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Versions: (draft-maenpaa-p2psip-self-tuning) 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 RFC 7363

P2PSIP Working Group                                          J. Maenpaa
Internet-Draft                                              G. Camarillo
Intended status: Standards Track                                Ericsson
Expires: January 17, 2013                                  J. Hautakorpi
                                                  Nokia Siemens Networks
                                                           July 16, 2012


  A Self-tuning Distributed Hash Table (DHT) for REsource LOcation And
                           Discovery (RELOAD)
                  draft-ietf-p2psip-self-tuning-06.txt

Abstract

   REsource LOcation And Discovery (RELOAD) is a peer-to-peer (P2P)
   signaling protocol that provides an overlay network service.  Peers
   in a RELOAD overlay network collectively run an overlay algorithm to
   organize the overlay, and to store and retrieve data.  This document
   describes how the default topology plugin of RELOAD can be extended
   to support self-tuning, that is, to adapt to changing operating
   conditions such as churn and network size.

Status of this Memo

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

   Internet-Drafts are working documents of the Internet Engineering
   Task Force (IETF).  Note that other groups may also distribute
   working documents as Internet-Drafts.  The list of current Internet-
   Drafts is at http://datatracker.ietf.org/drafts/current/.

   Internet-Drafts are draft documents valid for a maximum of six months
   and may be updated, replaced, or obsoleted by other documents at any
   time.  It is inappropriate to use Internet-Drafts as reference
   material or to cite them other than as "work in progress."

   This Internet-Draft will expire on January 17, 2013.

Copyright Notice

   Copyright (c) 2012 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



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   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.


Table of Contents

   1.  Introduction . . . . . . . . . . . . . . . . . . . . . . . . .  3
   2.  Terminology  . . . . . . . . . . . . . . . . . . . . . . . . .  3
   3.  Introduction to Stabilization in DHTs  . . . . . . . . . . . .  5
     3.1.  Reactive vs. Periodic Stabilization  . . . . . . . . . . .  5
     3.2.  Configuring Periodic Stabilization . . . . . . . . . . . .  6
     3.3.  Adaptive Stabilization . . . . . . . . . . . . . . . . . .  7
   4.  Introduction to Chord  . . . . . . . . . . . . . . . . . . . .  7
   5.  Extending Chord-reload to Support Self-tuning  . . . . . . . .  9
     5.1.  Update Requests  . . . . . . . . . . . . . . . . . . . . .  9
     5.2.  Neighbor Stabilization . . . . . . . . . . . . . . . . . . 10
     5.3.  Finger Stabilization . . . . . . . . . . . . . . . . . . . 11
     5.4.  Adjusting Finger Table Size  . . . . . . . . . . . . . . . 11
     5.5.  Detecting Partitioning . . . . . . . . . . . . . . . . . . 11
     5.6.  Leaving the Overlay  . . . . . . . . . . . . . . . . . . . 11
   6.  Self-tuning Chord Parameters . . . . . . . . . . . . . . . . . 12
     6.1.  Estimating Overlay Size  . . . . . . . . . . . . . . . . . 12
     6.2.  Determining Routing Table Size . . . . . . . . . . . . . . 13
     6.3.  Estimating Failure Rate  . . . . . . . . . . . . . . . . . 13
       6.3.1.  Detecting Failures . . . . . . . . . . . . . . . . . . 14
     6.4.  Estimating Join Rate . . . . . . . . . . . . . . . . . . . 14
     6.5.  Estimate Sharing . . . . . . . . . . . . . . . . . . . . . 15
     6.6.  Calculating the Stabilization Interval . . . . . . . . . . 16
   7.  Overlay Configuration Document Extension . . . . . . . . . . . 17
   8.  Security Considerations  . . . . . . . . . . . . . . . . . . . 17
   9.  IANA Considerations  . . . . . . . . . . . . . . . . . . . . . 17
     9.1.  Message Extensions . . . . . . . . . . . . . . . . . . . . 18
   10. References . . . . . . . . . . . . . . . . . . . . . . . . . . 18
     10.1. Normative References . . . . . . . . . . . . . . . . . . . 18
     10.2. Informative References . . . . . . . . . . . . . . . . . . 18
   Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 20












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1.  Introduction

   REsource LOcation And Discovery (RELOAD) [I-D.ietf-p2psip-base] is a
   peer-to-peer signaling protocol that can be used to maintain an
   overlay network, and to store data in and retrieve data from the
   overlay.  For interoperability reasons, RELOAD specifies one overlay
   algorithm, called chord-reload, that is mandatory to implement.  This
   document extends the chord-reload algorithm by introducing self-
   tuning behavior.

   DHT-based overlay networks are self-organizing, scalable and
   reliable.  However, these features come at a cost: peers in the
   overlay network need to consume network bandwidth to maintain routing
   state.  Most DHTs use a periodic stabilization routine to counter the
   undesirable effects of churn on routing.  To configure the parameters
   of a DHT, some characteristics such as churn rate and network size
   need to be known in advance.  These characteristics are then used to
   configure the DHT in a static fashion by using fixed values for
   parameters such as the size of the successor set, size of the routing
   table, and rate of maintenance messages.  The problem with this
   approach is that it is not possible to achieve a low failure rate and
   a low communication overhead by using fixed parameters.  Instead, a
   better approach is to allow the system to take into account the
   evolution of network conditions and adapt to them.  This document
   extends the mandatory-to-implement chord-reload algorithm by making
   it self-tuning.  Two main advantages of self-tuning are that users no
   longer need to tune every DHT parameter correctly for a given
   operating environment and that the system adapts to changing
   operating conditions.

   The remainder of this document is structured as follows: Section 2
   provides definitions of terms used in this document.  Section 3
   discusses alternative approaches to stabilization operations in DHTs,
   including reactive stabilization, periodic stabilization, and
   adaptive stabilization.  Section 4 gives an introduction to the Chord
   DHT algorithm.  Section 5 describes how this document extends the
   stabilization routine of the chord-reload algorithm.  Section 6
   describes how the stabilization rate and routing table size are
   calculated in an adaptive fashion.


2.  Terminology

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
   document are to be interpreted as described in RFC 2119 [RFC2119].

   This document uses the terminology and definitions from the Concepts



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   and Terminology for Peer to Peer SIP [I-D.ietf-p2psip-concepts]
   draft.


   Chord Ring:  The Chord DHT orders identifiers on an identifier circle
      of size 2^numBitsInNodeId (numBitsInNodeId is the number of bits
      in node identifiers).  This identifier circle is called the Chord
      ring.

   DHT:  Distributed Hash Tables (DHTs) are a class of decentralized
      distributed systems that provide a lookup service similar to a
      hash table.  Given a key, any participating peer can retrieve the
      value associated with that key.  The responsibility for
      maintaining the mapping from keys to values is distributed among
      the peers.

   Finger Table:  A data structure with up to numBitsInNodeId entries
      maintained by each peer in a Chord-based overlay.  The ith entry
      in the finger table of peer n contains the identity of the first
      peer that succeeds n by at least 2^(numBitsInNodeId-i) on the
      Chord ring.  This peer is called the ith finger of peer n.  As an
      example, the first entry in the finger table of peer n contains a
      peer half-way around the Chord ring from peer n.  The purpose of
      the finger table is to accelerate lookups.

   log2(N):  Logarithm of N with base 2.

   n.id:  Peer-ID of peer n.

   Neighborhood Set:  Consists of successor and predecessor lists.

   numBitsInNodeId:  Number of bits in a Node-ID.

   O(g(n)):  Informally, saying that some equation f(n) = O(g(n)) means
      that f(n) is less than some constant multiple of g(n).

   Omega(g(n)):  Informally, saying that some equation f(n) =
      Omega(g(n)) means that f(n) is more than some constant multiple of
      g(n).

   Predecessor List:  A data structure containing the predecessors of a
      peer on the Chord ring.

   Routing Table:  The set of peers that a node can use to route overlay
      messages.  The routing table consists of the finger table,
      successor list and predecessor list.





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   Successor List:  A data structure containing the first r successors
      of a peer on the Chord ring.



3.  Introduction to Stabilization in DHTs

   DHTs use stabilization routines to counter the undesirable effects of
   churn on routing.  The purpose of stabilization is to keep the
   routing information of each peer in the overlay consistent with the
   constantly changing overlay topology.  There are two alternative
   approaches to stabilization: periodic and reactive [rhea2004].
   Periodic stabilization can either use a fixed stabilization rate or
   calculate the stabilization rate in an adaptive fashion.

3.1.  Reactive vs. Periodic Stabilization

   In reactive stabilization, a peer reacts to the loss of a peer in its
   neighborhood set or to the appearance of a new peer that should be
   added to its neighborhood set by sending a copy of its neighbor table
   to all peers in the neighborhood set.  Periodic recovery, in
   contrast, takes place independently of changes in the neighborhood
   set.  In periodic recovery, a peer periodically shares its
   neighborhood set with each or a subset of the members of that set.

   The chord-reload algorithm [I-D.ietf-p2psip-base] supports both
   reactive and periodic stabilization.  It has been shown in [rhea2004]
   that reactive stabilization works well for small neighborhood sets
   (i.e., small overlays) and moderate churn.  However, in large-scale
   (e.g., 1000 peers or more [rhea2004]) or high-churn overlays,
   reactive stabilization runs the risk of creating a positive feedback
   cycle, which can eventually result in congestion collapse.  In
   [rhea2004], it is shown that a 1000-peer overlay under churn uses
   significantly less bandwidth and has lower latencies when periodic
   stabilization is used than when reactive stabilization is used.
   Although in the experiments carried out in [rhea2004], reactive
   stabilization performed well when there was no churn, its bandwidth
   use was observed to jump dramatically under churn.  At higher churn
   rates and larger scale overlays, periodic stabilization uses less
   bandwidth and the resulting lower contention for the network leads to
   lower latencies.  For this reason, most DHTs such as CAN [CAN], Chord
   [Chord], Pastry [Pastry], Bamboo [rhea2004], etc. use periodic
   stabilization [ghinita2006].  As an example, the first version of
   Bamboo used reactive stabilization, which caused Bamboo to suffer
   from degradation in performance under churn.  To fix this problem,
   Bamboo was modified to use periodic stabilization.




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   In Chord, periodic stabilization is typically done both for
   successors and fingers.  An alternative strategy is analyzed in
   [krishnamurthy2008].  In this strategy, called the correction-on-
   change maintenance strategy, a peer periodically stabilizes its
   successors but does not do so for its fingers.  Instead, finger
   pointers are stabilized in a reactive fashion.  The results obtained
   in [krishnamurthy2008] imply that although the correction-on-change
   strategy works well when churn is low, periodic stabilization
   outperforms the correction-on-change strategy when churn is high.

3.2.  Configuring Periodic Stabilization

   When periodic stabilization is used, one faces the problem of
   selecting an appropriate execution rate for the stabilization
   procedure.  If the execution rate of periodic stabilization is high,
   changes in the system can be quickly detected, but at the
   disadvantage of increased communication overhead.  Alternatively, if
   the stabilization rate is low and the churn rate is high, routing
   tables become inaccurate and DHT performance deteriorates.  Thus, the
   problem is setting the parameters so that the overlay achieves the
   desired reliability and performance even in challenging conditions,
   such as under heavy churn.  This naturally results in high cost
   during periods when the churn level is lower than expected, or
   alternatively, poor performance or even network partitioning in worse
   than expected conditions.

   In addition to selecting an appropriate stabilization interval,
   regardless of whether periodic stabilization is used or not, an
   appropriate size needs to be selected for the neighborhood set and
   for the finger table.

   The current approach is to configure overlays statically.  This works
   in situations where perfect information about the future is
   available.  In situations where the operating conditions of the
   network are known in advance and remain static throughout the
   lifetime of the system, it is possible to choose fixed optimal values
   for parameters such as stabilization rate, neighborhood set size and
   routing table size.  However, if the operating conditions (e.g., the
   size of the overlay and its churn rate) do not remain static but
   evolve with time, it is not possible to achieve both a low lookup
   failure rate and a low communication overhead by using fixed
   parameters [ghinita2006].

   As an example, to configure the Chord DHT algorithm, one needs to
   select values for the following parameters: size of successor list,
   stabilization interval, and size of the finger table.  To select an
   appropriate value for the stabilization interval, one needs to know
   the expected churn rate and overlay size.  According to



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   [liben-nowell2002], a Chord network in a ring-like state remains in a
   ring-like state as long as peers send Omega(log2^2(N)) messages
   before N new peers join or N/2 peers fail.  Thus, in a 500-peer
   overlay churning at a rate such that one peer joins and one peer
   leaves the network every 30 seconds, an appropriate stabilization
   interval would be on the order of 93s.  According to [Chord], the
   size of the successor list and finger table should be on the order of
   log2(N).  Having a successor list of size O(log2(N)) makes it
   unlikely that a peer will lose all of its successors, which would
   cause the Chord ring to become disconnected.  Thus, in a 500-peer
   network each peer should maintain on the order of nine successors and
   fingers.  However, if the churn rate doubles and the network size
   remains unchanged, the stabilization rate should double as well.
   That is, the appropriate maintenance interval would now be on the
   order of 46s.  On the other hand, if the churn rate becomes e.g. six-
   fold and the size of the network grows to 2000 peers, on the order of
   eleven fingers and successors should be maintained and the
   stabilization interval should be on the order of 42s.  If one
   continued using the old values, this could result in inaccurate
   routing tables, network partitioning, and deteriorating performance.

3.3.  Adaptive Stabilization

   A self-tuning DHT takes into consideration the continuous evolution
   of network conditions and adapts to them.  In a self-tuning DHT, each
   peer collects statistical data about the network and dynamically
   adjusts its stabilization rate, neighborhood set size, and finger
   table size based on the analysis of the data [ghinita2006].
   Reference [mahajan2003] shows that by using self-tuning, it is
   possible to achieve high reliability and performance even in adverse
   conditions with low maintenance cost.  Adaptive stabilization has
   been shown to outperform periodic stabilization in terms of both
   lookup failures and communication overhead [ghinita2006].


4.  Introduction to Chord

   Chord [Chord] is a structured P2P algorithm that uses consistent
   hashing to build a DHT out of several independent peers.  Consistent
   hashing assigns each peer and resource a fixed-length identifier.
   Peers use SHA-1 as the base hash fuction to generate the identifiers.
   As specified in RELOAD base, the length of the identifiers is
   numBitsInNodeId=128 bits.  The identifiers are ordered on an
   identifier circle of size 2^numBitsInNodeId.  On the identifier
   circle, key k is assigned to the first peer whose identifier equals
   or follows the identifier of k in the identifier space.  The
   identifier circle is called the Chord ring.




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   Different DHTs differ significantly in performance when bandwidth is
   limited.  It has been shown that when compared to other DHTs, the
   advantages of Chord include that it uses bandwidth efficiently and
   can achieve low lookup latencies at little cost [li2004].

   A simple lookup mechanism could be implemented on a Chord ring by
   requiring each peer to only know how to contact its current successor
   on the identifier circle.  Queries for a given identifier could then
   be passed around the circle via the successor pointers until they
   encounter the first peer whose identifier is equal to or larger than
   the desired identifier.  Such a lookup scheme uses a number of
   messages that grows linearly with the number of peers.  To reduce the
   cost of lookups, Chord maintains also additional routing information;
   each peer n maintains a data structure with up to numBitsInNodeId
   entries, called the finger table.  The first entry in the finger
   table of peer n contains the peer half-way around the ring from peer
   n.  The second entry contains the peer that is 1/4th of the way
   around, the third entry the peer that is 1/8th of the way around,
   etc.  In other words, the ith entry in the finger table at peer n
   contains the identity of the first peer s that succeeds n by at least
   2^(numBitsInNodeId-i) on the Chord ring.  This peer is called the ith
   finger of peer n.  The interval between two consecutive fingers is
   called a finger interval.  The ith finger interval of peer n covers
   the range [n.id + 2^(numBitsInNodeId-i), n.id +
   2^(numBitsInNodeId-i+1)) on the Chord ring.  In an N-peer network,
   each peer maintains information about O(log2(N)) other peers in its
   finger table.  As an example, if N=100000, it is sufficient to
   maintain 17 fingers.

   Chord needs all peers' successor pointers to be up to date in order
   to ensure that lookups produce correct results as the set of
   participating peers changes.  To achieve this, peers run a
   stabilization protocol periodically in the background.  The
   stabilization protocol of the original Chord algorithm uses two
   operations: successor stabilization and finger stabilization.
   However, the Chord algorithm of RELOAD base defines two additional
   stabilization components, as will be discussed below.

   To increase robustness in the event of peer failures, each Chord peer
   maintains a successor list of size r, containing the peer's first r
   successors.  The benefit of successor lists is that if each peer
   fails independently with probability p, the probability that all r
   successors fail simultaneously is only p^r.

   The original Chord algorithm maintains only a single predecessor
   pointer.  However, multiple predecessor pointers (i.e., a predecessor
   list) can be maintained to speed up recovery from predecessor
   failures.  The routing table of a peer consists of the successor



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   list, finger table, and predecessor list.


5.  Extending Chord-reload to Support Self-tuning

   This section describes how the mandatory-to-implement chord-reload
   algorithm defined in RELOAD base [I-D.ietf-p2psip-base] can be
   extended to support self-tuning.

   The chord-reload algorithm supports both reactive and periodic
   recovery strategies.  When the self-tuning mechanisms defined in this
   document are used, the periodic recovery strategy MUST be used.
   Further, chord-reload specifies that at least three predecessors and
   three successors need to be maintained.  When the self-tuning
   mechanisms are used, the appropriate sizes of the successor list and
   predecessor list are determined in an adaptive fashion based on the
   estimated network size, as will be described in Section 6.

   As specified in RELOAD base, each peer MUST maintain a stabilization
   timer.  When the stabilization timer fires, the peer MUST restart the
   timer and carry out the overlay stabilization routine.  Overlay
   stabilization has four components in chord-reload:

   1.  Update the neighbor table.  We refer to this as neighbor
       stabilization.
   2.  Refreshing the finger table.  We refer to this as finger
       stabilization.
   3.  Adjusting finger table size.
   4.  Detecting partitioning.  We refer to this as strong
       stabilization.

   As specified in RELOAD base [I-D.ietf-p2psip-base], a peer sends
   periodic messages as part of the neighbor stabilization, finger
   stabilization, and strong stabilization routines.  In neighbor
   stabilization, a peer periodically sends an Update request to every
   peer in its Connection Table.  The default time is every ten minutes.
   In finger stabilization, a peer periodically searches for new peers
   to include in its finger table.  This time defaults to one hour.
   This document specifies how the neighbor stabilization and finger
   stabilization intervals can be determined in an adaptive fashion
   based on the operating conditions of the overlay.  The subsections
   below describe how this document extends the four components of
   stabilization.

5.1.  Update Requests

   As described in RELOAD base [I-D.ietf-p2psip-base], the neighbor and
   finger stabilization procedures are implemented using Update



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   requests.  RELOAD base defines three types of Update requests:
   'peer_ready', 'neighbors', and 'full'.  Regardless of the type, all
   Update requests include an 'uptime' field.  Since the self-tuning
   extensions require information on the uptimes of peers in the routing
   table, the sender of an Update request MUST include its current
   uptime in seconds in the 'uptime' field.

   When self-tuning is used, each peer decides independently the
   appropriate size for the successor list, predecessor list and finger
   table.  Thus, the 'predecessors', 'successors', and 'fingers' fields
   included in RELOAD Update requests are of variable length.  As
   specified in RELOAD [I-D.ietf-p2psip-base], variable length fields
   are on the wire preceded by length bytes.  In the case of the
   successor list, predecessor list, and finger table, there are two
   length bytes (allowing lengths up to 2^16-1).  The number of NodeId
   structures included in each field can be calculated based on the
   length bytes since the size of a single NodeId structure is 16 bytes.
   If a peer receives more entries than fit into its successor list,
   predecessor list or finger table, the peer MUST ignore the extra
   entries.  If a peer receives less entries than it currently has in
   its own data structure, the peer MUST NOT drop the extra entries from
   its data structure.

5.2.  Neighbor Stabilization

   In the neighbor stabilization operation of chord-reload, a peer
   periodically sends an Update request to every peer in its Connection
   Table.  In a small, low-churn overlay, the amount of traffic this
   process generates is typically acceptable.  However, in a large-scale
   overlay churning at a moderate or high churn rate, the traffic load
   may no longer be acceptable since the size of the connection table is
   large and the stabilization interval relatively short.  The self-
   tuning mechanisms described in this document are especially designed
   for overlays of the latter type.  Therefore, when the self-tuning
   mechanisms are used, each peer MUST send a periodic Update request
   only to its first predecessor and first successor on the Chord ring.

   The neighbor stabilization routine MUST be executed when the
   stabilization timer fires.  To begin the neighbor stabilization
   routine, a peer MUST send an Update request to its first successor
   and its first predecessor.  The type of the Update request MUST be
   'neighbors'.  The Update request MUST include the successor and
   predecessor lists of the sender.  If a peer receiving such an Update
   request learns from the predecessor and successor lists included in
   the request that new peers can be included in its neighborhood set,
   it MUST send Attach requests to the new peers.

   After a new peer has been added to the predecessor or successor list,



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   an Update request of type 'peer_ready' MUST be sent to the new peer.
   This allows the new peer to insert the sender into its neighborhood
   set.

5.3.  Finger Stabilization

   Chord-reload specifies two alternative methods for searching for new
   peers to the finger table.  Both of the alternatives can be used with
   the self-tuning extensions defined in this document.

   Immediately after a new peer has been added to the finger table, a
   Probe request MUST be sent to the new peer to fetch its uptime.  The
   requested_info field of the Probe request MUST be set to contain the
   ProbeInformationType 'uptime' defined in RELOAD base
   [I-D.ietf-p2psip-base].

5.4.  Adjusting Finger Table Size

   The chord-reload algorithm defines how a peer can make sure that the
   finger table is appropriately sized to allow for efficient routing.
   Since the self-tuning mechanisms specified in this document produce a
   network size estimate, this estimate can be directly used to
   calculate the optimal size for the finger table.  This mechanism MUST
   be used instead of the one specified by chord-reload.  A peer MUST
   use the network size estimate to determine whether it needs to adjust
   the size of its finger table each time when the stabilization timer
   fires.  The way this is done is explained in Section 6.2.

5.5.  Detecting Partitioning

   This document does not require any changes to the mechanism chord-
   reload uses to detect network partitioning.

5.6.  Leaving the Overlay

   As specified in RELOAD base [I-D.ietf-p2psip-base], a leaving peer
   SHOULD send a Leave request to all members of its neighbor table
   prior to leaving the overlay.  The overlay_specific_data field MUST
   contain the ChordLeaveData structure.  The Leave requests that are
   sent to successors MUST contain the predecessor list of the leaving
   peer.  The Leave requests that are sent to the predecessors MUST
   contain the successor list of the leaving peer.  If a given successor
   can identify better predecessors than are already included in its
   predecessor lists by investigating the predecessor list it receives
   from the leaving peer, it MUST send Attach requests to them.
   Similarly, if a given predecessor identifies better successors by
   investigating the successor list it receives from the leaving peer,
   it MUST send Attach requests to them.



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6.  Self-tuning Chord Parameters

   This section specifies how to determine an appropriate stabilization
   rate and routing table size in an adaptive fashion.  The proposed
   mechanism is based on [mahajan2003], [liben-nowell2002], and
   [ghinita2006].  To calculate an appropriate stabilization rate, the
   values of three parameters MUST be estimated: overlay size N, failure
   rate U, and join rate L. To calculate an appropriate routing table
   size, the estimated network size N can be used.  Peers in the overlay
   MUST re-calculate the values of the parameters to self-tune the
   chord-reload algorithm at the end of each stabilization period before
   re-starting the stabilization timer.

6.1.  Estimating Overlay Size

   Techniques for estimating the size of an overlay network have been
   proposed for instance in [mahajan2003], [horowitz2003],
   [kostoulas2005], [binzenhofer2006], and [ghinita2006].  In Chord, the
   density of peer identifiers in the neighborhood set can be used to
   produce an estimate of the size of the overlay, N [mahajan2003].
   Since peer identifiers are picked randomly with uniform probability
   from the numBitsInNodeId-bit identifier space, the average distance
   between peer identifiers in the successor set is
   (2^numBitsInNodeId)/N.

   To estimate the overlay network size, a peer MUST compute the average
   inter-peer distance d between the successive peers starting from the
   most distant predecessor and ending to the most distant successor in
   the successor list.  The estimated network size MUST be calculated
   as:

                         2^numBitsInNodeId
                    N = -------------------
                                d

   This estimate has been found to be accurate within 15% of the real
   network size [ghinita2006].  Of course, the size of the neighborhood
   set affects the accuracy of the estimate.

   During the join process, a joining peer fills its routing table by
   sending a series of Ping and Attach requests, as specified in RELOAD
   base [I-D.ietf-p2psip-base].  Thus, a joining peer immediately has
   enough information at its disposal to calculate an estimate of the
   network size.







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6.2.  Determining Routing Table Size

   As specified in RELOAD base, the finger table must contain at least
   16 entries.  When the self-tuning mechanisms are used, the size of
   the finger table MUST be set to max(log2(N), 16) using the estimated
   network size N.

   The size of the successor list MUST be set to log2(N).  An
   implementation MAY place a lower limit on the size of the successor
   list.  As an example, the implementation might require the size of
   the successor list to be always at least three.

   A peer MAY choose to maintain a fixed-size predecessor list with only
   three entries as specified in RELOAD base.  However, it is
   RECOMMENDED that a peer maintains log2(N) predecessors.

6.3.  Estimating Failure Rate

   A typical approach is to assume that peers join the overlay according
   to a Poisson process with rate L and leave according to a Poisson
   process with rate parameter U [mahajan2003].  The value of U can be
   estimated using peer failures in the finger table and neighborhood
   set [mahajan2003].  If peers fail with rate U, a peer with M unique
   peer identifiers in its routing table should observe K failures in
   time K/(M*U).  Every peer in the overlay MUST maintain a history of
   the last K failures.  The current time MUST be inserted into the
   history when the peer joins the overlay.  The estimate of U MUST be
   calculated as:

                             k
                     U = --------,
                          M * Tk

   where M is the number of unique peer identifiers in the routing
   table, Tk is the time between the first and the last failure in the
   history, and k is the number of failures in the history.  If k is
   smaller than K, the estimate MUST be computed as if there was a
   failure at the current time.  It has been shown that an estimate
   calculated in a similar manner is accurate within 17% of the real
   value of U [ghinita2006].

   The size of the failure history K affects the accuracy of the
   estimate of U. One can increase the accuracy by increasing K.
   However, this has the side effect of decreasing responsiveness to
   changes in the failure rate.  On the other hand, a small history size
   may cause a peer to overreact each time a new failure occurs.  In
   [ghinita2006], K is set 25% of the routing table size.  Use of this
   approach is RECOMMENDED.



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6.3.1.  Detecting Failures

   A new failure MUST be inserted to the failure history in the
   following cases:

   1.  A Leave request is received from a neigbhor.
   2.  A peer fails to reply to a Ping request sent in the situation
       explained below.  If no packets have been received on a
       connection during the past 2*Tr seconds (where Tr is the
       inactivity timer defined by ICE [I-D.ietf-mmusic-ice]), a RELOAD
       Ping request MUST be sent to the remote peer.  RELOAD mandates
       the use of STUN [RFC5389] for keepalives.  STUN keepalives take
       the form of STUN Binding Indication transactions.  As specified
       in ICE [I-D.ietf-mmusic-ice], a peer sends a STUN Binding
       Indication if there has been no packet sent on a connection for
       Tr seconds.  Tr is configurable and has a default of 15 seconds.
       Although STUN Binding Indications do not generate a response, the
       fact that a peer has failed can be learned from the lack of
       packets (Binding Indications or application protocol packets)
       received from the peer.  If the remote peer fails to reply to the
       Ping request, the sender MUST consider the remote peer to have
       failed.

   As an alternative to relying on STUN keepalives to detect peer
   failure, a peer could send additional, frequent RELOAD messages to
   every peer in its Connection Table.  These messages could be Update
   requests, in which case they would serve two purposes: detecting peer
   failure and stabilization.  However, as the cost of this approach can
   be very high in terms of bandwidth consumption and traffic load,
   especially in large-scale overlays experiencing churn, its use is NOT
   RECOMMENDED.

6.4.  Estimating Join Rate

   Reference [ghinita2006] proposes that a peer can estimate the join
   rate based on the uptime of the peers in its routing table.  An
   increase in peer join rate will be reflected by a decrease in the
   average age of peers in the routing table.  Thus, each peer MUST
   maintain an array of the ages of the peers in its routing table
   sorted in increasing order.  Using this information, an estimate of
   the global peer join rate L MUST be calculated as:

                         N           1
                    L = --- * ---------------,
                         4     Ages[rsize/4]

   where Ages is an array containing the ages of the peers in the
   routing table sorted in increasing order and rsize is the size of the



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   routing table.  It is RECOMMENDED that only the ages of the 25% of
   the youngest peers in the routing table (i.e., the 25th percentile)
   are used to reduce the bias that a small number of peers with very
   old ages can cause [ghinita2006].  It has been shown that the
   estimate obtained by using this method is accurate within 22% of the
   real join rate [ghinita2006].  Of course, the size of the routing
   table affects the accuracy.

   In order for this mechanism to work, peers need to exchange
   information about the time they have been present in the overlay.
   Peers receive the uptimes of their successors and predecessors during
   the stabilization operations since all Update requests carry uptime
   values.  A joining peer learns the uptime of the admitting peer since
   it receives an Update from the admitting peer during the join
   procedure.  Peers learn the uptimes of new fingers since they can
   fetch the uptime using a Probe request after having attached to the
   new finger.

6.5.  Estimate Sharing

   To improve the accuracy of network size, join rate, and leave rate
   estimates, peers MUST share their estimates.  When the stabilization
   timer fires, a peer MUST select number-of-peers-to-probe random peers
   from its finger table and send each of them a Probe request.  The
   targets of Probe requests are selected from the finger table rather
   than from the neighbor table since neighbors are likely to make
   similar errors when calculating their estimates. number-of-peers-to-
   probe is a new element in the overlay configuration document.  It is
   defined in Section 7 and has a default value of 4.  Both the Probe
   request and the answer returned by the target peer MUST contain a new
   message extension whose MessageExtensionType is 'self_tuning_data'.
   This extension type is defined in Section 9.1.  The
   extension_contents field of the MessageExtension structure MUST
   contain a SelfTuningData structure:

               struct {
                 uint32                   network_size;
                 uint32                   join_rate;
                 uint32                   leave_rate;
               } SelfTuningData;


   The contents of the SelfTuningData structure are as follows:








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   network_size
      The latest network size estimate calculated by the sender.

   join_rate
      The latest join rate estimate calculated by the sender.

   leave_rate
      The latest leave rate estimate calculated by the sender.


   The join and leave rates are expressed as joins or failures per 24
   hours.  As an example, if the global join rate estimate a peer has
   calculated is 0.123 peers/s, it would include in the join_rate field
   the value 10627 (24*60*60*0.123 = 10627.2).

   The 'type' field of the MessageExtension structure MUST be set to
   contain the value 'self_tuning_data'.  The 'critical' field of the
   structure MUST be set to False.

   A peer MUST store all estimates it receives in Probe requests and
   answers during a stabilization interval.  When the stabilization
   timer fires, the peer MUST calculate the estimates to be used during
   the next stabilization interval by taking the 75th percentile of a
   data set containing its own estimate and the received estimates.

6.6.  Calculating the Stabilization Interval

   According to [liben-nowell2002], a Chord network in a ring-like state
   remains in a ring-like state as long as peers send Omega(log2^2(N))
   messages before N new peers join or N/2 peers fail.  We can use the
   estimate of peer failure rate, U, to calculate the time Tf in which
   N/2 peers fail:

                                  1
                           Tf = ------
                                 2*U

   Based on this estimate, a stabilization interval Tstab-1 MUST be
   calculated as:

                                         Tf
                           Tstab-1 = -----------
                                      log2^2(N)

   On the other hand, the estimated join rate L can be used to calculate
   the time in which N new peers join the overlay.  Based on the
   estimate of L, a stabilization interval Tstab-2 MUST be calculated
   as:



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                                             N
                            Tstab-2 = ---------------
                                       L * log2^2(N)

   Finally, the actual stabilization interval Tstab that MUST be used
   can be obtained by taking the minimum of Tstab-1 and Tstab-2.

   The results obtained in [maenpaa2009] indicate that making the
   stabilization interval too small has the effect of making the overlay
   less stable (e.g., in terms of detected loops and path failures).
   Thus, a lower limit should be used for the stabilization period.
   Based on the results in [maenpaa2009], a lower limit of 15s is
   RECOMMENDED, since using a stabilization period smaller than this
   will with a high probability cause too much traffic in the overlay.


7.  Overlay Configuration Document Extension

   This document extends the RELOAD overlay configuration document by
   adding one new element, "number-of-peers-to-probe", inside each
   "configuration" element.

   self-tuning:number-of-peers-to-probe:  The number of fingers to which
      Probe requests are sent to obtain their network size, join rate,
      and leave rate estimates.  The default value is 4.

   This new element is formally defined as follows:

   namespace self-tuning = "urn:ietf:params:xml:ns:p2p:self-tuning"

   parameter &= element self-tuning:number-of-peers-to-probe { xsd:
   unsignedInt }

   This namespace is added into the <mandatory-extension&rt; element in
   the overlay configuration file.


8.  Security Considerations

   There are no new security considerations introduced in this document.
   The security considerations of RELOAD [I-D.ietf-p2psip-base] apply.


9.  IANA Considerations







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9.1.  Message Extensions

   This document introduces one additional extension to the "RELOAD
   Extensions" Registry:

                  +------------------+-------+---------------+
                  | Extension Name   |  Code | Specification |
                  +------------------+-------+---------------+
                  | self_tuning_data |     1 |      RFC-AAAA |
                  +------------------+-------+---------------+


   The contents of the extension are defined in Section 6.5.


10.  References

10.1.  Normative References

   [I-D.ietf-mmusic-ice]
              Rosenberg, J., "Interactive Connectivity Establishment
              (ICE): A Protocol for Network Address Translator (NAT)
              Traversal for Offer/Answer Protocols",
              draft-ietf-mmusic-ice-19 (work in progress), October 2007.

   [I-D.ietf-p2psip-base]
              Jennings, C., Lowekamp, B., Rescorla, E., Baset, S., and
              H. Schulzrinne, "REsource LOcation And Discovery (RELOAD)
              Base Protocol", draft-ietf-p2psip-base-21 (work in
              progress), March 2012.

   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119, March 1997.

   [RFC5389]  Rosenberg, J., Mahy, R., Matthews, P., and D. Wing,
              "Session Traversal Utilities for NAT (STUN)", RFC 5389,
              October 2008.

10.2.  Informative References

   [CAN]      Ratnasamy, S., Francis, P., Handley, M., Karp, R., and S.
              Schenker, "A scalable content-addressable network", In
              Proc. of the 2001 Conference on Applications,
              Technologies, Architectures and Protocols for Computer
              Communications 2001, pp. 161.172.

   [Chord]    Stoica, I., Morris, R., Liben-Nowell, D., Karger, D.,
              Kaashoek, M., Dabek, F., and H. Balakrishnan, "Chord: A



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              Scalable Peer-to-peer Lookup Service for Internet
              Applications", IEEE/ACM Transactions on Networking Volume
              11, Issue 1, 17-32, Feb 2003.

   [I-D.ietf-p2psip-concepts]
              Bryan, D., Willis, D., Shim, E., Matthews, P., and S.
              Dawkins, "Concepts and Terminology for Peer to Peer SIP",
              draft-ietf-p2psip-concepts-04 (work in progress),
              October 2011.

   [Pastry]   Rowstron, A. and P. Druschel, "Pastry: Scalable,
              Decentralized Object Location and Routing for Large-Scale
              Peer-to-Peer Systems", In Proc. of the IFIP/ACM
              International Conference on Distribued Systems
              Platforms Nov. 2001, pp. 329-350.

   [binzenhofer2006]
              Binzenhofer, A., Kunzmann, G., and R. Henjes, "A scalable
              algorithm to monitor chord-based P2P systems at runtime",
              20th International Parallel and Distributed Processing
              Symposium April 2006.

   [ghinita2006]
              Ghinita, G. and Y. Teo, "An adaptive stabilization
              framework for distributed hash tables", 20th International
              Parallel and Distributed Processing Symposium April 2006.

   [horowitz2003]
              Horowitz, K. and D. Malkhi, "Estimating network size from
              local information", Information Processing Letters Dec.
              2003, Volume 88, Issue 5, pp. 237-243.

   [kostoulas2005]
              Kostoulas, D., Psaltoulis, D., Gupta, I., Birman, K., and
              A. Demers, "Decentralized schemes for size estimation in
              large and dynamic groups", Fourth IEEE International
              Symposium on Network Computing and Applications July 2005,
              pp. 41-48.

   [krishnamurthy2008]
              Krishnamurthy, S., El-Ansary, S., Aurell, E., and S.
              Haridi, "Comparing maintenance strategies for overlays",
              In Proc. of 16th Euromicro Conference on Parallel,
              Distributed and Network-Based Processing Feb. 2008, pp.
              473-482.

   [li2004]   Li, J., Strinbling, J., Gil, T., and M. Kaashoek,
              "Comparing the performance of distributed hash tables



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              under churn", In Proc. of the 3rd International Workshop
              on Peer-to-Peer Systems 2004.

   [liben-nowell2002]
              Liben-Nowell, D., Balakrishnan, H., and D. Karger,
              "Observations on the dynamic evolution of peer-to-peer
              networks", In Proc. of the First International Workshop on
              Peer-to-Peer Systems March 2002.

   [maenpaa2009]
              Maenpaa, J. and G. Camarillo, "A study on maintenance
              operations in a Chord-based Peer-to-Peer Session
              Initiation Protocol overlay network", In Proc. of IPDPS
              2009 May 2009.

   [mahajan2003]
              Mahajan, R., Castro, M., and A. Rowstron, "Controlling the
              cost of reliability in peer-to-peer overlays", In
              Proceedings of the 2nd International Workshop on Peer-to-
              Peer Systems Feb. 2003.

   [rhea2004]
              Rhea, S., Geels, D., Roscoe, T., and J. Kubiatowicz,
              "Handling churn in a DHT", In Proc. of the USENIX Annual
              Techincal Conference June 2004.


Authors' Addresses

   Jouni Maenpaa
   Ericsson
   Hirsalantie 11
   Jorvas  02420
   Finland

   Email: Jouni.Maenpaa@ericsson.com


   Gonzalo Camarillo
   Ericsson
   Hirsalantie 11
   Jorvas  02420
   Finland

   Email: Gonzalo.Camarillo@ericsson.com






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   Jani Hautakorpi
   Nokia Siemens Networks
   Linnoitustie 6
   Espoo  02600
   Finland

   Email: Jani.Hautakorpi@nsn.com












































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