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Network Working Group                                        S. Yasukawa
Internet-Draft                                                       NTT
Intended Status: Informational                                 A. Farrel
Created: December 14, 2008                            Old Dog Consulting
Expires: June 14, 2009                                       O. Komolafe
                                                           Cisco Systems


        An Analysis of Scaling Issues in MPLS-TE Core Networks

              draft-ietf-mpls-te-scaling-analysis-05.txt


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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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Contents
   1. Introduction ..................................................  3
   1.1 Overview .....................................................  3
   1.2 Glossary of Notation .........................................  4
   2. Issues of Concern for Scaling .................................  5
   2.1 LSP State ...................................................   5
   2.2 Processing Overhead ..........................................  5
   2.3 RSVP-TE Implications .........................................  6
   2.4 Management ...................................................  7
   3. Network Topologies ............................................  7
   3.1 The Snowflake Network Topology ...............................  8
   3.2 The Ladder Network Topology .................................. 10
   3.3 Commercial Drivers for Selected Configurations ............... 12
   3.4 Other Network Topologies ..................................... 13
   4. Required Network Sizes ........................................ 14
   4.1 Practical Numbers ............................................ 14
   5. Scaling in Flat Networks ...................................... 14
   5.1 Snowflake Networks ........................................... 15
   5.2 Ladder Networks .............................................. 16
   6. Scaling Snowflake Networks with Forwarding Adjacencies ........ 19
   6.1 Two Layer Hierarchy .......................................... 20
   6.1.1 Tuning the Network Topology to Suit the Two Layer Hierarchy  21
   6.2 Alternative Two Layer Hierarchy .............................. 21
   6.3 Three Layer Hierarchy ........................................ 22
   6.4 Issues with Hierarchical LSPs  ............................... 23
   7. Scaling Ladder Networks with Forwarding Adjacencies............ 24
   7.1 Two Layer Hierarchy .......................................... 24
   7.2 Three Layer Hierarchy ........................................ 25
   7.3 Issues with Hierarchical LSPs ................................ 26
   8. Scaling Improvements Through Multipoint-to-Point LSPs ......... 26
   8.1 Overview of MP2P LSPs ........................................ 27
   8.2 LSP State: A Better Measure of Scalability ................... 27
   8.3 Scaling Improvements for Snowflake Networks .................. 28
   8.3.1 Comparison with Other Scenarios ............................ 29
   8.4 Scaling Improvements for Ladder Networks ..................... 30
   8.4.1 Comparison with Other Scenarios ............................ 31
   8.4.2 LSP State Compared with LSP Numbers ........................ 33
   8.5 Issues with MP2P LSPs ........................................ 33
   9. Combined Models ............................................... 34
   10. An Alternate Solution ........................................ 35
   10.1 Pros and Cons of the Alternate Solution ..................... 36
   11. Management Considerations .................................... 37
   12. Security Considerations ...................................... 37
   13. Recommendations .............................................. 38
   14. IANA Considerations .......................................... 38
   15. Acknowledgements ............................................. 38
   16. Intellectual Property Consideration .......................... 39
   17. Normative References ......................................... 40
   18. Informative References ....................................... 40
   19. Authors' Addresses ........................................... 41

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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 snow-flake
   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 snow-flake
   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.

   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

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   among these are 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 Re-route (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 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 thier 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
   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

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   parameters of the networks that are analyzed. These terms are defined
   as they are introduced though-out 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 of 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 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.

   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

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   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 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.

   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) for every LSP it supports every 30 seconds. 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 nearly remove 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

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   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 are maintained
   through the use of Hello message exchanges. Although [RFC3209]
   suggests that Hello messages should be retransmitted every 5ms, 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.

   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 anElement
   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, 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 consideration encourage a reduction in the number of
   LSPs supported within the network and at any particular LSR.

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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.

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),
   and 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

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   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.

   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
   including down to 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 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 network 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 make up two spars connected by six rungs.

                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.



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   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.

   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)


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   So 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

     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.

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   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 by 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

   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 chasis 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 (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. As much of a problem
   is likely to be the physical shape and topography of the country in
   which the network is laid. 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.

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      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.

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 each other LSP. Thus, if
   there are S(PE) PEs in the network, there are S(PE)*(S(PE) - 1) LSPs.



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   Define L(n) as the number of LSPs handled by a level (n) LSR.

   L(PE) = 2*(S(PE) - 1)

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 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
   that each 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 the 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
   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:

   o  E*(E-1)
   o  M(1)*M(2)*(M(2)-1) = E*(M(2) - 1)
   o  2*E*E*(S(1) - 1)


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   The number of LSPs in transit is more complicated to compute. It is
   simplified by not considering the ends of the ladders, but 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 the Figure
   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 so are only
   included once in the sum 2a+b.

   So L(1) = a + b/2 -
             (locally terminated transit LSPs)/2 +
             (locally contained LSPs)

   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.

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   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 each 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 for n=1+R/2. Above these limits the
   contribution made by spar-only LSPs decays as (n-R/2)*2X. 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.









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   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 sytem
   S(PE)*(S(PE) - 1) which is 1039380 and 3998000 respectively.

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.

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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)

   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

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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 because L(1) is now 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.

   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. And 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

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   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
   it is not considered further in this document.

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 as 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 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.

   Protocol techniques (such as IGP auto-mesh [RFC4972]) have been
   developed to reduce the configuration necessary to build this type of
   multi-level network. In the case of auto-mesh, the routing protocol
   is used to advertise the membership of a 'mesh group', and all
   members of the mesh can discover each other and connect with LSP

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   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 Re-Route (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
   o all of the LSPs due to subtended PEs.

   This is a substantial reduction because 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)


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   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
   o all of the LSPs due to subtended P(2) nodes.

   No PE-to-PE LSPs are seen at the P(1) nodes.

   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 it is also an end point for a set of P(2)-to-P(2)
   tunnels. Thus L(2) increases to:


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   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].

   It is significant, however, that the scaling problem at the P(2)
   nodes cannot be improved by using tunnels, and 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.




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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 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 demerging is required. For example, if the payload is IP traffic
   belonging to the same client network, no additional demerging
   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.

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

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   completely manageable levels.

   But 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.

   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 each other PE

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   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 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 each
   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 subtended
   P(2) (since the aggregation form the subtended PEs has already
   happened at the P(2) nodes). It also has one downstream segment to
   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



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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:

        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

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     And 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 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.

   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
   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


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   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

   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 2-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 3-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



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   Example A: S(1) = 6, M(1) = 10, and M(2) = 17
   Example B: S(1) = 10, M(1) = 10, and M(2) = 20

   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 1-level hierarchical model, and is
   considerably better at the core. But MP2P compares less will with the
   2-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

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   fewer LSPs, they will be more complicated and will, in fact, need to
   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 although 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 Re-route (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 would 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 QoS parameters.
   Therefore, it may be necessary to increase the number of MP2P LSPs
   arriving at an egress.

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

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   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 LSP 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.


       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

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   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.

   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 preselect the link to be used and to direct
   the traffic to that link using a PE-PE LSP. Note that multihoming

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   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 problems 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
   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

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   the security provided by those extensions. Note that we are talking
   about tunneling techniques used within the network and 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 realtionship between scaling and security are
   covered in Section 1.1, but the details are beyond the scope of this
   document. Readers are refered 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:

   - 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. IANA Considerations

   This document makes no requests for IANA action.

15. Acknowledgements

   The authors are grateful to Jean-Louis Le Roux for discussions and
   review input. Thanks to Ben Niven-Jenkins, JP Vasseur, Loa Andersson,

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   Anders Gavler, and Tom Polk for their comments. Thanks to Dave Allen
   for useful discussion of the math.

16. Intellectual Property Consideration

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   considered to be definitive versions of these Legal Provisions.

   For the avoidance of doubt, each Contributor to the IETF Standards
   Process licenses each Contribution that he or she makes as part of
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   Contributor, or included with or in such Contribution.







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17. 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.

18. 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., et al., "Multi-Protocol Label Switching
               (MPLS) Support of Differentiated Services", RFC 3270, May
               2002.

   [RFC3473]   Berger, L., et al., Editor, "Generalized Multi-Protocol
               Label Switching (GMPLS) Signaling Resource ReserVation
               Protocol-Traffic Engineering (RSVP-TE) Extensions",
               RFC 3473, January 2003.

   [RFC3985]   Bryant, S., and Pate, P., "Pseudo Wire Emulation Edge-to-
               Edge (PWE3) Architecture", RFC 3985, March 2005.

   [RFC4090]   P. Pan, G. Swallow, A. Atlas (Editors), "Fast Reroute
               Extensions to RSVP-TE for LSP Tunnels", RFC 4090, May
               2005.

   [RFC4110]   Callon, R., and Suzuki, M., "A Framework for Layer 3
               Provider-Provisioned Virtual Private Networks (PPVPNs)",
               RFC 4110, July 2005.

   [RFC4972]   Vasseur, JP., and Le Roux, JL., "Routing Extensions for
               Discovery of Multiprotocol (MPLS) Label Switch Router
               (LSR) Traffic Engineering (TE) Mesh Membership",
               RFC 4972, July 2007.

   [RFC5036]   Andersson, L., Doolan, P., Feldman, N., Fredette, A., and
               B. Thomas, "LDP Specification", RFC 5036, October 2007.

   [MP2P-RSVP] Yasukawa, Y., "Supporting Multipoint-to-Point Label
               Switched Paths in Multiprotocol Label Switching Traffic
               Engineering", draft-yasukawa-mpls-mp2p-rsvpte, work in
               progress.


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   [MPLS-SEC]  Fang, L. (Ed.), "Security Framework for MPLS and GMPLS
               Networks", draft-ietf-mpls-mpls-and-gmpls-security-
               framework, work in progress.

19. 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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   Copyright (c) 2008 IETF Trust and the persons identified as the
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