ROLL                                                         K. Iwanicki
Internet-Draft                                      University of Warsaw
Intended status: Standards Track                            1 March 2022
Expires: 2 September 2022


            RNFD: Fast border router crash detection in RPL
                        draft-ietf-roll-rnfd-00

Abstract

   By and large, a correct operation of a RPL network requires border
   routers to be up.  In many applications, it is beneficial for the
   nodes to detect a crash of a border router as soon as possible to
   trigger fallback actions.  This document describes RNFD, an extension
   to RPL that expedites border router failure detection, even by an
   order of magnitude, by having nodes collaboratively monitor the
   status of a given border router.  The extension introduces an
   additional state at each node, a new type of RPL Control Message
   Options for synchronizing this state among different nodes, and the
   coordination algorithm itself.

Status of This Memo

   This Internet-Draft is submitted in full conformance with the
   provisions of BCP 78 and BCP 79.

   Internet-Drafts are working documents of the Internet Engineering
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   This Internet-Draft will expire on 2 September 2022.

Copyright Notice

   Copyright (c) 2022 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 (https://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



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   and restrictions with respect to this document.  Code Components
   extracted from this document must include Revised BSD License text as
   described in Section 4.e of the Trust Legal Provisions and are
   provided without warranty as described in the Revised BSD License.

Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
     1.1.  Effects of LBR Crashes  . . . . . . . . . . . . . . . . .   3
     1.2.  Design Principles . . . . . . . . . . . . . . . . . . . .   4
   2.  Terminology . . . . . . . . . . . . . . . . . . . . . . . . .   5
   3.  Overview  . . . . . . . . . . . . . . . . . . . . . . . . . .   6
     3.1.  Protocol State Machine  . . . . . . . . . . . . . . . . .   7
     3.2.  Counters and Communication  . . . . . . . . . . . . . . .   8
   4.  The RNFD Option . . . . . . . . . . . . . . . . . . . . . . .   9
     4.1.  General CFRC Requirements . . . . . . . . . . . . . . . .   9
     4.2.  Format of the Option  . . . . . . . . . . . . . . . . . .  10
   5.  RPL Router Behavior . . . . . . . . . . . . . . . . . . . . .  12
     5.1.  Joining a DODAG Version and Changing the RNFD Role  . . .  12
     5.2.  Detecting and Verifying Problems with the DODAG Root  . .  13
     5.3.  Disseminating Observations and Reaching Agreement . . . .  15
     5.4.  DODAG Root's Behavior . . . . . . . . . . . . . . . . . .  16
     5.5.  Activating and Deactivating the Protocol on Demand  . . .  17
     5.6.  Processing CFRCs of Incompatible Lengths  . . . . . . . .  17
     5.7.  Summary of RNFD's Interactions with RPL . . . . . . . . .  18
     5.8.  Summary of RNFD's Constants . . . . . . . . . . . . . . .  19
   6.  Manageability Considerations  . . . . . . . . . . . . . . . .  19
     6.1.  Role Assignment and CFRC Size Adjustment  . . . . . . . .  20
     6.2.  Virtual DODAG Roots . . . . . . . . . . . . . . . . . . .  20
   7.  Security Considerations . . . . . . . . . . . . . . . . . . .  21
   8.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  22
   9.  Acknowledgements  . . . . . . . . . . . . . . . . . . . . . .  22
   10. References  . . . . . . . . . . . . . . . . . . . . . . . . .  22
     10.1.  Normative References . . . . . . . . . . . . . . . . . .  22
     10.2.  Informative References . . . . . . . . . . . . . . . . .  23
   Author's Address  . . . . . . . . . . . . . . . . . . . . . . . .  24

1.  Introduction

   RPL is an IPv6 routing protocol for low-power and lossy networks
   (LLNs) [RFC6550].  Such networks are usually constrained in device
   energy and channel capacity.  They are formed largely of nodes that
   offer little processing power and memory, and links that are of
   variable qualities and support low data rates.  Therefore, the main
   challenge that a routing protocol for LLNs has to address is
   minimizing resource consumption without sacrificing reaction time to
   network changes.




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   One of the main design principles adopted in RPL to minimize node
   resource consumption is delegating much of the responsibility for
   routing to LLN border routers (LBRs).  A network is organized into
   destination-oriented directed acyclic graphs (DODAGs), each
   corresponding to an LBR and having all its paths terminate at the
   LBR.  To this end, every node is dynamically assigned a rank
   representing its distance, measured in some metric, to a given LBR,
   with the LBR having the minimal rank, which reflects its role as the
   DODAG root.  The ranks allow each non-LBR node to select from among
   its neighbors (i.e., nodes to which the node has links) those ones
   that are closer to the LBR than the node itself: the node's parents
   in the graph.  The resulting DODAG paths, consisting of the node-
   parent links, are utilized for routing packets upward: to the LBR and
   outside the LLN.  They are also used by nodes to periodically report
   their connectivity upward to the LBR, which allows in turn for
   directing packets downward, from the LBR to these nodes, for
   instance, by means of source routing [RFC6554].  All in all, not only
   do LBRs participate in routing but also drive the process of DODAG
   construction and maintenance underlying the protocol.

   To play this central role, LBRs are expected to be more capable than
   regular LLN nodes.  They are assumed not to be constrained in
   computing power, memory, and energy, which often entails a more
   involved hardware-software architecture and tethered power supply.
   This, however, also makes them more prone to failures, especially
   since in large deployments it is often difficult to ensure a backup
   power supply for every LBR.

1.1.  Effects of LBR Crashes

   When an LBR crashes, the nodes in its DODAG lose the ability to
   communicate with other Internet hosts.  In addition, a significant
   fraction of DODAG paths interconnecting the nodes become invalid, as
   they pass through the LBR.  The others also degenerate as a result of
   DODAG repair attempts, which are bound to fail.  In effect, routing
   inside the DODAG also becomes largely impossible.  Consequently, it
   is desirable that an LBR crash be detected by the nodes fast, so that
   they can leave the broken DODAG and join another one or trigger
   additional application- or deployment-dependent fallback mechanisms,
   thereby minimizing the negative impact of the disconnection.











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   Since all DODAG paths lead to the corresponding LBR, detecting its
   crash by a node entails dropping all parents and adopting an infinite
   rank, which reflects the node's inability to reach the LBR.
   Depending on the deployment settings, the node can then remain in
   such a state, join a different DODAG, or even become itself the root
   of a floating DODAG.  In any case, however, achieving this state for
   all nodes is slow, can generate heavy traffic, and is difficult to
   implement correctly [Iwanicki16] [Paszkowska19] [Ciolkosz19].

   To start with, tearing down all DODAG paths requires each of the
   LBR's neighbors to detect that its link with the LBR is no longer up.
   Otherwise, any of the neighbors unaware of this fact can keep
   advertising a finite rank and can thus be other nodes' parent or
   ancestor in the DODAG: such nodes will incorrectly believe they have
   a valid path to the LBR.  Detecting a crash of a link by a node
   normally happens when the node has observed sufficiently many
   forwarding failures over the link.  Therefore, considering the low-
   data-rate applications of LLNs, the period from the crash to the
   moment of eliminating from the DODAG the last link to the LBR may be
   long.  Subsequently learning by all nodes that none of their links
   can form any path leading to the LBR also adds latency, partly due to
   parent changes that the nodes independently perform in attempts to
   repair their broken paths locally.  Since a non-LBR node has only
   local knowledge of the network, potentially inconsistent with that of
   other nodes, such parent changes often produce paths containing
   loops, which have to be broken before all nodes can conclude that no
   path to the LBR exists globally.  Even with RPL's dedicated loop
   detection mechanisms [RFC6553], this also requires traffic, and hence
   time.  Finally, switching a parent or discovering a loop can also
   generate cascaded bursts of control traffic, owing to the adaptive
   Trickle algorithm for exchanging DODAG information [RFC6202].
   Overall, the behavior of the network when handling an LBR crash is
   highly suboptimal, thereby not being in line with RPL's goal of
   minimizing resource consumption and reaction latencies.

1.2.  Design Principles

   To address this issue, this document proposes an extension to RPL,
   dubbed Root Node Failure Detector (RNFD).  To minimize the time and
   traffic required to handle an LBR crash, the RNFD algorithm adopts
   the following design principles, derived directly from the previous
   observations:

   1.  Explicitly coordinating LBR monitoring between nodes instead of
       relying only on the emergent behavior resulting from their
       independent operation.





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   2.  Avoiding probing all links to the dead LBR so as to reduce the
       tail latency when eliminating these links from the DODAG.

   3.  Exploiting concurrency by prompting proactive checking for a
       possible LBR crash when some nodes suspect such a failure may
       have taken place, which aims to further reduce the critical path.

   4.  Minimizing changes to RPL's existing algorithms by operating in
       parallel and largely independently (in the background), and
       introducing few additional assumptions.

   While these principles do improve RPL's performance under a wide
   range of LBR crashes, their probabilistic nature precludes hard
   guarantees for all possible corner cases.  In particular, in some
   scenarios, RNFD's operation may result in false negatives, but these
   situations are peculiar and will eventually be handled by RPL's own
   aforementioned mechanisms.  Likewise, in some scenarios, notably
   involving highly unstable links, false positives may occur, but they
   can be alleviated as well.  In any case, the principles also
   guarantee that RNFD can be deactivated at any time, if needed, in
   which case RPL's operation is unaffected.

2.  Terminology

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and
   "OPTIONAL" in this document are to be interpreted as described in BCP
   14 [RFC2119] [RFC8174] when, and only when, they appear in all
   capitals, as shown here.

   The Terminology used in this document is consistent with and
   incorporates that described in "Terms Used in Routing for Low-Power
   and Lossy Networks (LLNs)" [RFC7102], "RPL: IPv6 Routing Protocol for
   Low-Power and Lossy Networks" [RFC6550], and "The Routing Protocol
   for Low-Power and Lossy Networks (RPL) Option for Carrying RPL
   Information in Data-Plane Datagrams" [RFC6553].  Other terms in use
   in LLNs can be found in "Terminology for Constrained-Node Networks"
   [RFC7228].

   In particular, the following acronyms appear in the document:

   DIO  DODAG Information Object (a RPL message)

   DIS  DODAG Information Solicitation (a RPL message)

   DODAG  Destination-Oriented Directed Acyclic Graph

   LLN  Low-power and Lossy Network



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   LBR  LLN Border Router

   In addition, the document introduces the following concepts:

   Sentinel  One of the two roles that a node can play in RNFD.  For a
      given DODAG Version, a Sentinel node is the DODAG root's neighbor
      that monitors the DODAG root's status.  There are normally
      multiple Sentinels for a DODAG root.  However, being the DODAG
      root's neighbor need not imply being Sentinel.

   Acceptor  The other of the two roles that a node can play in RNFD.
      For a given DODAG Version, an Acceptor node is a node that is not
      Sentinel.

   Locally Observed DODAG Root's State (LORS)  A node's local knowledge
      of the DODAG root's status, specifying in particular whether the
      DODAG root is up.

   Conflict-Free Replicated Counter (CFRC)  Conceptually represents a
      dynamic set whose cardinality can be estimated.  It defines a
      partial order on its values and supports element addition and
      union.  The union operation is order- and duplicate-insensitive,
      that is, idempotent, commutative, and associative.

3.  Overview

   As mentioned previously, LBRs are DODAG roots in RPL, and hence a
   crash of an LBR is global in that it affects all nodes in the
   corresponding DODAG.  Therefore, each node running RNFD for a given
   DODAG explicitly tracks the DODAG root's current condition, which is
   referred to as Locally Observed DODAG Root's State (LORS), and
   synchronizes its local knowledge with other nodes.

   Since monitoring the condition of the DODAG root is performed by
   tracking the status of its links (i.e., whether they are up or down),
   it must be done by the root's neighbors; other nodes must accept
   their observations.  Consequently, depending on their roles, non-root
   nodes are divided in RNFD into two disjoint groups: Sentinels and
   Acceptors.  A Sentinel node is the DODAG root's neighbor that
   monitors its link with the root.  The DODAG root thus normally has
   multiple Sentinels but being its neighbor need not imply being
   Sentinel.  An Acceptor node is in turn a node that is not Sentinel.
   Acceptors thus mainly collect and propagate Sentinels' observations.
   More information on Sentinel selection can be found in Section 6.1.







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3.1.  Protocol State Machine

   The possible values of LORS and transitions between them are depicted
   in Figure 1.  States "UP" and "GLOBALLY DOWN" can be attained by both
   Sentinels and Acceptors; states "SUSPECTED DOWN" and "LOCALLY DOWN"--
   by Sentinels only.

     +---------------------------------------------------------+
     |                      |---------------------------+   3a |
     |    +-----------------+---------+              3b |      |
     |    | 2b              |         v                 v      v
   +-+----+-+   1 +---------+-+     +-----------+     +-+------+-+
   |   UP   +---->+ SUSPECTED +---->+  LOCALLY  +---->+ GLOBALLY |
   |        +<----+    DOWN   | 2a  |    DOWN   | 3c  |   DOWN   |
   +-+----+-+  4a +-----------+     +-+---------+     +-+--------+
     ^    ^                           |                 |
     |    |                        4b |                 |
     |    +---------------------------+               5 |
     +--------------------------------------------------+

                   Figure 1: RNFD States and Transitions

   To begin with, when any node joins a DODAG Version, the DODAG root
   must appear alive, so the node initializes RNFD with its LORS equal
   to "UP".  For a properly working DODAG root, the node remains in
   state "UP".

   However, when a node--acting as Sentinel--starts suspecting that the
   root may have crashed, it changes its LORS to "SUSPECTED DOWN"
   (transition 1 in Figure 1).  The transition from "UP" to "SUSPECTED
   DOWN" can happen based on the node's observations at either the data
   plane, for instance, link-layer triggers about missing hop-by-hop
   acknowledgments for packets forwarded over the node's link to the
   root, or the control plane, for example, a significant growth in the
   number of Sentinels already suspecting the root to be dead.  In state
   "SUSPECTED DOWN", the Sentinel node may verify its suspicion and/or
   inform other nodes about the suspicion.  When this has been done, it
   changes its LORS to "LOCALLY DOWN" (transition 2a).  In some cases,
   the verification need not be performed and, as an optimization, a
   direct transition from "UP" to "LOCALLY DOWN" (transition 2b) can be
   done instead.

   If sufficiently many Sentinels have their LORS equal to "LOCALLY
   DOWN", all nodes--Sentinels and Acceptors--consent globally that the
   DODAG root must have crashed and set their LORS to "GLOBALLY DOWN",
   irrespective of the previous value (transitions 3a, 3b, and 3c).
   State "GLOBALLY DOWN" is terminal in that the only transition any
   node can perform from this to another state (transition 5) takes



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   place when the node joins a new DODAG version.  When a node is in
   state "GLOBALLY DOWN", RNFD forces RPL to maintain an infinite rank
   and no parent, thereby preventing routing packets upward in the
   DODAG.  In other words, this state represents a situation in which
   all non-root nodes agree that the current DODAG version is unusable,
   and hence, to recover, the root has to give a proof of being alive by
   initiating a new DODAG Version.

   In contrast, if a node--either Sentinel or Acceptor--is in state
   "UP", RNFD does not influence RPL's packet forwarding: a node can
   route packets upward if it has a parent.  The same is true for a
   Sentinel node in states "SUSPECTED DOWN" and "LOCALLY DOWN".
   Finally, while in any of the two states, a Sentinel node may observe
   some activity of the DODAG root, and hence decide that its suspicion
   is a mistake.  In such a case, it returns to state "UP" (transitions
   4a and 4b).

3.2.  Counters and Communication

   To enable arriving at a global conclusion that the DODAG root has
   crashed (i.e., transiting to state "GLOBALLY DOWN"), all nodes count
   locally and synchronize among each other the number of Sentinels
   considering the root to be dead (i.e., those in state "LOCALLY
   DOWN").  This process employs structures referred to as conflict-free
   replicated counters (CFRCs).  They are stored and modified
   independently by each node and are disseminated throughout the
   network in options added to RPL link-local control messages: DODAG
   Information Objects (DIOs) and DODAG Information Solicitations
   (DISs).  Upon reception of such an option from its neighbor, a node
   merges the received counter with its local one, thereby obtaining a
   new content for its local counter.

   The merging operation is idempotent, commutative, and associative.
   Moreover, all possible counter values are partially ordered.  This
   enables ensuring eventual consistency of the counters acros all
   nodes, irrespective of the particular sequence of merges, shape of
   the DODAG, or general network topology.

   Each node in RNFD maintains two CFRCs for a DODAG:

   *  PositiveCFRC, counting Sentinels that have considered or still
      consider the root node as alive in the current DODAG Version,

   *  NegativeCFRC, counting Sentinels that have considered or still
      consider the root node as dead in the current DODAG Version.






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   PositiveCFRC is always greater than or equal to the NegativeCFRC in
   terms of the partial order defined for the counters.  The difference
   between the value of PositiveCFRC and the value of NegativeCFRC is
   thus nonnegative and estimates the number of Sentinels that still
   consider the DODAG root node as alive.

4.  The RNFD Option

   RNFD state synchronization between nodes takes place through the RNFD
   Option.  It is a new type of RPL Control Message Options that is
   carried in link-local RPL control messages, notably DIOs and DISs.
   Its main task is allowing the receivers to merge their two CFRCs with
   the sender's CFRCs.

4.1.  General CFRC Requirements

   CFRCs in RNFD MUST support the following operations:

   value(c)  Returns a non-negative integer value corresponding to the
      number of nodes counted by a given CFRC, c.

   zero()  Returns a CFRC that counts no nodes, that is, has its value
      equal to 0.

   self()  Returns a CFRC that counts only the node executing the
      operation.

   infinity()  Returns a CFRC that counts all possible nodes and
      represents a special value, infinity.

   merge(c1, c2)  Returns a CFRC that is a union of c1 and c2 (i.e.,
      counts all nodes that are counted by either c1, c2, or both c1 and
      c2).

   compare(c1, c2)  Returns the result of comparing c1 to c2.

   saturated(c)  Returns TRUE if a given CFRC, c, is saturated (i.e., no
      more new nodes should be counted by it), or FALSE otherwise.

   The partial ordering of CFRCs implies that the result of compare(c1,
   c2) can be either:

   *  smaller, if c1 is ordered before c2 (i.e., c2 counts all nodes
      that c1 counts and at least one node that c1 does not count);

   *  greater, if c1 is ordered after c2 (i.e., c1 counts all nodes that
      c2 counts and at least one node that c2 does not count);




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   *  equal, if c1 and c2 are the same (i.e., they count the same
      nodes);

   *  incomparable, otherwise.

   In particular, zero() is smaller than all other values and infinity()
   is greater than any other value.

   The properties of merging in turn can be formalized as follows for
   any c1, c2, and c3:

   *  idempotence: c1 = merge(c1, c1);

   *  commutativity: merge(c1, c2) = merge(c2, c1);

   *  associativity: merge(c1, merge(c2, c3)) = merge(merge(c1, c2),
      c3).

   In particular, merge(c, zero()) always equals c while merge(c,
   infinity()) always equals infinity().

   There are many algorithmic structures that can provide the
   aforementioned properties of CFRC.  Although in principle RNFD does
   not rely on any specific one, the option adopts so-called linear
   counting [Whang90].

4.2.  Format of the Option

   The format of the RNFD Option conforms to the generic format of RPL
   Control Message Options:

      0                   1                   2                   3
      0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |   Type = TBD1 | Option Length |                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+                               +
     |                                                               |
     +                                                               +
     |               PosCFRC, NegCFRC (Variable Length*)             |
     .                                                               .
     .                                                               .
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

   The '*' denotes that the fields have equal lengths of at least one
   octet each. In effect, together they occupy at least two octets.

                    Figure 2: Format of the RNFD Option




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   Option Type  TBD1

   Option Length  8-bit unsigned integer.  Denotes the length of the
      option in octets excluding the Option Type and Option Length
      fields.  Its value MUST be even.  A value of 0 denotes that RNFD
      is disabled in the current DODAG Version.

   PosCFRC, NegCFRC  Two variable-length, octet-aligned bit arrays
      carrying the sender's PositiveCFRC and NegativeCFRC, respectively.

   The length of the arrays constituting the PosCFRC and NegCFRC fields
   is the same and is derived from Option Length as follows.  The value
   of Option Length is divided by 2 to obtain the number of octets each
   of the two arrays occupies.  The resulting number of octets is
   multiplied by 8 which yields an upper bound on the number of bits in
   each array.  As the actual bit length of each of the arrays, the
   largest prime number less than the upper bound is assumed.  For
   example, if the value of Option Length is 16, then each array
   occupies 8 octets, and its actual bit length is 61, as this is the
   largest prime number less than 64.

   Furthermore, for any bit equal to 1 in the NegCFRC, the bit with the
   same index MUST be equal to 1 also in the PosCFRC.  Any unused bits
   (i.e., the bits beyond the actual bit length of each of the arrays)
   MUST be equal to 0.  Finally, if PosCFRC has all its bits equal to 1,
   then NegCFRC MUST also have all its bits equal to 1.

   The CFRC operations are defined for such bit arrays of a given length
   as follows:

   value(c)  Returns the smallest integer value not less than -LT*ln(L0/
      LT), where ln() is the natural logarithm function, L0 is the
      number of bits equal to 0 in the array corresponding to c and LT
      is the bit length of the array.

   zero()  Returns an array with all bits equal to 0.

   self()  Returns an array with a single bit, selected uniformly at
      random, equal to 1.

   infinity()  Returns an array with all bits equal to 1.

   merge(c1, c2)  Returns a bit array that constitutes a bitwise OR of
      c1 and c2, that is, a bit in the resulting array is equal to 0
      only if the same bit is equal to 0 in both c1 and c2.

   compare(c1, c2)  Returns:




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   *  equal if each bit of c1 is equal to the corresponding bit of c2;

   *  less if c1 and c2 are not equal and, for each bit equal to 1 in
      c1, the corresponding bit in c2 is also equal to 1;

   *  greater if c1 and c2 are not equal and, for each bit equal to 1 in
      c2, the corresponding bit in c1 is also equal to 1;

   *  incomparable, otherwise.

   saturated(c)  Returns TRUE, if more than 63% of the bits in c are
      equal to 1, or FALSE, otherwise.

5.  RPL Router Behavior

   Although RNFD operates largely independently of RPL, it does need
   interact with RPL and the overall protocol stack.  These interactions
   are described next and can be realized, for instance, by means of
   event triggers.

5.1.  Joining a DODAG Version and Changing the RNFD Role

   Whenever RPL running at a node joins a DODAG Version, RNFD--if
   active--MUST assume for the node the role of Acceptor.  Accordingly,
   it MUST set its LORS to "UP" and its PositiveCFRC and NegativeCFRC to
   zero().

   The role MAY then change between Acceptor and Sentinel at any time.
   However, while a switch from Sentinel to Acceptor has no
   preconditions, for a switch from Acceptor to Sentinel to be possible,
   _all_ of the following conditions MUST hold:

   1.  LORS is "UP";

   2.  saturated(PositiveCFRC) is FALSE;

   3.  a neighbor entry for the DODAG root is present in RPL's DODAG
       parent set;

   4.  the neighbor is considered reachable via its link-local IPv6
       address.










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   A role change also REQUIRES appropriate updates to LORS and CFRCs, so
   that the node is properly accounted for.  More specifically, when
   changing its role from Acceptor to Sentinel, the node MUST add itself
   to its PositiveCFRC as follows.  It MUST generate a new CFRC value,
   selfc = self(), and MUST replace its PositiveCFRC, denoted oldpc,
   with newpc = merge(oldpc, selfc).  In contrast, the effects of a
   switch from Sentinel to Acceptor vary depending on the node's value
   of LORS before the switch:

   *  for "GLOBALLY DOWN", the node MUST NOT modify its LORS,
      PositiveCFRC, and NegativeCFRC;

   *  for "LOCALLY DOWN", the node MUST set its LORS to "UP" but MUST
      NOT modify its PositiveCFRC and NegativeCFRC;

   *  for "UP" and "SUSPECTED DOWN", the node MUST set its LORS to "UP",
      MUST NOT modify it PositiveCFRC, but MUST add itself to
      NegativeCFRC, that is, replace its NegativeCFRC, denoted oldnc,
      with newnc = merge(oldnc, selfc), where selfc is the counter
      generated with self() when the node last added itself to its
      PositiveCFRC.

5.2.  Detecting and Verifying Problems with the DODAG Root

   Only nodes that are Sentinels take active part in detecting crashes
   of the DODAG Root; Acceptors just disseminate their observations,
   reflected in the CFRCs.
























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   The DODAG root monitoring SHOULD be based on both internal inputs,
   notably the values of CFRCs and LORS, and external inputs, such as
   triggers from RPL and other protocols.  External input monitoring
   SHOULD be performed preferably in a reactive fashion, also
   independently of RPL, and at both data plane and control plane.  In
   particular, it is RECOMMENDED that RNFD be directly notified of
   events relevant to the routing adjacency maintenance mechanisms on
   which RPL relies, such as Layer 2 triggers [RFC5184] or the Neighbor
   Unreachability Detection [RFC4861] mechanism.  Only events concerning
   the DODAG root need be monitored to this end.  For example, RNFD can
   conclude that there may be problems with the DODAG root if it
   observes a lack of multiple consecutive L2 acknowledgments for
   packets transmitted by the node via the link to the DODAG root.
   Internally, in turn, it is RECOMMENDED that RNFD take action whenever
   there is a change to its local CFRCs, so that a node can have a
   chance to participate in detecting potential problems even when
   normally it would not exchange packets over the link with the DODAG
   root during some period.  In particular, RNFD SHOULD conclude that
   there may be problems with the DODAG root, when the fraction
   value(NegativeCFRC)/value(PositiveCFRC) has grown by at least
   RNFD_SUSPICION_GROWTH_THRESHOLD since the node last set its LORS to
   "UP".

   Whenever having its LORS set to "UP" RNFD concludes--based on either
   external or internal inputs--that there may be problems with the link
   with the DODAG root, it MUST set its LORS to either "SUSPECTED DOWN"
   or, as an optimization, to "LOCALLY DOWN".

   The "SUSPECTED DOWN" value of LORS is temporary: its aim is to give
   RNFD an additional opportunity to verify whether the link with the
   DODAG root is indeed down.  Depending on the outcome of such
   verification, RNFD MUST set its LORS to either "UP", if the link has
   been confirmed not to be down, or "LOCALLY DOWN", otherwise.  The
   verification can be performed, for example, by transmitting RPL DIS
   or ICMPv6 Echo Request messages to the DODAG root's link-local IPv6
   address and expecting replies confirming that the root is up and
   reachable through the link.  Care SHOULD be taken not to overload the
   DODAG root with traffic due to simultaneous probes, for instance,
   random backoffs can be employed to this end.  It is RECOMMENDED that
   the "SUSPECTED DOWN" value of LORS is attained and verification takes
   place if RNFD's conclusion on the state of the DODAG root is based
   only on indirect observations, for example, the aforementioned growth
   of the CFRC values.  In contrast, for direct observations, such as
   missing L2 acknowledgments, the verification MAY be skipped, with the
   node's LORS effectively changing from "UP" directly to "LOCALLY
   DOWN".





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   For consistency with RPL, when detecting potential problems with the
   DODAG root, RNFD also MUST make use of RPL's independent knowledge.
   More specifically, a node MUST switch its LORS from "UP" or
   "SUSPECTED DOWN" directly to "LOCALLY DOWN" if a neighbor entry for
   the DODAG root is removed from RPL's DODAG parent set or the neighbor
   ceases to be considered reachable via its link-local IPv6 address.

   Finally, while having its LORS already equal to "LOCALLY DOWN", a
   node may make an observation confirming that its link with the DODAG
   root is actually up.  In such a case, it SHOULD set its LORS back to
   "UP" but MUST NOT do this before the previous conditions 2-4
   necessary for a node to change its role from Acceptor to Sentinel all
   hold.

   To appropriately account for the node's observations on the state of
   the DODAG root, the aforementioned LORS transitions are accompanied
   by changes to the node's local CFRCs as follows.  Changes between
   "UP" and "SUSPECTED DOWN" do not affect any of the two CFRCs.  During
   a switch from "UP" or "SUSPECTED DOWN" to "LOCALLY DOWN", in turn,
   the node MUST add itself to its NegativeCFRC, as explained
   previously.  By symmetry, a transition from "LOCALLY DOWN" to "UP"
   REQUIRES the node to add itself to its PositiveCFRC, again, as
   explained previously.

5.3.  Disseminating Observations and Reaching Agreement

   Nodes disseminate their observations by exchanging CFRCs in the RNFD
   Options embedded in link-local RPL control messages, notably DIOs and
   DISs.  When processing such a received option, a node--acting as
   Sentinel or Acceptor--MUST update its PositiveCFRC and NegativeCFRC
   to respectively newpc = merge(oldpc, recvpc) and newnc = merge(oldnc,
   recvnc), where oldpc and oldnc are the values of the node's
   PositiveCFRC and NegativeCFRC before the update, while recvpc and
   recvnc are the received values of option fields PosCFRC and NegCFRC,
   respectively.

   In effect, the node's value of fraction
   value(NegativeCFRC)/value(PositiveCFRC) may change.  If the fraction
   reaches at least RNFD_CONSENSUS_THRESHOLD (with value(PositiveCFRC)
   being greater than zero), then the node consents on the DODAG root
   being down.  Accordingly, it MUST change its LORS to "GLOBALLY DOWN"
   and set its PositiveCFRC and NegativeCFRC both to infinity().

   The "GLOBALLY DOWN" value of LORS is terminal: the node MUST NOT
   change it and MUST NOT modify its CFRCs until it joins a new DODAG
   Version.  With this value of LORS, RNFD at the node MUST also prevent
   RPL from having any DODAG parent and advertising any Rank other than
   INFINITE_RANK.



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   Since the RNFD Option is embedded, among others, in RPL DIO control
   messages, updates to a node's CFRCs may affect the sending schedule
   of these messages, which is driven by the DIO Trickle timer
   [RFC6206].  It is RECOMMENDED to use for RNFD a dedicated Trickle
   timer, different from RPL's DIO Trickle timer.  In such a setting,
   whenever RNFD's timer fires and no DIO message containing the RNFD
   Option has been sent to the link-local all-RPL-nodes multicast IPv6
   address since the previous firing, the node sends a DIO message
   containing the RNFD Option to the address.  In contrast, in the
   absence of a dedicated Trickle timer for RNFD, an implementation
   SHOULD ensure that the RNFD Option is present in multicast DIO
   messages sufficiently often to quickly propagate changes to the
   node's CFRCs.  In either case, a node MUST reset its Trickle timer
   when it changes its LORS to "GLOBALLY DOWN", so that information
   about the detected crash of the DODAG root is disseminated in the
   DODAG fast.  Likewise, a node SHOULD reset its Trickle timer when any
   of its local CFRCs changes significantly.

5.4.  DODAG Root's Behavior

   The DODAG root node MUST assume the role of Acceptor in RNFD and MUST
   NOT ever switch this role.  It MUST also monitor its LORS and local
   CFRCs, so that it can react to various events.

   To start with, the DODAG root MUST generate a new DODAG Version,
   thereby restarting the protocol, if it changes its LORS to "GLOBALLY
   DOWN", which may happen when the root has restarted after a crash or
   the nodes have falsely detected its crash.  It MAY also generate a
   new DODAG Version if fraction value(NegativeCFRC)/value(PositiveCFRC)
   approaches RNFD_CONSENSUS_THRESHOLD, so as to avoid potential
   interruptions to routing.

   Furthermore, the DODAG root SHOULD either generate a new DODAG
   Version or increase the bit length of its CFRCs if
   saturated(PositiveCFRC) becomes TRUE.  This is a self-regulation
   mechanism that helps adjust the CFRCs to a potentially large number
   of Sentinels (see Section 6.1).

   In general, issuing a new DODAG Version effectively restarts RNFD.
   The DODAG root MAY thus perform this operation also in other
   situations.










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5.5.  Activating and Deactivating the Protocol on Demand

   RNFD CAN be activated and deactivated on demand, once per DODAG
   Version.  The particular policies for activating and deactivating the
   protocol are outside the scope of this document.  However, the
   activation and deactivation SHOULD be done at the DODAG root node;
   other nodes MUST comply.

   More specifically, when a non-root node joins a DODAG Version, RNFD
   at the node is initially inactive.  The node MUST NOT activate the
   protocol unless it receives for this DODAG Version a valid RNFD
   Option containing some CFRCs, that is, having its Option Length field
   positive.  In particular, if the option accompanies the message that
   causes the node to join the DODAG Version, the protocol SHOULD be
   active from the moment of the joining.  RNFD then remains active at
   the node until it is explicitly deactivated or the node joins a new
   DODAG Version.  An explicit deactivation MUST take place when the
   node receives an RNFD Option for the DODAG Version with no CFRCs,
   that is, having its Option Length field equal to zero.  When
   explicitly deactivated, RNFD MUST NOT be reactivated unless the node
   joins a new DODAG Version.  In particular, when the first RNFD Option
   received by the node has its Option Length field equal to zero, the
   protocol MUST remain deactivated for the entire time the node belongs
   to the current DODAG Version.

   When RNFD at a node is initially inactive for a DODAG Version, the
   node MUST NOT attach any RNFD Option to the messages it sends (in
   particular, because it may not know the desired CFRC length--see
   Section 5.6).  When the protocol has been explicitly deactivated, the
   node MAY also decide not to attach the option to its outgoing
   messages.  However, it is RECOMMENDED that it sends sufficiently many
   messages with the option to the link-local all-RPL-nodes multicast
   IPv6 address to allow its neighbors to learn that RNFD has been
   deactivated in the current DODAG version.  In particular, it MAY
   reset its Trickle timer to this end but also MAY use some reactive
   mechanisms, for example, replying with a unicast DIO or DIS
   containing the RNFD Option with no CFRCs to a message from a neighbor
   that contains the option with some CFRCs, as such a neighbor appears
   not to have learned about the deactivation of RNFD.

5.6.  Processing CFRCs of Incompatible Lengths

   The merge() and compare() operations on CFRCs require both arguments
   to be compatible, that is, to have the same bit length.  However, the
   processing rules for the RNFD Option (see Section 4.2) do not
   necessitate this.  This fact is made use of not only in the
   mechanisms for activating and deactivating the protocol (see
   Section 5.5), but also in mechanisms for dynamic adjustments of



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   CFRCs, which aim to enable deployment-specific policies (see
   Section 6.1).  A node thus MUST be prepared to receive the RNFD
   Option with fields PosCFRC and NegCFRC of a different bit length than
   the node's own PositiveCFRC and NegativeCFRC.  Assuming that it has
   RNFD active and that fields PosCFRC and NegCFRC in the option have a
   positive length, the node MUST react as follows.

   If the bit length of fields PosCFRC and NegCFRC is the same as that
   of the node's local PositiveCFRC and NegativeCFRC, then the node MUST
   perform the merges, as detailed previously (see Section 5.3).

   If the bit length of fields PosCFRC and NegCFRC is smaller than that
   of the node's local PositiveCFRC and NegativeCFRC, then the node MUST
   ignore the option and MAY reset its Trickle timer.

   If the bit length of fields PosCFRC and NegCFRC is greater than that
   of the node's local PositiveCFRC and NegativeCFRC, then the node MUST
   extend the bit length of its local CFRCs to be equal to that in the
   option and set the CFRCs as follows:

   *  If the node's LORS is "GLOBALLY DOWN", then both its local CFRCs
      MUST be set to infinity().

   *  Otherwise, they both MUST be set to zero(), and the node MUST
      account for itself in so initialized CFRCs.  More specifically, if
      the node is Sentinel, then it MUST add itself to its PositiveCFRC,
      as detailed previously.  In addition, if its LORS is "LOCALLY
      DOWN", then it MUST also add itself to its NegativeCFRC, again, as
      explained previously.  Finally, the node MUST perform merges of
      its local CFRCs and the ones received in the option (see
      Section 5.3) and MAY reset its Trickle timer.

   In contrast, if the node is unable to extend its local CFRCs, for
   example, because it lacks resources, then it MUST stop participating
   in RNFD, that is, until it joins a new DODAG Version, it MUST NOT
   send the RNFD Option and MUST ignore this option in received
   messages.

5.7.  Summary of RNFD's Interactions with RPL

   In summary, RNFD interacts with RPL in the following manner:

   *  While having its LORS equal to "GLOBALLY DOWN", RNFD prevents RPL
      from routing packets and advertising upward routes in the
      corresponding DODAG (see Section 5.3).

   *  In some scenarios, RNFD triggers RPL to issue a new DODAG Version
      (see Section 5.4).



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   *  Depending on the implementation, RNFD may cause RPL's DIO Trickle
      timer resets (see Section 5.3, Section 5.5, and Section 5.6).

   *  RNFD monitors events relevant to routing adjacency maintenance as
      well as those affecting RPL's DODAG parent set (see Section 5.1
      and Section 5.2).

   *  Using RNFD entails embedding the RNFD Option into link-local RPL
      control messages (see Section 4.2).

5.8.  Summary of RNFD's Constants

   The following is a summary of RNFD's constants:

   RNFD_SUSPICION_GROWTH_THRESHOLD  A threshold concerning the value of
      fraction value(NegativeCFRC)/value(PositiveCFRC).  If the value at
      a Sentinel node grows at least by this threshold since the time
      the node's LORS was last set to "UP", then the node's LORS is set
      to "SUSPECTED DOWN" or "LOCALLY DOWN", which implies that the node
      suspects or assumes a crash of the DODAG root (see Section 5.2).
      The default value of the threshold is 0.12.  The higher the value
      the longer the detection period but the lower risk of increased
      traffic due suspicion verification.

   RNFD_CONSENSUS_THRESHOLD  A threshold concerning the value of
      fraction value(NegativeCFRC)/value(PositiveCFRC).  If the value at
      a Sentinel or Acceptor node reaches the threshold, then the node's
      LORS is set to "GLOBALLY DOWN", which implies that consensus has
      been reached on the DODAG root node being down (see Section 5.3).
      The default value of the threshold is 0.51.  The higher the value
      the longer the detection period but the lower the risk of false
      positives.

   The means of configuring the constants at individual nodes are
   outside the scope of this document.

6.  Manageability Considerations

   RNFD is largely self-managed, with the exception of protocol
   activation and deactivation, as well as node role assignment and the
   related CFRC size adjustment, for which only the aforementioned
   mechanisms are defined, so as to enable adopting deployment-specific
   policies.  This section outlines some of the possible policies.








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6.1.  Role Assignment and CFRC Size Adjustment

   One approach to node role and CFRC size selection is to manually
   designate specific nodes as Sentinels in RNFD, assuming that they
   will have chances to satisfy the necessary conditions for attaining
   this role (see Section 5.1), and fixing the CFRC bit length to
   accommodate these nodes.

   Another approach is to automate the selection process: in principle,
   any node satisfying the necessary conditions for becoming Sentinel
   (see Section 5.1) can attain this role.  However, in networks where
   the DODAG root node has many neighbors, this approach may lead to
   saturated(PositiveCFRC) quickly becoming TRUE, which--without
   additional measures--may degrade RNFD's performance.  This issue can
   be handled with a probabilistic solution: if PositiveCFRC becomes
   saturated with little or no increase in NegativeCFRC, then a new
   DODAG Version can be issued and a node satisfying the necessary
   conditions can become Sentinel in this version only with probability
   1/2.  This process can be continued with the probability being halved
   in each new DODAG Version until PositiveCFRC is no longer quickly
   saturated.  Another solution is to increase, potentially multiple
   times the bit length of the CFRCs by the DODAG root if PositiveCFRC
   becomes saturated with little or no growth in NegativeCFRC, which
   does not require issuing a new DODAG Version but lengthens the RNFD
   Option.  In this way, again, a sufficient bit length can be
   dynamically discovered or the root can conclude that a given bit
   length is excessive for (some) nodes and resort to the previous
   solution.  Increasing the bit length can be done, for instance, by
   doubling it, respecting the condition that it has to be a prime
   number (see Section 4.2).

   In either of the solutions, Sentinel nodes SHOULD preferably be
   stable themselves and have stable links to the DODAG root.
   Otherwise, they may often exhibit LORS transitions between "UP" and
   "LOCALLY DOWN" or switches between Acceptor and Sentinel roles, which
   gradually saturates CFRCs.  Although as a mitigation the number of
   such transitions and switches per node MAY be limited, having
   Sentinels stable SHOULD be preferred.

6.2.  Virtual DODAG Roots

   RPL allows a DODAG to have a so-called virtual root, that is, a
   collection of nodes coordinating to act as a single root of the
   DODAG.  The details of the coordination process are left open in the
   specification [RFC6550] but, from RNFD's perspective, two possible
   realizations are worth consideration:





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   *  Just a single (primary) node of the nodes comprising the virtual
      root acts as the actual root of the DODAG.  Only when this node
      fails, does another (backup) node take over.  As a result, at any
      time, at most one of the nodes comprising the virtual root is the
      actual root.

   *  More than one of the nodes comprising the virtual root act as
      actual roots of the DODAG, all advertising the same Rank in the
      DODAG.  When some of the nodes fail, the other nodes may or may
      not react in any specific way.  In other words, at any time, more
      than one node can be the actual root.

   In the first realization, RNFD's operation is largely unaffected.
   The necessary conditions for a node to become Sentinel (Section 5.1)
   guarantee that only the current primary root node is monitored by the
   protocol.  This SHOULD be taken into account in the policies for node
   role assignment, CFRC size selection, and, possibly, the setting of
   the two thresholds (Section 5.8).  Moreover, when a new primary has
   been elected, to avoid polluting CFRCs with observations on the
   previous primary, it is RECOMMENDED to issue a new DODAG Version,
   especially if the new primary has different neighbors compared to the
   old one.

   In the second realization, the fact that the virtual root consists of
   multiple nodes is transparent to RNFD.  Therefore, employing RNFD is
   such a setting can be beneficial only if the nodes comprising the
   virtual root may suffer from correlated crashes, for instance, due to
   global power outages.

7.  Security Considerations

   RNFD is an extension to RPL and is thus both vulnerable to and
   benefits from the security issues and solutions described in
   [RFC6550] and [RFC7416].  Its specification in this document does not
   introduce new traffic patterns or new messages, for which specific
   mitigation techniques would be required beyond what can already be
   adopted for RPL.














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   In particular, RNFD depends on information exchanged in the RNFD
   Option.  If the contents of this option were compromised, then
   failure misdetection may occur.  One possibility is that the DODAG
   root may be falsely detected as crashed, which would result in an
   inability of the nodes to route packets, at least until a new DODAG
   Version is issued by the root.  Another possibility is that a crash
   of the DODAG root may not be detected by RNFD, in which case RPL
   would have to rely on its own mechanisms.  Moreover, compromising the
   contents of the RNFD Option may also lead to increased traffic due to
   DIO Trickle timer resets.  Consequently, RNFD deployments are
   RECOMMENDED to use RPL security mechanisms if there is a risk that
   control information might be modified or spoofed.

   In this context, RNFD's two features are worth highlighting.  First,
   unless a DODAG root's all neighbors are compromised, a false positive
   can always be detected by the root based on its local CFRCs.  If the
   frequency of such false positives becomes problematic, RNFD can be
   disabled altogether, for instance, until the problem has been
   diagnosed.  This procedure can be largely automated at LBRs.  Second,
   some types of false negatives can also be detected this way.  Those
   that pass undetected, in turn, are likely not to have major negative
   consequences on RPL apart from the lack of improvement to its
   performance upon a DODAG root's crash, at least if RPL's other
   components are not attacked as well.

8.  IANA Considerations

   To represent the RNFD Option, IANA is requested to allocate the value
   TBD1 from the "RPL Control Message Options" sub-registry
   (https://www.iana.org/assignments/rpl/rpl.xhtml#control-message-
   options) of the "Routing Protocol for Low Power and Lossy Networks
   (RPL)" registry.

9.  Acknowledgements

   The authors would like to acknowledge Piotr Ciolkosz and Agnieszka
   Paszkowska.  Agnieszka contributed to deeper understanding and
   formally proving various aspects of RPL's behavior upon an LBR crash.
   Piotr in turn developed a prototype implementation of RNFD dedicated
   for RPL to verify earlier performance claims.

   _TODO_ More likely to follow.

10.  References

10.1.  Normative References





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   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119,
              DOI 10.17487/RFC2119, March 1997,
              <https://www.rfc-editor.org/info/rfc2119>.

   [RFC6206]  Levis, P., Clausen, T., Hui, J., Gnawali, O., and J. Ko,
              "The Trickle Algorithm", RFC 6206, DOI 10.17487/RFC6206,
              March 2011, <https://www.rfc-editor.org/info/rfc6206>.

   [RFC6550]  Winter, T., Ed., Thubert, P., Ed., Brandt, A., Hui, J.,
              Kelsey, R., Levis, P., Pister, K., Struik, R., Vasseur,
              JP., and R. Alexander, "RPL: IPv6 Routing Protocol for
              Low-Power and Lossy Networks", RFC 6550,
              DOI 10.17487/RFC6550, March 2012,
              <https://www.rfc-editor.org/info/rfc6550>.

   [RFC6553]  Hui, J. and JP. Vasseur, "The Routing Protocol for Low-
              Power and Lossy Networks (RPL) Option for Carrying RPL
              Information in Data-Plane Datagrams", RFC 6553,
              DOI 10.17487/RFC6553, March 2012,
              <https://www.rfc-editor.org/info/rfc6553>.

   [RFC6554]  Hui, J., Vasseur, JP., Culler, D., and V. Manral, "An IPv6
              Routing Header for Source Routes with the Routing Protocol
              for Low-Power and Lossy Networks (RPL)", RFC 6554,
              DOI 10.17487/RFC6554, March 2012,
              <https://www.rfc-editor.org/info/rfc6554>.

   [RFC8174]  Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC
              2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174,
              May 2017, <https://www.rfc-editor.org/info/rfc8174>.

10.2.  Informative References

   [Ciolkosz19]
              Ciolkosz, P., "Integration of the RNFD Algorithm for
              Border Router Failure Detection with the RPL Standard for
              Routing IPv6 Packets", Master's Thesis, University of
              Warsaw, 2019.

   [Iwanicki16]
              Iwanicki, K., "RNFD: Routing-layer detection of DODAG
              (root) node failures in low-power wireless networks",
              In IPSN 2016: Proceedings of the 15th ACM/IEEE
              International Conference on Information Processing in
              Sensor Networks, IEEE, pp. 1--12,
              DOI 10.1109/IPSN.2016.7460720, 2016,
              <https://doi.org/10.1109/IPSN.2016.7460720>.



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   [Paszkowska19]
              Paszkowska, A. and K. Iwanicki, "Failure Handling in RPL
              Implementations: An Experimental Qualitative Study", In
              Mission-Oriented Sensor Networks and Systems: Art and
              Science (Habib M. Ammari ed.), Springer International
              Publishing, pp. 49--95, DOI 10.1007/978-3-319-91146-5_3,
              2019, <https://doi.org/10.1007/978-3-319-91146-5_3>.

   [RFC4861]  Narten, T., Nordmark, E., Simpson, W., and H. Soliman,
              "Neighbor Discovery for IP version 6 (IPv6)", RFC 4861,
              DOI 10.17487/RFC4861, September 2007,
              <https://www.rfc-editor.org/info/rfc4861>.

   [RFC5184]  Teraoka, F., Gogo, K., Mitsuya, K., Shibui, R., and K.
              Mitani, "Unified Layer 2 (L2) Abstractions for Layer 3
              (L3)-Driven Fast Handover", RFC 5184,
              DOI 10.17487/RFC5184, May 2008,
              <https://www.rfc-editor.org/info/rfc5184>.

   [RFC6202]  Loreto, S., Saint-Andre, P., Salsano, S., and G. Wilkins,
              "Known Issues and Best Practices for the Use of Long
              Polling and Streaming in Bidirectional HTTP", RFC 6202,
              DOI 10.17487/RFC6202, April 2011,
              <https://www.rfc-editor.org/info/rfc6202>.

   [RFC7102]  Vasseur, JP., "Terms Used in Routing for Low-Power and
              Lossy Networks", RFC 7102, DOI 10.17487/RFC7102, January
              2014, <https://www.rfc-editor.org/info/rfc7102>.

   [RFC7228]  Bormann, C., Ersue, M., and A. Keranen, "Terminology for
              Constrained-Node Networks", RFC 7228,
              DOI 10.17487/RFC7228, May 2014,
              <https://www.rfc-editor.org/info/rfc7228>.

   [RFC7416]  Tsao, T., Alexander, R., Dohler, M., Daza, V., Lozano, A.,
              and M. Richardson, Ed., "A Security Threat Analysis for
              the Routing Protocol for Low-Power and Lossy Networks
              (RPLs)", RFC 7416, DOI 10.17487/RFC7416, January 2015,
              <https://www.rfc-editor.org/info/rfc7416>.

   [Whang90]  Whang, K.-Y., Vander-Zanden, B.T., and H.M. Taylor, "A
              Linear-time Probabilistic Counting Algorithm for Database
              Applications", In ACM Transactions on Database Systems,
              DOI 10.1145/78922.78925, 1990,
              <https://doi.org/10.1145/78922.78925>.

Author's Address




Iwanicki                Expires 2 September 2022               [Page 24]


Internet-Draft                    RNFD                        March 2022


   Konrad Iwanicki
   University of Warsaw
   Banacha 2
   02-097 Warszawa
   Poland
   Phone: +48 22 55 44 428
   Email: iwanicki@mimuw.edu.pl












































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