2*S(PE) - M(2)*(M(1) + 1)))
 In the two-level hierarchy, we have:
   X(2) = 2*(2*M(2)*(S(PE) - 1) - M(2)*(M(2) - 1))
   X(1) = S(1)*S(1) + 2*S(1) + 4*E*E*(S(1) - 1) - 2*E*M(2) - 2
 In the three-level hierarchy, we have:
   X(2) = 2*(2*M(2)*(S(PE) - 1) - M(2)*(M(2) - 1)) + 2*(S(1)*M(1) - 1)
   X(1) = S(1)*S(1) + 2*S(1) + 4*M(1)*M(1)*S(1) - 2*M(1)(M(1) + 1) - 2
 Example A: S(1) = 6, M(1) = 10, and M(2) = 17
 Example B: S(1) = 10, M(1) = 10, and M(2) = 20

Yasukawa, et al. Informational [Page 36] RFC 5439 Scaling in MPLS-TE February 2009

 Example| Count | Unmodified |  2-Level   |  3-Level    |  MP2P
        |       |            | Hierarchy  | Hierarchy   |
 -------+-------+------------+------------+-------------+-------
 A      | X(2)  |     68748  |    68748   |    68866    |  18360
        | X(1)  |   1554820  |   572266   |     2226    |  12580
 -------+-------+------------+------------+-------------+-------
 B      | X(2)  |    159160  |   159160   |   159358    |  42000
        | X(1)  |   5032000  |  1433998   |     3898    |  26000

8.4.2. LSP State Compared with LSP Numbers

 Recall that in Section 8.3, the true benefit of MP2P was analyzed
 with respect to the LSP segment state required, rather than the
 actual number of LSPs.  This proved to be a more accurate comparison
 of the techniques because the MP2P LSPs require state on each branch
 of the LSP, so the saving is not linear with the reduced number of
 LSPs.
 A similar analysis could be performed here for the ladder network.
 The net effect is that it increases the state by an order of two for
 all transit LSPs in the P2P models, and by a multiplier equal to the
 degree of a node in the MP2P model.
 A rough estimate shows that, as with snowflake networks, MP2P
 provides better scaling than the one-level hierarchical model and is
 considerably better at the core.  But MP2P compares less will with
 the two-level hierarchy especially in the core.

8.5. Issues with MP2P LSPs

 The biggest challenges for MP2P LSPs are the provision of support in
 the control and data planes.  To some extent, support must also be
 provided in the management plane.
 Control plane support is just a matter of defining the protocols and
 procedures [MP2P-RSVP], although it must be clearly understood that
 this will introduce some complexity to the control plane.
 Hardware issues may be a little more tricky.  For example, the
 capacity of the upstream segments must never (allowing for
 statistical over-subscription) exceed the capacity of the downstream
 segment.  Similarly, data planes must be equipped with sufficient
 buffers to handle incoming packet collisions.
 The management plane will be impacted in several ways.  Firstly, the
 management applications will need to handle LSPs with multiple
 senders.  This means that, although the applications need to process
 fewer LSPs, they will be more complicated and will, in fact, need to

Yasukawa, et al. Informational [Page 37] RFC 5439 Scaling in MPLS-TE February 2009

 process the same number of ingresses and egresses.  Other issues like
 diagnostics and OAM would also need to be enhanced to support MP2P,
 but might be borrowed heavily from LDP networks.
 Lastly, note that when the MP2P solution is used, the receiver (the
 single egress PE of an MP2P tunnel) cannot use the incoming label as
 an indicator of the source of the data.  Contrast this with P2P LSPs.
 Depending on deployment, this might not be an issue since the PE-PE
 connectivity may in any case be a tunnel with inner labels to
 discriminate the data flows.
 In other deployments, it may be considered necessary to include
 additional PE-PE P2P LSPs and tunnel these through the MP2P LSPs.
 This would require the PEs to support twice as many LSPs.  Since PEs
 are not usually as fully specified as P-routers, this may cause some
 concern; however, the use of penultimate hop popping on the MP2P LSPs
 might help to reduce this issue.
 In all cases, care must be taken not to confuse the reduction in the
 number of LSPs with a reduction in the LSP state that is required.
 In fact, the discussion in Section 8.3 is slightly optimistic since
 LSP state toward the destination will probably need to include sender
 information and so will increase depending on the number of senders
 for the MP2P LSP.  Section 8.4, on the other hand, counts LSP state
 rather than LSPs.  This issue is clearly dependent on the protocol
 solution for MP2P RSVP-TE, which is out of scope for this document.
 MPLS Fast Reroute (FRR) [RFC4090] is an attractive scheme for
 providing rapid local protection from node or link failures.  Such a
 scheme has, however, not been designed for MP2P at the time of
 writing, so it remains to be seen how practical it could be,
 especially in the case of the failure of a merge node.  Initial
 examination of this case suggests that FRR would not be a problem for
 MP2P, given that each flow can be handled separately.
 As a final note, observe that the MP2P scenario presented in this
 document may be optimistic.  MP2P LSP merging may be hard to achieve
 between LSPs with significantly different traffic and Quality of
 Service (QoS) parameters.  Therefore, it may be necessary to increase
 the number of MP2P LSPs arriving at an egress.

Yasukawa, et al. Informational [Page 38] RFC 5439 Scaling in MPLS-TE February 2009

9. Combined Models

 There is nothing to prevent the combination of hierarchical and MP2P
 solutions within a network.
 Note that if MP2P LSPs are tunneled through P2P FA LSPs across the
 core, none of the benefit of LSP merging is seen for the hops during
 which the MP2P LSPs are tunneled.
 On the other hand, it is possible to construct solutions where MP2P
 FA LSPs are constructed within the network, resulting in savings from
 both modes of operation.

10. An Alternate Solution

 A simple solution to reducing the number of LSP tunnels handled by
 any node in the network has been proposed.  In this solution it is
 observed that part of the problem is caused purely by the total
 number of LSP in the network, and that this is a function of the
 number of PEs since a full mesh of PE-PE LSPs is required.  The
 conclusion of this observation is to move the tunnel end-points
 further into the network so that, instead of having a full mesh of
 PE-PE tunnels, we have only a full mesh of P(n)-P(n) tunnels.
 Obviously, there is no change in the physical network topology, so
 the PEs remain subtended to the P(n) nodes, and the consequence is
 that there is no TE on the links between PEs and P(n) nodes.
 In this case, we have already done the hard work for computing the
 number of LSPs in the previous sections.  The power of the analysis
 in the earlier sections is demonstrated by its applicability to this
 new model -- all we need to do is make minor changes to the formulae.
 This is most simply done by removing a layer from the network.  We
 introduce the term "tunnel end-point" (TEP) and replace the P(n)
 nodes with TEPs.  Thus, the example of a flat snowflake network in
 Figure 3 becomes as shown in Figure 7.  Corresponding changes can be
 made to all of the sample topologies.

Yasukawa, et al. Informational [Page 39] RFC 5439 Scaling in MPLS-TE February 2009

      PE    PE  PE     PE  PE     PE
        \     \/         \/      /
     PE--TEP  TEP        TEP  TEP--PE
            \ |            | /
             \|            |/
    PE--TEP---P(1)------P(1)---TEP--PE
       /          \    /          \
     PE            \  /            PE
                    \/
                    P(1)
                    /|\
                   / | \
                  /  |  \
           PE--TEP  TEP  TEP--PE
              /      /\     \
            PE     PE  PE    PE
    Figure 7 : An Example Snowflake Network with Tunnel End-Points
 To perform the scaling calculations we need only replace the PE
 counts in the formulae with TEP counts, and observe that there is one
 fewer layer in the network.  For example, in the flat snowflake
 network shown in Figure 7, we can see that the number of LSPs seen at
 a TEP is:
 L(TEP) = 2*(S(TPE) - 1)
 In our sample networks, S(TPE) is typically of the order of 50 or 100
 (the original values of S(2)), so L(TEP) is less than 200, which is
 quite manageable.
 Similarly, the number of LSPs handled by a P(1) node can be derived
 from the original formula for the number of LSPs seen at a P(2) node,
 since all we have done is reduce n in P(n) from 2 to 1.  So our new
 formula is:
 L(1) = M(1)*(2*S(TEP) - M(1) - 1)
 With figures for M(1) = 10 and S(TEP) = 100, this gives us L(1) =
 1890.  This is also very manageable.

10.1. Pros and Cons of the Alternate Solution

 On the face of it, this alternate solution seems very attractive.
 Simply by contracting the edges of the tunnels into the network, we
 have shown a dramatic reduction in the number of tunnels needed, and
 there is no requirement to apply any additional scaling techniques.

Yasukawa, et al. Informational [Page 40] RFC 5439 Scaling in MPLS-TE February 2009

 But what of the PE-P(n) links?  In the earlier sections of this
 document, we have assumed that there was some requirement for PE-PE
 LSPs with TE properties that extended to the PE-P(n) links at both
 ends of each LSP.  That means that there was a requirement to provide
 reservation-based QoS on those links, to be able to discriminate
 traffic flows for priority-based treatment, and to be able to
 distinguish applications and sources that send data based on the LSPs
 that carry the data.
 It might be argued that, since the PE-P(n) links do not offer any
 routing options (each such link provides the only access to the
 network for a PE), most of the benefits of tunnels are lost on these
 peripheral links.  However, TE is not just about routing.  Just as
 important are the abilities to make resource reservations, to
 prioritize traffic, and to discriminate between traffic from
 different applications, customers, or VPNs.
 Furthermore, in multihoming scenarios where each PE is connected to
 more than one P(n) or where a PE has multiple links to a single P(n),
 there may be a desire to pre-select the link to be used and to direct
 the traffic to that link using a PE-PE LSP.  Note that multihoming
 has not been considered in this document.
 Operationally, P(n)-P(n) LSPs offer the additional management
 overhead that is seen for hierarchical LSPs described in Section 6.
 That is, the LSPs have to be configured and established through
 additional configuration or management operations that are not
 carried out at the PEs.  As described in Section 6, automesh
 [RFC4972] could be used to ease this task.  But it must be noted
 that, as mentioned above, some of the key uses of tunnels require
 that traffic is classified and placed in an appropriate tunnel
 according to its traffic class, end-points, originating application,
 and customer (such as client VPN).  This information may not be
 readily available for each packet at the P(n) nodes since it is PE-
 based information.  Of course, it is possible to conceive of
 techniques to make this information available, such as assigning a
 different label for each class of traffic, but this gives rise to the
 original problem of larger numbers of LSPs.
 Our conclusion is, therefore, that this alternate technique may be
 suitable for the general distribution of traffic based solely on the
 destination, or on a combination of the destination and key fields
 carried in the IP header.  In this case, it can provide a very
 satisfactory answer to the scaling issues in an MPLS-TE network.  But
 if more sophisticated packet classification and discrimination is
 required, this technique will make the desired function hard to

Yasukawa, et al. Informational [Page 41] RFC 5439 Scaling in MPLS-TE February 2009

 achieve, and the trade-off between scaling and feature-level will
 swing too far towards solving the scaling issue at the expense of
 delivery of function to the customer.

11. Management Considerations

 The management issues of the models presented in this document have
 been discussed in-line.  No one solution is without its management
 overhead.
 Note, however, that scalability of management tools is one of the
 motivators for this work and that network scaling solutions that
 reduce the active management of LSPs at the cost of additional effort
 to manage the more static elements of the network represent a
 benefit.  That is, it is worth the additional effort to set up MP2P
 or FA LSPs if it means that the network can be scaled to a larger
 size without being constrained by the management tools.
 The MP2P technique may prove harder to debug through OAM methods than
 the FA LSP approach.

12. Security Considerations

 The techniques described in this document use existing or yet-to-be-
 defined signaling protocol extensions and are subject to the security
 provided by those extensions.  Note that we are talking about
 tunneling techniques used within the network and that both approaches
 are vulnerable to the creation of bogus tunnels that deliver data to
 an egress or consume network resources.
 The fact that the MP2P technique may prove harder to debug through
 OAM methods than the FA LSP approach is a security concern since it
 is important to be able to detect misconnections.
 General issues of the relationship between scaling and security are
 covered in Section 1.1, but the details are beyond the scope of this
 document.  Readers are referred to [MPLS-SEC] for details of MPLS
 security techniques.

13. Recommendations

 The analysis in this document suggests that the ability to signal
 MP2P MPLS-TE LSPs is a desirable addition to the operator's MPLS-TE
 toolkit.
 At this stage, no further recommendations are made, but it would be
 valuable to consult more widely to discover:

Yasukawa, et al. Informational [Page 42] RFC 5439 Scaling in MPLS-TE February 2009

  1. The concerns of other service providers with respect to network

scalability.

  1. More opinions on the realistic constraints to the network

parameters listed in Section 4.

  1. Desirable values for the cost-effectiveness of the network

(parameter K).

  1. The applicability, manageability, and support for the two

techniques described.

  1. The feasibility of combining the two techniques, as discussed in

Section 9.

  1. The level of concern over the loss of functionality that would

occur if the alternate solution described in Section 10 was

   adopted.

14. Acknowledgements

 The authors are grateful to Jean-Louis Le Roux for discussions and
 review input.  Thanks to Ben Niven-Jenkins, JP Vasseur, Loa
 Andersson, Anders Gavler, Ben Campbell, and Tim Polk for their
 comments.  Thanks to Dave Allen for useful discussion of the math.

15. Normative References

 [RFC4206]   Kompella, K. and Y. Rekhter, "Label Switched Paths (LSP)
             Hierarchy with Generalized Multi-Protocol Label Switching
             (GMPLS) Traffic Engineering (TE)", RFC 4206, October
             2005.

16. Informative References

 [RFC2961]   Berger, L., Gan, D., Swallow, G., Pan, P., Tommasi, F.,
             and S. Molendini, "RSVP Refresh Overhead Reduction
             Extensions", RFC 2961, April 2001.
 [RFC3209]   Awduche, D., Berger, L., Gan, D., Li, T., Srinivasan, V.,
             and G. Swallow, "RSVP-TE: Extensions to RSVP for LSP
             Tunnels", RFC 3209, December 2001.
 [RFC3270]   Le Faucheur, F., Wu, L., Davie, B., Davari, S., Vaananen,
             P., Krishnan, R., Cheval, P., and J. Heinanen, "Multi-
             Protocol Label Switching (MPLS) Support of Differentiated
             Services", RFC 3270, May 2002.

Yasukawa, et al. Informational [Page 43] RFC 5439 Scaling in MPLS-TE February 2009

 [RFC3473]   Berger, L., Ed., "Generalized Multi-Protocol Label
             Switching (GMPLS) Signaling Resource ReserVation
             Protocol-Traffic Engineering (RSVP-TE) Extensions", RFC
             3473, January 2003.
 [RFC3985]   Bryant, S., Ed., and P. Pate, Ed., "Pseudo Wire Emulation
             Edge-to-Edge (PWE3) Architecture", RFC 3985, March 2005.
 [RFC4090]   Pan, P., Ed., Swallow, G., Ed., and A. Atlas, Ed., "Fast
             Reroute Extensions to RSVP-TE for LSP Tunnels", RFC 4090,
             May 2005.
 [RFC4110]   Callon, R. and M. Suzuki, "A Framework for Layer 3
             Provider-Provisioned Virtual Private Networks (PPVPNs)",
             RFC 4110, July 2005.
 [RFC4972]   Vasseur, JP., Ed., Leroux, JL., Ed., Yasukawa, S.,
             Previdi, S., Psenak, P., and P. Mabbey, "Routing
             Extensions for Discovery of Multiprotocol (MPLS) Label
             Switch Router (LSR) Traffic Engineering (TE) Mesh
             Membership", RFC 4972, July 2007.
 [RFC5036]   Andersson, L., Ed., Minei, I., Ed., and B. Thomas, Ed.,
             "LDP Specification", RFC 5036, October 2007.
 [MP2P-RSVP] Yasukawa, Y., "Supporting Multipoint-to-Point Label
             Switched Paths in Multiprotocol Label Switching Traffic
             Engineering", Work in Progress, October 2008.
 [MPLS-SEC]  Fang, L., Ed., "Security Framework for MPLS and GMPLS
             Networks", Work in Progress, November 2008.

Yasukawa, et al. Informational [Page 44] RFC 5439 Scaling in MPLS-TE February 2009

Authors' Addresses

 Seisho Yasukawa
 NTT Corporation
 9-11, Midori-Cho 3-Chome
 Musashino-Shi, Tokyo 180-8585 Japan
 Phone: +81 422 59 4769
 EMail: s.yasukawa@hco.ntt.co.jp
 Adrian Farrel
 Old Dog Consulting
 EMail: adrian@olddog.co.uk
 Olufemi Komolafe
 Cisco Systems
 96 Commercial Street
 Edinburgh
 EH6 6LX
 United Kingdom
 EMail: femi@cisco.com

Yasukawa, et al. Informational [Page 45]

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