    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.

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       Copyright (c) 2009 IETF Trust and the persons identified as the
       document authors.  All rights reserved.

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    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.

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    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

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       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.

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       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

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       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.

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       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.

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       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.

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       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.

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    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.

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       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

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            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:

       - connection to one or more other spars,
       - connection to a tree of other core nodes,
       - 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.

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                    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:

       - There are precisely two spars in the core network.

       - Every spar-node connects to precisely one spar-node on the other
         spar.  That is, each spar-node is attached to precisely one rung.

       - Each spar-node connects to either one (end-spar) or two (core-spar)
         other spar-nodes on the same spar.

       - 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.

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       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

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          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

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       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.

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    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:

       - The network should have at least 1000 PEs.
       - 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)

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    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:

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       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:

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       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)

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       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.

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    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.

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       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.

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       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].

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       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.

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    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.

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       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

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       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:

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            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.

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       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

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       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

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       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

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       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.

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    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.

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            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.

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       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

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       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:

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       - The concerns of other service providers with respect to network
         scalability.

       - More opinions on the realistic constraints to the network
         parameters listed in Section 4.

       - Desirable values for the cost-effectiveness of the network
         (parameter K).

       - The applicability, manageability, and support for the two
         techniques described.

       - The feasibility of combining the two techniques, as discussed in
         Section 9.

       - 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.

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    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.

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    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

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