Internet Engineering Task Force (IETF)                          M. Shand
Request for Comments: 6976                        Individual Contributor
Category: Informational                                        S. Bryant
ISSN: 2070-1721                                               S. Previdi
                                                             C. Filsfils
                                                           Cisco Systems
                                                             P. Francois
                                                Institute IMDEA Networks
                                                          O. Bonaventure
                                        Universite catholique de Louvain
                                                               July 2013


                  Framework for Loop-Free Convergence
     Using the Ordered Forwarding Information Base (oFIB) Approach

Abstract

   This document describes an illustrative framework of a mechanism for
   use in conjunction with link-state routing protocols that prevents
   the transient loops that would otherwise occur during topology
   changes.  It does this by correctly sequencing the forwarding
   information base (FIB) updates on the routers.

   This mechanism can be used in the case of non-urgent (management
   action) link or node shutdowns and restarts or link metric changes.
   It can also be used in conjunction with a fast reroute mechanism that
   converts a sudden link or node failure into a non-urgent topology
   change.  This is possible where a complete repair path is provided
   for all affected destinations.

   After a non-urgent topology change, each router computes a rank that
   defines the time at which it can safely update its FIB.  A method for
   accelerating this loop-free convergence process by the use of
   completion messages is also described.

   The technology described in this document has been subject to
   extensive simulation using pathological convergence behavior and real
   network topologies and costs.  However, the mechanisms described in
   this document are purely illustrative of the general approach and do
   not constitute a protocol specification.  This document represents a
   snapshot of the work of the Routing Area Working Group at the time of
   publication and is published as a document of record.  Further work
   is needed before implementation or deployment.







Shand, et al.                 Informational                     [Page 1]


RFC 6976            Loop-Free Convergence Using oFIB           July 2013


Status of This Memo

   This document is not an Internet Standards Track specification; it is
   published for informational purposes.

   This document is a product of the Internet Engineering Task Force
   (IETF).  It represents the consensus of the IETF community.  It has
   received public review and has been approved for publication by the
   Internet Engineering Steering Group (IESG).  Not all documents
   approved by the IESG are a candidate for any level of Internet
   Standard; see Section 2 of RFC 5741.

   Information about the current status of this document, any errata,
   and how to provide feedback on it may be obtained at
   http://www.rfc-editor.org/info/rfc6976.

Copyright Notice

   Copyright (c) 2013 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

   This document is subject to BCP 78 and the IETF Trust's Legal
   Provisions Relating to IETF Documents
   (http://trustee.ietf.org/license-info) in effect on the date of
   publication of this document.  Please review these documents
   carefully, as they describe your rights and restrictions with respect
   to this document.  Code Components extracted from this document must
   include Simplified BSD License text as described in Section 4.e of
   the Trust Legal Provisions and are provided without warranty as
   described in the Simplified BSD License.





















Shand, et al.                 Informational                     [Page 2]


RFC 6976            Loop-Free Convergence Using oFIB           July 2013


Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   4
     1.1.  The Purpose of This Document  . . . . . . . . . . . . . .   4
     1.2.  Overview  . . . . . . . . . . . . . . . . . . . . . . . .   4
   2.  The Required FIB Update Order . . . . . . . . . . . . . . . .   6
     2.1.  Single Link Events  . . . . . . . . . . . . . . . . . . .   6
       2.1.1.  Link Down / Metric Increase . . . . . . . . . . . . .   6
       2.1.2.  Link Up / Metric Decrease . . . . . . . . . . . . . .   7
     2.2.  Multi-Link Events . . . . . . . . . . . . . . . . . . . .   8
       2.2.1.  Router Down Events  . . . . . . . . . . . . . . . . .   8
       2.2.2.  Router Up Events  . . . . . . . . . . . . . . . . . .   8
       2.2.3.  Line-Card Failure/Restoration Events  . . . . . . . .   8
   3.  Applying Ordered FIB Updates  . . . . . . . . . . . . . . . .   9
     3.1.  Deducing the Topology Change  . . . . . . . . . . . . . .   9
     3.2.  Deciding If Ordered FIB Updates Apply . . . . . . . . . .   9
   4.  Computation of the Ordering . . . . . . . . . . . . . . . . .  10
     4.1.  Link Down, Router Down, or Metric Increase  . . . . . . .  10
     4.2.  Link Up, Router Up, or Metric Decrease  . . . . . . . . .  11
   5.  Acceleration of Ordered Convergence . . . . . . . . . . . . .  11
     5.1.  Construction of the Waiting List and Notification List  .  12
       5.1.1.  Down Events . . . . . . . . . . . . . . . . . . . . .  12
       5.1.2.  Up Events . . . . . . . . . . . . . . . . . . . . . .  12
     5.2.  Format of Completion Messages . . . . . . . . . . . . . .  13
   6.  Fallback to Conventional Convergence  . . . . . . . . . . . .  13
   7.  oFIB State Machine  . . . . . . . . . . . . . . . . . . . . .  13
     7.1.  OFIB_STABLE . . . . . . . . . . . . . . . . . . . . . . .  14
     7.2.  OFIB_HOLDING_DOWN . . . . . . . . . . . . . . . . . . . .  15
     7.3.  OFIB_HOLDING_UP . . . . . . . . . . . . . . . . . . . . .  16
     7.4.  OFIB_ONGOING  . . . . . . . . . . . . . . . . . . . . . .  17
     7.5.  OFIB_ABANDONED  . . . . . . . . . . . . . . . . . . . . .  18
   8.  Management Considerations . . . . . . . . . . . . . . . . . .  18
   9.  Security Considerations . . . . . . . . . . . . . . . . . . .  18
   10. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . .  18
   11. Informative References  . . . . . . . . . . . . . . . . . . .  19
   Appendix A.  Candidate Methods of Safely Abandoning Loop-Free
                Convergence (AAH)  . . . . . . . . . . . . . . . . .  20
     A.1.  Possible Solutions  . . . . . . . . . . . . . . . . . . .  20
     A.2.  Hold-Down Timer Only  . . . . . . . . . . . . . . . . . .  20
     A.3.  AAH Messages  . . . . . . . . . . . . . . . . . . . . . .  21
       A.3.1.  Per-Router State Machine  . . . . . . . . . . . . . .  22
       A.3.2.  Per-Neighbor State Machine  . . . . . . . . . . . . .  24
   Appendix B.  Synchronization of Loop-Free Timer Values  . . . . .  25
     B.1.  Introduction  . . . . . . . . . . . . . . . . . . . . . .  25
     B.2.  Required Properties . . . . . . . . . . . . . . . . . . .  25
     B.3.  Mechanism . . . . . . . . . . . . . . . . . . . . . . . .  26
     B.4.  Security Considerations Related to Router Timer Values  .  27




Shand, et al.                 Informational                     [Page 3]


RFC 6976            Loop-Free Convergence Using oFIB           July 2013


1.  Introduction

1.1.  The Purpose of This Document

   This document describes an illustrative framework of a mechanism for
   use in conjunction with link-state routing protocols that prevents
   the transient loops that would otherwise occur during topology
   changes.  It does this by correctly sequencing the forwarding
   information base (FIB) updates on the routers.

   At the time of publication there is no demand to deploy this
   technology; however, in view of the subtleties involved in the design
   of extensions for loop-free convergence routing protocols, the
   Routing Area Working Group considered it desirable to publish this
   document to place on record the design consideration of the ordered
   FIB (oFIB) approach.

   The mechanisms presented in this document are purely illustrative of
   the general approach and do not constitute a protocol specification.
   This document represents a snapshot of the work of the working group
   at the time of publication and is published as a document of record.
   Additional work is needed to specify the necessary routing protocol
   extensions necessary to support this IP fast reroute (FRR) method
   before implementation or deployment.

1.2.  Overview

   With link-state protocols, such as IS-IS [ISO10589] and OSPF
   [RFC2328], each time the network topology changes, some routers need
   to modify their forwarding information bases (FIBs) to take into
   account the new topology.  Each topology change causes a convergence
   phase.  During this phase, routers may transiently have inconsistent
   FIBs, which may lead to packet loops and losses, even if the
   reachability of the destinations is not compromised after the
   topology change.  Packet losses and transient loops can also occur in
   the case of a link down event implied by a maintenance operation,
   even if this operation is predictable and not urgent.  When the link-
   state change is a metric update and when a new link is brought up in
   the network, there is no direct loss of connectivity, but transient
   packet loops and loss can still occur.

   In this document, a distinction is made between urgent and non-urgent
   network events.  Urgent events are those that arise from
   unpredictable network outages (such as node or link failures) that
   are traditionally resolved through the convergence of routing
   protocols or by protection mechanisms reliant on fault detection and
   reporting (such as through Operations, Administration, and
   Maintenance).  Non-urgent events are those that arise from



Shand, et al.                 Informational                     [Page 4]


RFC 6976            Loop-Free Convergence Using oFIB           July 2013


   predictable events such as the controlled shutdown of network
   resources by a management system, or the modification of network
   parameters (such as routing metrics).  Typically, non-urgent events
   can be planned around, while urgent events must be handled by dynamic
   systems.  All network events, both urgent and non-urgent, may lead to
   transient packet loops and loss.

   For example, in Figure 1, if the link between X and Y is shut down by
   an operator, packets destined to X can loop between R and Y when Y
   has updated its FIB while R has not yet updated its FIB, and packets
   destined to Y can loop between X and S if X updates its FIB before S.
   According to the current behavior of IS-IS and OSPF, this scenario
   will happen most of the time because X and Y are the first routers to
   be aware of the failure, so that they will update their FIBs first.

                                     1
                       X-------------/-------------Y
                       |                           |
                       |                           |
                       |                           |
                       |                           |
                     1 |                           | 1
                       |                           |
                       |                           |
                       |                           |
                       |                           |
                       S---------------------------R
                                     2

                        Figure 1: A Simple Topology

   It should be noted that the loops can occur remotely from the
   failure, not just adjacent to it.

   [RFC5715] provides an introduction to a number of loop-free
   convergence methods, and readers unfamiliar with this technology are
   recommended to read it before studying this document in detail.  Note
   that in common with other loop-free convergence methods, oFIB is only
   capable of providing loop-free convergence in the presence of a
   single failure.

   The goal of this document is to describe a mechanism that sequences
   the router FIB updates to maintain consistency throughout the
   network.  By correctly setting the FIB change order, no looping or
   packet loss can occur.  This mechanism may be applied to the case of
   managed link-state changes, i.e., link metric change, manual link
   down/up, manual router down/up, and managed state changes of a set of
   links attached to one router.  It may also be applied to the case



Shand, et al.                 Informational                     [Page 5]


RFC 6976            Loop-Free Convergence Using oFIB           July 2013


   where one or more network elements are protected by a fast reroute
   mechanism (FRR) [RFC5714] [RFC4090].  The mechanisms that are used in
   the failure case are exactly the same as those used for managed
   changes.  For simplicity, this document makes no further distinction
   between managed and unplanned changes.

   It is assumed in the description that follows that all routers in the
   routing domain are oFIB capable.  This can be verified in an
   operational network by having the routers report oFIB capability
   using the IGP.  Where non-oFIB-capable routers exist in the network,
   normal convergence would be used by all routers.  The operation of
   mixed-mode networks is for further study.

   The technology described in this document has been subject to
   extensive simulation using pathological convergence behavior and real
   network topologies and costs.  A variant of the technology described
   here has been experimentally deployed in a production network.

2.  The Required FIB Update Order

   This section provides an overview of the required ordering of the FIB
   updates.  A more detailed analysis of the rerouting dynamics and
   correctness proofs of the mechanism can be found in [refs.PFOB07].

2.1.  Single Link Events

   For simplicity, the correct ordering for single link changes are
   described first.  The document then builds on this to demonstrate
   that the same principles can be applied to more complex scenarios
   such as line-card or node changes.

2.1.1.  Link Down / Metric Increase

   First, consider the non-urgent failure of a link (i.e., where an
   operator or a network management system (NMS) shuts down a link,
   thereby removing it from the currently active topology) or the
   increase of a link metric by the operator or NMS.  In this case, a
   router R must not update its FIB until all other routers that send
   traffic via R and the affected link have first updated their FIBs.

   The following argument shows that this rule ensures the correct order
   of FIB changes when the link X->Y is shut down or its metric is
   increased.

   An "outdated" FIB entry for a destination is defined as being a FIB
   entry that still reflects the shortest path(s) in use before the
   topology change.  Once a packet reaches a router R that has an
   outdated FIB entry for the packet destination, then, provided the



Shand, et al.                 Informational                     [Page 6]


RFC 6976            Loop-Free Convergence Using oFIB           July 2013


   oFIB ordering is respected, the packet will continue to X only
   traversing routers that also have an outdated FIB entry for the
   destination.  The packet thus reaches X without looping and will be
   forwarded to Y via X->Y (or in the case of FRR, the X->Y repair path)
   and will reach its destination.

   Since it can be assumed that the original topology was loop-free, Y
   will never use the link Y->X to reach the destination, and hence the
   path(s) between Y and the destination are guaranteed to be unaffected
   by the topology change.  It therefore follows that the packet
   arriving at Y will reach its destination without looping.

   Since it can also be assumed that the new topology is loop-free, by
   definition a packet cannot loop while being forwarded exclusively by
   routers with an updated FIB entry.

   In other words, when the oFIB ordering is respected, if a packet
   reaches an outdated router, it can never subsequently reach an
   updated router, and it cannot loop because from this point on it will
   only be forwarded on the consistent path that was used before the
   event.  If it does not reach an outdated router, it will only be
   forwarded on the loop-free path that will be used after the
   convergence.

   According to the proposed ordering, X will be the last router to
   update its FIB.  Once it has updated its FIB, the link X->Y can
   actually be shut down (or the repair removed).

   If the link X-Y is bidirectional, a similar process must be run to
   order the FIB update for destinations using the link in the direction
   Y->X.  As has already been shown, no packet ever traverses the X-Y
   link in both directions, and hence the operation of the two ordering
   processes is orthogonal.

2.1.2.  Link Up / Metric Decrease

   In the case of link up events or metric decreases, a router R must
   update its FIB before all other routers that will use R to reach the
   affected link.

   The following argument shows that this rule ensures the correct order
   of FIB changes when the link X->Y is brought into service or its
   metric is decreased.

   Firstly, when a packet reaches a router R that has already updated
   its FIB, all the routers on the path from R to X will also have
   updated their FIB, so that the packet will reach X and be forwarded
   along X->Y, ultimately reaching its destination.



Shand, et al.                 Informational                     [Page 7]


RFC 6976            Loop-Free Convergence Using oFIB           July 2013


   Secondly, a packet cannot loop between routers that have not yet
   updated their FIB.  This proves that no packet can loop.

2.2.  Multi-Link Events

   The following sections describe the required ordering for single
   events that may manifest as multiple link events.  For example, the
   failure of a router may be notified to the rest of the network as the
   individual failure of all its attached links.  The means of
   identifying the event type from the collection of received link
   events is described in Section 3.1.

2.2.1.  Router Down Events

   In the case of the non-urgent shutdown of a router, a router R must
   not update its FIB until all other routers that send traffic via R
   and the affected router have first updated their FIBs.

   Using a proof similar to that for link failure, it can be shown that
   no loops will occur if this ordering is respected [refs.PFOB07].

2.2.2.  Router Up Events

   In the case of a router being brought into service, a router R must
   update its FIB BEFORE all other routers that WILL use R to reach the
   affected router.

   A proof similar to that for link up shows that no loops will occur if
   this ordering is respected [refs.PFOB07].

2.2.3.  Line-Card Failure/Restoration Events

   The failure of a line card involves the failure of a set of links,
   all of which have a single node in common, i.e., the parent router.
   The ordering to be applied is the same as if it were the failure of
   the parent router.

   In a similar way, the restoration of an entire line card to service
   as a single event can be treated as if the parent router were
   returning to service.











Shand, et al.                 Informational                     [Page 8]


RFC 6976            Loop-Free Convergence Using oFIB           July 2013


3.  Applying Ordered FIB Updates

3.1.  Deducing the Topology Change

   As has been described, a single event such as the failure or
   restoration of a single link, single router, or line card may be
   notified to the rest of the network as a set of individual link
   change events.  It is necessary to deduce from this collection of
   link-state notifications the type of event that has occurred in the
   network and hence the required ordering.

   When a link change event is received that impacts the receiving
   router's FIB, the routers at the near and far end of the link are
   noted.

   If all events received within some hold-down period (the time that a
   router waits to acquire a set of Link State Packets (LSPs) that
   should be processed together) have a single router in common, then it
   is assumed that the change reflects an event (line-card or router
   change) concerning that router.

   In the case of a link change event, the router at the far end of the
   link is deemed to be the common router.

   All ordering computations are based on treating the common router as
   the root for both link and node events.

3.2.  Deciding If Ordered FIB Updates Apply

   There are some events (for example, a subsequent failure with
   conflicting repair requirements occurring before the ordered FIB
   process has completed) that cannot be correctly processed by this
   mechanism.  In these cases, it is necessary to ensure that
   convergence falls back to the conventional mode of operation (see
   Section 6).

   In all cases, it is necessary to wait some hold-down period after
   receiving the first notification to ensure that all routers have
   received the complete set of link-state notifications associated with
   the single event.

   At any time, if a link change notification is received that would
   have no effect on the receiving router's FIB, then it may be ignored.

   If no other event is received during the hold-down time, the event is
   treated as a link event.  Note that the IGP reverse connectivity
   check means that only the first failure event or second up event has
   an effect on the FIB.



Shand, et al.                 Informational                     [Page 9]


RFC 6976            Loop-Free Convergence Using oFIB           July 2013


   If an event that is received within the hold-down period does NOT
   reference the common router (R), then, in this version of the
   specification, normal convergence is invoked immediately (see
   Section 6).

   Network reconvergence using the ordered FIB approach takes longer
   than the normal reconvergence process.  Where the failure is
   protected by an FRR mechanism, this additional delay in convergence
   causes no packet loss.  When the sudden failure of a link or a set of
   links that are not protected using an FRR mechanism occurs, the
   failure must be processed using the conventional (faster) mode of
   operation to minimize packet loss during reconvergence.

   In summary, an ordered FIB process is applicable if the set of link
   state notifications received between the first event and the hold-
   down period reference a common router R, and one of the following
   assertions is verified:

   o  The set of notifications refers to link down events concerning
      protected links and metric increase events.

   o  The set of notifications refers to link up events and metric
      decrease events.

4.  Computation of the Ordering

   This section describes how the required ordering is computed.

   This computation required the introduction of the concept of a
   reverse Shortest Path Tree (rSPT).  The rSPT uses the cost towards
   the root (rather than from it) and yields the best paths towards the
   root from other nodes in the network [IPFRR-TUNNELS].

4.1.  Link Down, Router Down, or Metric Increase

   To respect the proposed ordering, routers compute a rank that will be
   used to determine the time at which they are permitted to perform
   their FIB update.  In the case of a failure event rooted at router Y
   or an increase of the metric of link X->Y, router R computes the rSPT
   in the topology before the failure (rSPT_old) rooted at Y.  This rSPT
   gives the shortest paths to reach Y before the failure.  The branch
   of the rSPT that is below R corresponds to the set of shortest paths
   to R that are used by the routers that reach Y via R.

   The rank of router R is defined as the depth (in number of hops) of
   this branch.  In the case of Equal Cost Multipath (ECMP), the maximum
   depth of the ECMP path set is used.




Shand, et al.                 Informational                    [Page 10]


RFC 6976            Loop-Free Convergence Using oFIB           July 2013


   Router R is required to update its FIB at time

      T0 + H + (rank * MAX_FIB)

   where T0 is the arrival time of the Link State Packet containing the
   topology change, H is the hold-down time, and MAX_FIB is a network-
   wide constant that reflects the maximum time required to update a FIB
   irrespective of the change required.  The value of MAX_FIB is network
   specific, and its determination is out of the scope of this document.
   This value must be agreed to by all the routers in the network.  This
   agreement can be performed by using a capability TLV as defined in
   Appendix B.

   All the routers that use R to reach Y will compute a lower rank than
   R, and hence the correct order will be respected.  It should be noted
   that only the routers that used Y before the event need to compute
   their rank.

4.2.  Link Up, Router Up, or Metric Decrease

   In the case of a link or router up event rooted at Y or a link metric
   decrease affecting link Y->W, a router R must have a rank that is
   higher than the rank of the routers that it will use to reach Y,
   according to the rule described in Section 2.  Thus, the rank of R is
   the number of hops between R and Y in its renewed Shortest Path Tree.
   When R has multiple equal-cost paths to Y, the rank is the length in
   hops of the longest ECMP path to Y.

   Router R is required to update its FIB at time

      T0 + H + (rank * MAX_FIB)

   It should be noted that only the routers that use Y after the event
   have to compute a rank, i.e., only the routers that have Y in their
   SPT after the link-state change.

5.  Acceleration of Ordered Convergence

   The mechanism described above is conservative and hence may be
   relatively slow.  The purpose of this section is to describe a method
   of accelerating the controlled convergence in such a way that ordered
   loop-free convergence is still guaranteed.

   In many cases, a router will complete its required FIB changes in a
   time much shorter than MAX_FIB, and in many other cases, a router
   will not have to perform any FIB change at all.





Shand, et al.                 Informational                    [Page 11]


RFC 6976            Loop-Free Convergence Using oFIB           July 2013


   This section describes the use of completion messages to speed up the
   convergence by providing a means for a router to inform those routers
   waiting for it that it has completed any required FIB changes.  When
   a router has been advised of completion by all the routers for which
   it is waiting, it can safely update its own FIB without further
   delay.  In most cases, this can result in a sub-second reconvergence
   time, which is comparable with a normal convergence time.

   Routers maintain a waiting list of the neighbors from which a
   completion message must be received.  Upon reception of a completion
   message from a neighbor, a router removes this neighbor from its
   waiting list.  Once its waiting list becomes empty, the router is
   allowed to update its FIB immediately even if its ranking timer has
   not yet expired.  Once this is done, the router sends a completion
   message to the neighbors that are waiting for it to complete.  Those
   routers are listed in a list called the Notification List.
   Completion messages contain an identification of the event to which
   they refer.

   Note that, since this is only an optimization, any loss of completion
   messages will result in the routers waiting their defined ranking
   time, and hence the loop-free properties will be preserved.

5.1.  Construction of the Waiting List and Notification List

5.1.1.  Down Events

   Consider a link or node down event rooted at router Y or the cost
   increase of the link X->Y.  A router R will compute rSPT_old(Y) to
   determine its rank.  When doing this, R also computes the set of
   neighbors that R uses to reach the failing node or link, and the set
   of neighbors that are using R to reach the failing node or link.  The
   notification list of R is equal to the former set, and the waiting
   list of R is equal to the latter.

   Note that R could include all its neighbors in the notification list
   except those in the waiting list; this would have no impact on the
   correctness of the protocol but would be unnecessarily inefficient.

5.1.2.  Up Events

   Consider a link or node up event rooted at router Y or the cost
   decrease of the link Y->X.  A router R will compute its new SPT
   (SPT_new(R)).  The waiting list is the set of next-hop routers that R
   uses to reach Y in SPT_new(R).






Shand, et al.                 Informational                    [Page 12]


RFC 6976            Loop-Free Convergence Using oFIB           July 2013


   In a simple implementation, the notification list of R is all the
   neighbors of R excluding those in the waiting list.  This may be
   further optimized by computing rSPT_new(Y) to determine those routers
   that are waiting for R to complete.

5.2.  Format of Completion Messages

   The format of completion messages and means of their delivery is
   routing protocol dependent and is outside the scope of this document.

   The following information is required:

   o  Identity of the sender.

   o  List of routing notifications being considered in the associated
      FIB change.  Each notification is defined as:

         Node ID of the near end of the link

         Node ID of the far end of the link

         Inclusion or removal of link

         Old metric

         New metric

6.  Fallback to Conventional Convergence

   In circumstances where a router detects that it is dealing with
   incomplete or inconsistent link-state information, or when a further
   topology event is received before completion of the current ordered
   FIB update process, it may be expedient to abandon the controlled
   convergence process.  A number of possible fallback mechanisms are
   described in Appendix A.  This mechanism is referred to as
   "Abandoning All Hope" (AAH).  The state machine defined in the body
   of this document does not make any assumption about which fallback
   mechanism will be used.

7.  oFIB State Machine

   An implementation must be capable of interworking with the model of
   an oFIB state machine described in this section.

   An oFIB-capable router maintains an oFIB state value, which is one
   of: OFIB_STABLE, OFIB_HOLDING_DOWN, OFIB_HOLDING_UP, OFIB_ABANDONED,
   or OFIB_ONGOING.




Shand, et al.                 Informational                    [Page 13]


RFC 6976            Loop-Free Convergence Using oFIB           July 2013


   An oFIB-capable router maintains a timer, Hold_down_timer.  An oFIB-
   capable router is configured with a value referred to as
   HOLD_DOWN_DURATION.  This configuration can be performed manually or
   using Appendix B.

   An oFIB-capable router maintains a timer, rank_timer.

7.1.  OFIB_STABLE

   OFIB_STABLE is the state of a router that is not currently involved
   in any convergence process.  This router is ready to process an event
   by applying oFIB.

   EVENT: Reception of a Link State Packet that describes an event of
   the type link X--Y down or metric increase and is to be processed
   using oFIB.

   ACTION:

      Set state to OFIB_HOLDING_DOWN.

      Start Hold_down_timer.

      ofib_current_common_set = {X,Y}.

      Compute rank with respect to the event, as defined in Section 4.

      Store the waiting list and notification list for X--Y obtained
      from the rank computation.

   EVENT: Reception of a Link State Packet that describes an event of
   the type link X--Y up or metric decrease and is to be processed using
   oFIB.

   ACTION:

      Set state to OFIB_HOLDING_UP.

      Start Hold_down_timer.

      ofib_current_common_set = {X,Y}.

      Compute rank with respect to the event, as defined in Section 4.

      Store the waiting list and notification list for X--Y obtained
      from the rank computation.





Shand, et al.                 Informational                    [Page 14]


RFC 6976            Loop-Free Convergence Using oFIB           July 2013


7.2.  OFIB_HOLDING_DOWN

   OFIB_HOLDING_DOWN is the state of a router that is collecting a set
   of link down or metric increase Link State Packets to be processed
   together using controlled convergence.

   EVENT: Reception of a Link State Packet that describes an event of
   the type link up or metric decrease and can be processed using oFIB.

   ACTION:

      Set state to OFIB_ABANDONED.

      Reset Hold_down_timer.

      Trigger AAH mechanism.

   EVENT: Reception of a Link State Packet that describes an event of
   the type link A--B down or metric increase and can be processed using
   oFIB.

   ACTION:

      ofib_current_common_set =
      intersection(ofib_current_common_set,{A,B}).

      If ofib_current_common_set is empty, then there is no longer a
      node in common in all the pending link-state changes.

         Set state to OFIB_ABANDONED.

         Reset Hold_down_timer.

         Trigger AAH mechanism.

      If ofib_current_common set is not empty, update the waiting list
      and notification list as defined in Section 4.  Note that in the
      case of a single link event, the Link State Packet received when
      the router is in this state describes the state change of the
      other direction of the link; hence, no changes will be made to the
      waiting and notification lists.










Shand, et al.                 Informational                    [Page 15]


RFC 6976            Loop-Free Convergence Using oFIB           July 2013


   EVENT: Hold_down_timer expires.

   ACTION:

      Set state to OFIB_ONGOING.

      Start rank_timer with computed rank.

   EVENT: Reception of a completion message.

   ACTION: Remove the sender from the waiting list associated with the
   event identified in the completion message.

7.3.  OFIB_HOLDING_UP

   OFIB_HOLDING_UP is the state of a router that is collecting a set of
   link up or metric decrease Link State Packets to be processed
   together using controlled convergence.

   EVENT: Reception of a Link State Packet that describes an event of
   the type link down or metric increase and is to be processed using
   oFIB.

   ACTION:

      Set state to OFIB_ABANDONED.

      Reset Hold_down_timer.

      Trigger AAH mechanism.

   EVENT: Reception of a Link State Packet that describes an event of
   the type link A--B up or metric decrease and is to be processed using
   oFIB.

   ACTION:

      ofib_current_common_set =
      intersection(ofib_current_common_set,{A,B}).

      If ofib_current_common_set is empty, then there is no longer a
      common node in the set of pending link-state changes.

         Set state to OFIB_ABANDONED.

         Reset Hold_down_timer.

         Trigger AAH mechanism.



Shand, et al.                 Informational                    [Page 16]


RFC 6976            Loop-Free Convergence Using oFIB           July 2013


      If ofib_current_common set is not empty, update the waiting list
      and notification list as defined in Section 4.  Note that in the
      case of a single link event, the Link State Packet received when
      the router is in this state describes the state change of the
      other direction of the link; hence, no changes will be made to the
      waiting and notification lists.

   EVENT: Reception of a completion message.

   ACTION: Remove the sender from the waiting list associated with the
   event identified in the completion message.

   EVENT: Hold_down_timer expires.

   ACTION:

      Set state to OFIB_ONGOING.

      Start rank_timer with computed rank.

7.4.  OFIB_ONGOING

   OFIB_ONGOING is the state of a router that is applying the ordering
   mechanism with respect to the set of Link State Packets collected
   when in OFIB_HOLDING_DOWN or OFIB_HOLDING_UP state.

   EVENT: rank_timer expires or waiting list becomes empty.

   ACTION:

      Perform FIB updates according to the change.

      Send completion message to each member of the notification list.

      Set state to OFIB_STABLE.

   EVENT: Reception of a completion message.

   ACTION: Remove the sender from the waiting list.

   EVENT: Reception of a Link State Packet describing a link-state
   change event.









Shand, et al.                 Informational                    [Page 17]


RFC 6976            Loop-Free Convergence Using oFIB           July 2013


   ACTION:

      Set state to OFIB_ABANDONED.

      Trigger AAH.

      Start Hold_down_timer.

7.5.  OFIB_ABANDONED

   OFIB_ABANDONED is the state of a router that has fallen back to fast
   convergence due to the reception of Link State Packets that cannot be
   dealt with together using oFIB.

   EVENT: Reception of a Link State Packet describing a link-state
   change event.

   ACTION: Trigger AAH, reset AAH_Hold_down_timer.

   EVENT: AAH_Hold_down_timer expires.

   ACTION: Set state to OFIB_STABLE.

8.  Management Considerations

   A system for recording the dynamics of the convergence process needs
   to be deployed in order to make a post hoc diagnosis of the
   reconvergence.  The sensitivity of applications to any packet
   reordering introduced by the delayed convergence process will need to
   be studied.  However, these needs apply to any loop-free convergence
   method and are not specific to the ordered FIB method described in
   this document.

9.  Security Considerations

   This document requires only minor modifications to existing routing
   protocols and therefore does not add significant additional security
   risks.  However, a full security analysis would need to be provided
   within the protocol-specific specifications proposed for deployment.

   Security considerations related to timer values set by routers are
   noted in Appendix B.4.

10.  Acknowledgments

   We would like to thank Jean-Philippe Vasseur and Les Ginsberg for
   their useful suggestions and comments.




Shand, et al.                 Informational                    [Page 18]


RFC 6976            Loop-Free Convergence Using oFIB           July 2013


11.  Informative References

   [IPFRR-TUNNELS]
              Bryant, S., Filsfils, C., Previdi, S., and M. Shand, "IP
              Fast Reroute using tunnels", Work in Progress, November
              2007.

   [ISO10589] International Organization for Standardization,
              "Intermediate system to Intermediate system intra-domain
              routing information exchange protocol for use in
              conjunction with the protocol for providing the
              connectionless-mode Network Service (ISO 8473)", ISO/IEC
              10589:2002, Second Edition, November 2002.

   [LF-TIMERS]
              Atlas, A., Bryant, S., and M. Shand, "Synchronisation of
              Loop Free Timer Values", Work in Progress, February 2008.

   [RFC2328]  Moy, J., "OSPF Version 2", STD 54, RFC 2328, April 1998.

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

   [RFC5714]  Shand, M. and S. Bryant, "IP Fast Reroute Framework", RFC
              5714, January 2010.

   [RFC5715]  Shand, M. and S. Bryant, "A Framework for Loop-Free
              Convergence", RFC 5715, January 2010.

   [refs.PFOB07]
              Francois, P. and O. Bonaventure, "Avoiding transient loops
              during the convergence of link-state routing protocols",
              IEEE/ACM Transactions on Networking, Vol. 15, No. 6, pp.
              1280-1292, December 2007,
              <http://dx.doi.org/10.1109/TNET.2007.902686>.















Shand, et al.                 Informational                    [Page 19]


RFC 6976            Loop-Free Convergence Using oFIB           July 2013


Appendix A.  Candidate Methods of Safely Abandoning Loop-Free
             Convergence (AAH)

   IP Fast Reroute [RFC5714] and loop-free convergence techniques
   [RFC5715] can deal with single topology change events, multiple
   correlated change events, and in some cases even certain uncorrelated
   events.  However, in all cases, there are events that cannot be dealt
   with, and the mechanism needs to quickly revert to normal
   convergence.  This is known as "Abandoning All Hope" (AAH).

   This appendix describes the outcome of a design study into the AAH
   problem and is included here to trigger discussion on the trade-offs
   between complexity and robustness in the AAH solution space.

A.1.  Possible Solutions

   Two approaches to this problem have been proposed:

   1.  Hold-down timer only.

   2.  Synchronization of AAH state using AAH messages.

   They are described below.

A.2.  Hold-Down Timer Only

   The "hold-down timer only" AAH method uses a hold-down to acquire a
   set of LSPs that should be processed together.  On expiry of the
   local hold-down timer, the router begins processing the batch of LSPs
   according to the loop-free prevention algorithm.

   There are a number of problems with this simple approach.  In some
   cases, the timer value will be too short to ensure that all the
   related events have arrived at all routers (perhaps because there was
   some unexpected propagation delay, or one or more of the events are
   slow in being detected).  In other cases, a completely unrelated
   event may occur after the timer has expired but before the processing
   is complete.  In addition, since the timer is started at each router
   on reception of the first LSP announcing a topology change, the
   actual starting time is dependent upon the propagation time of the
   first LSP.  So, for a subsequent event occurring around the time of
   the timer expiry, because of variations in propagation delay, it may
   reach some routers before the timer expires and others after it has
   expired.  In the former case, this LSP will be included in the set of
   changes to be considered; while in the latter, it will be excluded
   leading to serious routing inconsistency.  In such cases, continuing
   to operate the loop-free convergence protocol may exacerbate the
   situation.



Shand, et al.                 Informational                    [Page 20]


RFC 6976            Loop-Free Convergence Using oFIB           July 2013


   The simple approach to this would be to revert to normal convergence
   (AAH) whenever an LSP is received after the timer has expired.
   However, this also has problems for the reasons above and therefore
   AAH must be a synchronous operation, i.e., it is necessary to arrange
   that an AAH invoked anywhere in the network causes ALL routers to
   invoke AAH.

   It is also necessary to consider the means of exiting the AAH state.
   Again, the simplest method is to use a timer.  However, while in AAH
   state, any topology changes that are previously received or
   subsequently received should be processed immediately using the
   traditional convergence algorithms, i.e., without invoking controlled
   convergence.  If the exit from the AAH state is not correctly
   synchronized, a new event may be processed by some routers
   immediately (as AAH), while those that have already left AAH state
   will treat it as the first of a new batch of changes and attempt
   controlled convergence.  Thus, both entry and exit from the AAH state
   need to be synchronized.  A method of achieving this is described in
   Appendix A.3.

A.3.  AAH Messages

   Like the simple timer AAH method, the "AAH messages" method uses a
   hold-down to acquire a set of LSPs that should be processed together.
   On expiry of the local hold-down timer, the router begins processing
   the batch of LSPs according to the loop-free prevention algorithm.
   This is the same behavior as the hold-down timer only method.
   However, if any router, having started the loop-free convergence
   process receives an LSP that would trigger a topology change, it
   locally abandons the controlled convergence process and sends an AAH
   message to all its neighbors.  This eventually triggers all routers
   to abandon the controlled convergence.  The routers remain in AAH
   state (i.e., processing topology changes using normal "fast"
   convergence), until a period of quiescence has elapsed.  The exit
   from AAH state is synchronized by using a two-step process.  To
   achieve the required synchronization, two additional messages are
   required, AAH and AAH ACK.  The AAH message is reliably exchanged
   between neighbors using the AAH ACK message.  These could be
   implemented as a new message within the routing protocol or carried
   in existing routing hello messages.  Two types of state machines are
   needed -- a per-router AAH state machine and a per-neighbor AAH state
   machine (PNSM).  These are described below.









Shand, et al.                 Informational                    [Page 21]


RFC 6976            Loop-Free Convergence Using oFIB           July 2013


A.3.1.  Per-Router State Machine

   +-------------+----------+---------+--------+------------+----------+
   | EVENT       |    Q     |   Hold  |   CC   |     AAH    | AAH-hold |
   +=============+==========+=========+========+============+==========+
   | RX LSP      |  Start   |    -    | TX-AAH |  Restart   |  TX-AAH  |
   | triggering  |hold-down |         | Start  | AAH timer. |   Start  |
   | change      |  timer.  |         |  AAH   |   [AAH]    |    AAH   |
   |             |  [Hold]  |         | timer. |            |   timer. |
   |             |          |         | [AAH]  |            |   [AAH]  |
   +-------------+----------+---------+--------+------------+----------+
   | RX AAH      |  TX-AAH  |  TX-AAH | TX-AAH |    [AAH]   |  TX-AAH  |
   |(Neighbor's  |Start AAH |  Start  | Start  |            |   Start  |
   |  PNSM       |  timer.  |   AAH   |  AAH   |            |    AAH   |
   |  processes  |  [AAH]   |  timer. | timer. |            |   timer. |
   |  RX AAH.)   |          |  [AAH]  | [AAH]  |            |   [AAH]  |
   +-------------+----------+---------+--------+------------+----------+
   | Timer       |    -     | Trigger |    -   |    Start   |    [Q]   |
   | expiry      |          |   CC.   |        |  AAH-hold  |          |
   |             |          |  [CC]   |        |   timer.   |          |
   |             |          |         |        | [AAH-hold] |          |
   +-------------+----------+---------+--------+------------+----------+
   | Controlled  |    -     |    -    |   [Q]  |      -     |     -    |
   | convergence |          |         |        |            |          |
   | completed   |          |         |        |            |          |
   +-------------+----------+---------+--------+------------+----------+

    RX = Reception
    TX = Transmission
    TX-AAH = Send "go to TX-AAH" to all other PNSMs.

                          Per-Router State Table

   Operation of the per-router state machine is as follows:

   Operation of this state machine under normal topology change involves
   only states: Quiescent (Q), Hold-down (Hold) and Controlled
   Convergence (CC).  The remaining states are associated with an AAH
   event.

   The resting state is Quiescent.  When the router in the Quiescent
   state receives an LSP indicating a topology change, which would
   normally trigger an SPF, it starts the hold-down timer and changes
   state to Hold-down.  It normally remains in this state, collecting
   additional LSPs until the hold-down timer expires.  Note that all
   routers must use a common value for the hold-down timer.  When the
   hold-down timer expires, the router then enters Controlled




Shand, et al.                 Informational                    [Page 22]


RFC 6976            Loop-Free Convergence Using oFIB           July 2013


   Convergence (CC) state and executes the CC mechanism to reconverge
   the topology.  When the CC process has completed on the router, the
   router re-enters the Quiescent state.

   If this router receives a topology-changing LSP whilst it is in the
   CC state, it enters AAH state and sends a "go to TX-AAH" command to
   all per-neighbor state machines; this causes each per-neighbor state
   machine to signal this state change to its neighbor.  Alternatively,
   if this router receives an AAH message from any of its neighbors
   whilst in any state except AAH, it starts the AAH timer and enters
   the AAH state.  The per-neighbor state machine corresponding to the
   neighbor from which the AAH was received executes the RX AAH action
   (which causes it to send an AAH ACK), while the remainder of
   neighbors are sent the "go to TX-AAH" command.  The result is that
   the AAH is acknowledged to the neighbor from which it was received
   and propagated to all other neighbors.  On entering AAH state, all CC
   timers are expired, and normal convergence takes place.

   Whilst in the AAH state, LSPs are processed in the traditional
   manner.  Each time an LSP is received, the AAH timer is restarted.
   In an unstable network, ALL routers will remain in this state for
   some time, and the network will behave in the traditional
   uncontrolled convergence manner.

   When the AAH timer expires, the router enters AAH-hold state and
   starts the AAH-hold timer.  The purpose of the AAH-hold state is to
   synchronize the transition of the network from AAH to Quiescent.  The
   additional state ensures that the network cannot contain a mixture of
   routers in both AAH and Quiescent states.  If, whilst in AAH-hold
   state the router receives a topology changing LSP, it re-enters AAH
   state and commands all per-neighbor state machines to "go to TX-AAH".
   If, whilst in AAH-hold state, the router receives an AAH message from
   one of its neighbors, it re-enters the AAH state and commands all
   other per-neighbor state machines to "go to TX-AAH".  Note that the
   per-neighbor state machine receiving the AAH message will
   autonomously acknowledge receipt of the AAH message.  Commanding the
   per-neighbor state machine to "go to TX-AAH" is necessary, because
   routers may be in a mixture of Quiescent, Hold-down, and AAH-hold
   states, and it is necessary to rendezvous the entire network back to
   AAH state.

   When the AAH-hold timer expires, the router changes to Quiescent and
   is ready for loop-free convergence.








Shand, et al.                 Informational                    [Page 23]


RFC 6976            Loop-Free Convergence Using oFIB           July 2013


A.3.2.  Per-Neighbor State Machine

   +----------------------------+--------------+-----------------------+
   | EVENT                      | IDLE         | TX-AAH                |
   +============================+==============+=======================+
   | RX AAH                     | Send ACK.    | Send ACK.             |
   |                            | [IDLE]       | Cancel timer.         |
   |                            |              | [IDLE]                |
   +----------------------------+--------------+-----------------------+
   | RX ACK                     | ignore       | Cancel timer.         |
   |                            |              | [IDLE]                |
   +----------------------------+--------------+-----------------------+
   | RX "go to TX-AAH" from     | Send AAH     | ignore                |
   | Router State Machine       | [TX-AAH]     |                       |
   +----------------------------+--------------+-----------------------+
   | Timer expires              | impossible   | Send AAH              |
   |                            |              | Restart timer.        |
   |                            |              | [TX-AAH]              |
   +----------------------------+--------------+-----------------------+

                         Per-Neighbor State Table

   There is one instance of the per-neighbor state machine (PNSM) for
   each neighbor within the convergence control domain.

   The normal state is IDLE.

   On command ("go to TX-AAH") from the router state machine, the state
   machine enters TX-AAH state, transmits an AAH message to its
   neighbor, and starts a timer.

   On receipt of an AAH ACK in state TX-AAH, the state machine cancels
   the timer and enters IDLE state.

   In state IDLE, any AAH ACK message received is ignored.

   On expiry of the timer in state TX-AAH, the state machine transmits
   an AAH message to the neighbor and restarts the timer.  (The timer
   cannot expire in any other state.)

   In any state, receipt of an AAH causes the state machine to transmit
   an AAH ACK and enter the IDLE state.

   Note that for correct operation the state machine must remain in
   state TX-AAH until an AAH ACK or an AAH is received or until the
   state machine is deleted.  Deletion of the per-neighbor state machine
   occurs when routing determines that the neighbor has gone away or
   when the interface goes away.



Shand, et al.                 Informational                    [Page 24]


RFC 6976            Loop-Free Convergence Using oFIB           July 2013


   When routing detects a new neighbor, it creates a new instance of the
   per-neighbor state machine in state IDLE.  The consequent generation
   of the router's own LSP will then cause the router state machine to
   execute the LSP receipt actions that, if necessary, will result in
   the new per-neighbor state machine receiving a "go to TX-AAH" command
   and transitioning to TX-AAH state.

Appendix B.  Synchronization of Loop-Free Timer Values

   This appendix provides the reader with access to the design
   considerations originally described in [LF-TIMERS].

B.1.  Introduction

   Most of the loop-free convergence mechanisms [RFC5715] require one or
   more convergence delay timers that must have a duration that is
   consistent throughout the routing domain.  This time is the worst-
   case time that any router will take to calculate the new topology and
   to make the necessary changes to the FIB.  The timer is used by the
   routers to know when it is safe to transition between the loop-free
   convergence states.  The time taken by a router to complete each
   phase of the loop-free transition will be dependent on the size of
   the network and the design and implementation of the router.
   Therefore, it can be expected that the optimum delay will need to be
   tuned from time to time as the network evolves.  Manual configuration
   of the timer is fraught for two reasons.  Firstly, it is always
   difficult to ensure that the correct value is installed in all of the
   routers.  Secondly, if any change is introduced into the network that
   results in a need to change the timer (for example, due to a change
   in hardware or software version), then all of the routers need to be
   reconfigured to use the new timer value.  Therefore, it is desirable
   that a means be provided by which the convergence delay timer can be
   automatically synchronized throughout the network.

B.2.  Required Properties

   The timer synchronization mechanism must have the following
   properties:

   o  The convergence delay time must be consistent amongst all routers
      that are converging on the new topology.

   o  The convergence delay time must be the highest delay required by
      any router in the new topology.

   o  The mechanism must increase the delay when a new router that
      requires a higher delay than is currently in use is introduced to
      the network.



Shand, et al.                 Informational                    [Page 25]


RFC 6976            Loop-Free Convergence Using oFIB           July 2013


   o  When the router that had the longest delay requirements is removed
      from the topology, the convergence delay timer value must, within
      some reasonable time, be reduced to the longest delay required by
      the remaining routers.

   o  It must be possible for a router to change the convergence delay
      timer value that it requires.

   o  A router that is in multiple routing areas or is running multiple
      routing protocols may signal a different loop-free convergence
      delay for each area and for each protocol.

   How a router determines the time that it needs to execute each
   convergence phase is an implementation issue and outside the scope of
   this specification.  However, a router that dynamically determines
   its proposed timer value must do so in such a way that it does not
   cause the synchronized value to continually fluctuate.

B.3.  Mechanism

   The following mechanism is proposed.

   A new information element is introduced into the routing protocol
   that specifies the maximum time (in milliseconds) that the router
   will take to calculate the new topology and to update its FIB as a
   result of any topology change.

   When a topology change occurs, the longest convergence delay time
   required by any router in the new topology is used by the loop-free
   convergence mechanism.

   If a routing protocol message is issued that changes the convergence
   delay timer value but does not change the topology, the new timer
   value must be taken into consideration during the next loop-free
   transition but must not instigate a loop-free transition.

   If a routing protocol message is issued that changes the convergence
   timer value and changes the topology, a loop-free transition is
   instigated, and the new timer value is taken into consideration.

   The loop-free convergence mechanism should specify the action to be
   taken if a timer change (only) message and a topology change message
   are independently generated during the hold-off time.  A suitable
   action would be to take the same action that would be taken if two
   uncorrelated topology changes occurred in the network.






Shand, et al.                 Informational                    [Page 26]


RFC 6976            Loop-Free Convergence Using oFIB           July 2013


   All routers that support loop-free convergence must advertise a loop-
   free convergence delay time.  The loop-free convergence mechanism
   must specify the action to be taken if a router does not advertise a
   convergence delay time.

B.4.  Security Considerations Related to Router Timer Values

   If an abnormally large timer value is proposed by a router, then
   there is a danger that the loop-free convergence process will take an
   excessive amount of time.  If during that time the routing protocol
   signals the need for another transition, the loop-free transition
   will be abandoned and the default best-case (traditional) convergence
   mechanism used.

   It is still undesirable that the routers select a convergence delay
   time that has an excessive value.  The maximum value that can be
   specified in the LSP or Link State Advertisement (LSA) is limited
   (through the use of a 16-bit field) to about 65 seconds.  When
   sufficient implementation experience is gained, an architectural
   constant will be specified as the upper limit of the convergence
   delay timer.

Authors' Addresses

   Mike Shand
   Individual Contributor

   EMail: imc.shand@googlemail.com


   Stewart Bryant
   Cisco Systems
   10 New Square, Bedfont Lakes
   Feltham, Middlesex  TW18 8HA
   United Kingdom

   EMail: stbryant@cisco.com


   Stefano Previdi
   Cisco Systems
   Via Del Serafico 200
   00142 Roma
   Italy

   EMail: sprevidi@cisco.com





Shand, et al.                 Informational                    [Page 27]


RFC 6976            Loop-Free Convergence Using oFIB           July 2013


   Clarence Filsfils
   Cisco Systems
   Brussels
   Belgium

   EMail: cfilsfil@cisco.com


   Pierre Francois
   Institute IMDEA Networks
   Avda. del Mar Mediterraneo, 22
   Leganese  28918
   Spain

   EMail: pierre.francois@imdea.org


   Olivier Bonaventure
   Universite catholique de Louvain
   Place Ste Barbe, 2
   Louvain-la-Neuve  1348
   Belgium

   EMail: Olivier.Bonaventure@uclouvain.be
   URI:   http://inl.info.ucl.ac.be/


























Shand, et al.                 Informational                    [Page 28]