Internet DRAFT - draft-zahariadis-ietf-roll-metrics-composition

draft-zahariadis-ietf-roll-metrics-composition



 



ROLL                                                 Th. Zahariadis, Ed.
Internet Draft                                                    TEIHAL
Intended Status: Informational                          P. Trakadas, Ed.
Expires: March 3, 2012                                              ADAE
                                                         August 31, 2011

        Design Guidelines for Routing Metrics Composition in LLN
           draft-zahariadis-ietf-roll-metrics-composition-01


Abstract

   This document specifies the guidelines for designing efficient
   composite routing metrics to be applied to the Routing for Low Power
   and Lossy Networks (RPL) routing protocol.


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
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Copyright and License Notice

   Copyright (c) 2011 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
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   the Trust Legal Provisions and are provided without warranty as
   described in the Simplified BSD License.



Table of Contents

   1  Introduction  . . . . . . . . . . . . . . . . . . . . . . . . .  3
     1.1  Terminology . . . . . . . . . . . . . . . . . . . . . . . .  4
     1.2  Motivation  . . . . . . . . . . . . . . . . . . . . . . . .  5
   2  Basic and Derived Metrics Properties and Rules  . . . . . . . .  5
     2.1  Metric Domain . . . . . . . . . . . . . . . . . . . . . . .  6
     2.2  Metric Operator . . . . . . . . . . . . . . . . . . . . . .  6
     2.3  Metric Order Relation . . . . . . . . . . . . . . . . . . .  6
   3  Applicability to RPL  . . . . . . . . . . . . . . . . . . . . .  7
     3.1  Lexical Metric Composition  . . . . . . . . . . . . . . . .  8
     3.2  Additive Metric Composition . . . . . . . . . . . . . . . .  8
   4  Composition Metrics Requirements  . . . . . . . . . . . . . . .  8
     4.1  Metrics MUST be well-defined. . . . . . . . . . . . . . . .  8
     4.2  Metrics MUST reflect the basic characteristics of LLNs. . .  9
     4.3  Metrics MUST be orthogonal and not antagonistic.  . . . . . 11
     4.4  Metrics MUST exhibit continuity.  . . . . . . . . . . . . . 11
     4.5  Metrics MUST be scalable. . . . . . . . . . . . . . . . . . 11
     4.6  Metrics must have known and identified sources of
          inaccuracies and measurement uncertainties. . . . . . . . . 11
     4.7  Metrics MUST follow the same properties and rules.  . . . . 12
     4.8  Frequent metric values alterations SHALL NOT lead to 
          routing inconsistencies.  . . . . . . . . . . . . . . . . . 13
     4.9  Composite metric MUST hold properties of isotonicity and 
          monotonicity. . . . . . . . . . . . . . . . . . . . . . . . 15
     4.10  Metrics MUST be normalized.  . . . . . . . . . . . . . . . 17
   5  Conclusion  . . . . . . . . . . . . . . . . . . . . . . . . . . 17
   6  Security Considerations . . . . . . . . . . . . . . . . . . . . 17
   7  IANA Considerations . . . . . . . . . . . . . . . . . . . . . . 17
   8  Acknowledgement . . . . . . . . . . . . . . . . . . . . . . . . 17
   9  References  . . . . . . . . . . . . . . . . . . . . . . . . . . 18
     9.1  Normative References  . . . . . . . . . . . . . . . . . . . 18
     9.2  Informative References  . . . . . . . . . . . . . . . . . . 18
   Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 19






 


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1  Introduction

   Low Power and Lossy Networks (LLNs) have specific routing
   requirements, as described in [RFC5548], [RFC5673], [RFC5826], and
   [RFC5867]. In these RFCs, several (and sometimes contradicting)
   requirements are set by each application domain. In order to cope
   with them, a number of routing metrics and constraints has been
   spelled out in [I-D.ietf-roll-routing-metrics], consisting of
   link/node, qualitative/quantitative, static/dynamic metrics and
   constraints. According to [I-D.ietf-roll-rpl], these metrics and
   constraints are carried in objects that are OPTIONAL within RPL
   messages.

   Path computation algorithms for single metrics have already been
   proposed and used in current Internet Drafts [I-D.ietf-roll-of0], and
   [I-D.ietf-roll-minrank-hysteresis-of].

   For providing Quality-of-Service (QoS) routing in future
   applications, the Objective Function (OF) and Rank value might be
   built upon a composite metric, consisting of several basic and
   derived metrics, as defined in [I-D.ietf-roll-routing-metrics].

   The intention of this document is to set the guidelines for the
   proper selection of basic and derived metrics as well as the design
   of composite routing metrics for LLNs, taking into consideration the
   theoretical framework of [Sobrinho], as refined by [Yang]. Thus, the
   main target of this document is to examine the properties that
   routing metrics must hold to provide convergence, optimality and
   loop-freeness for the RPL routing protocol. In this way, each node
   will select the shortest path (or shortest constraint path, in the
   presence of constraints).

   The document does not intend to provide one composite metric that
   fits all cases, but rather to sketch out the guidelines for designing
   appropriate composite metrics, in line with specific application
   requirements. The purpose of this document is to provide a common
   framework for various classes of metrics that are composed of basic
   metrics.

   The effectiveness and performance of composite metrics used for IP
   performance evaluation is beyond the scope of this document and can
   be found in [RFC2330], [RFC5835] and [RFC6049].

   Finally, it is assumed that the reader is familiar with the concepts
   of [I-D.ietf-roll-rpl] and [I-D.ietf-roll-routing-metrics].



 


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1.1  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 RFC2119 [RFC2119].

   This document makes use of the terminology defined in [I-D.ietf-roll-
   terminology]. Moreover, this document defines the following terms, in
   accordance with [RFC5835] terminology:


   basic metric: a metric governed by specific rules and properties,
              capturing specific link or node characteristics. Examples
              of basic metrics are hop-count, ETX, LQL, etc.

   derived metric: a metric that is defined in terms of a basic metric,
              retaining the properties and rules of the basic metric.
              For example, (1-(1/ETX)) is an ETX derived metric, since
              it retains the rules and properties of the basic metric
              (ETX).

   composite metric: is defined as a routing metric consisting of
              several basic or/and derived metrics by applying a
              deterministic process or function (composition function).

   composition function: a deterministic process applied to primary
              and/or derived metrics to derive a composite metric.

   optimal path: is defined as a path in the DAG that minimizes (or
              maximizes, respectively) the Rank value between any given
              pair of source-destination nodes, as well as its sub-
              paths.

   sub-path: is defined as any portion of the path traversed between any
              given pair of source-destination nodes.

   path weight: a value representing link or/and node characteristics of
              a path. This definition coincides with 'path cost' defined
              in [I-D.ietf-roll-minrank-hysteresis-of]. Path weight is
              used by RPL to compare different paths.

   metric order relation: is used for path weight comparison with the
              same source and destination nodes, leading to the next hop
              neighbor selection. For example: '>' (greater than) is an
              order relation.

   metric operator: is used for the transformation of link and node
              weights into path weights. As an example, addition '+' is
 


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              defined as a metric operator.

1.2  Motivation

   Different metrics are defined to capture different link and node
   characteristics of a path. For example, some metrics capture network
   latency, some others take into account energy consumption of a node,
   while others focus on link reliability. The diversity of RPL routing
   protocol application domains, as described in [RFC5548], [RFC5673],
   [RFC5826], and [RFC5867] motivate the design of different composite
   routing metrics to cope with different routing application
   requirements.

   However, the selection of basic and derived metrics to design an
   efficient composite metric is neither an arbitrary nor a trivial
   task. Combining routing metrics of different types may lead to
   routing loops or selection of non-optimal paths.

   This document presents the guidelines for designing QoS routing
   strategies set by different applications, by identifying the
   properties that a composite metric must hold in order to work
   seamlessly with RPL routing protocol.

2  Basic and Derived Metrics Properties and Rules

   Routing metrics are the representation of an LLN in routing process.
   Thus, they might result in major implications on the complexity of
   optimal path computation, the existence of optimal path and the range
   of application requirements that can be supported.

   Path computation algorithms using one basic metric have been widely
   used in the literature and practice [I-D.ietf-roll-of0], [I-D.ietf-
   roll-minrank-hysteresis-of]. However, in order to support a wide
   range of QoS requirements dictated by different application domains,
   several routing metric forming a composite metric must be taken into
   account.

   RPL is a distance vector based, hop-by-hop routing protocol that
   builds Directed Acyclic Graphs (DAG) based on routing metrics and
   constraints. Following the routing algebra formalism presented in
   [Sobrinho] and [Yang], routing metrics must hold specific properties
   (isotonicity and monotonicity) in order to fulfil routing protocol
   requirements (convergence, optimality, and loop-freeness).

   In the following sections, basic metrics are examined and categorized
   according to their properties and rules. This exercise will provide
   useful information for the composition of efficient composite
   metrics.
 


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2.1  Metric Domain

   Basic metrics are defined in different domains. For example, Hop-
   Count (HP) has the value of 1 (per-hop), while ETX is defined in [1,
   512] and LQL in [0, 7], where 0 means undetermined, 1 indicates the
   highest and 7 the lowest link quality. Intuitively, the selection of
   the basic metrics to derive a composite metric MUST take into account
   the domain of each one of the selected basic metrics. This can be
   achieved by defining derived metrics, as will be explained later in
   this document. 

2.2  Metric Operator

   According to [I-D.ietf-roll-routing-metrics], a metric can either be
   recorded or aggregated along the path. In the former case, the metric
   can be of maximum type (A=0x01) or minimum type (A=0x02), while in
   the latter case, a metric can be of additive type (A=0x00) or
   multiplicative type (A=0x03).

   Let w(i,j) be the metric value for link and node characteristics
   between nodes i and j. Then, for any path p(i,j,k,...,q,r), we define
   that:

   - a metric is additive if: w(p)=w(i,j)+w(j,k)+...+w(q,r),

   - a metric is multiplicative if: w(p)=w(i,j)*w(j,k)*...*w(q,r),

   - a metric is concave if: w(p)=max[w(i,j),w(j,k),...,w(q,r)] or
   w(p)=min[w(i,j),w(j,k),...,w(q,r)].

   Metrics differ in the aggregation rule they follow. As an example, HP
   and ETX are defined as additive metrics, while RSSI is a
   multiplicative metric. Moreover, representative examples of concave
   metrics are Throughput and Bandwidth.

   Thus, the composite metric must also take into account the metric
   operators of the selected basic/derived metrics.

2.3  Metric Order Relation

   Another categorization of basic metrics is derived from the fact that
   some are 'maximizable' (the higher value, the better) while others
   are 'minimizable' (the lower value, the better). For example, a node
   selects as its DODAG parent the neighboring node that advertises (via
   DIO messages) the minimum hop-count (or aggregated ETX) value to
   reach DAG root node. On the other hand, if the Objective Function is
   based on RSSI (or Throughput) values, then the maximum value will
   lead the process of the DODAG parent selection.
 


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   In Figure 1, the properties and rules for some well-known basic
   metrics used in LLNs are presented.

    +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 
    | Metric      | Domain         | Aggregation Rule |Order Relation | 
    +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 
    | Hop-count   | 1              | additive         |  <            | 
    | ETX         | [1,512]*128    | additive         |  <            | 
    | LQL         | [0,7]          | concave (max.)   |  < (excl. 0)  | 
    | Latency     | 32-bit integer | addition         |  <            | 
    | Throughput  | 32-bit integer | concave (min.)   |  >            | 
    | RSSI        | [0,255]        | multiplicative   |  >            | 
    | Packet Loss%| [0,1]          | multiplicative   |  <            | 
    | Rem. Energy%| [0,1]          | concave (min.)   |  >            | 
    +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   Figure 1. Properties and rules of basic routing metrics used in LLNs.

   The properties and rules for the majority of routing metrics shown in
   this Figure follow the description presented in [I-D.ietf-roll-
   routing-metrics]. However, it is important to mention that a routing
   metric MAY follow different properties and rules. As an example,
   remaining energy percentage MAY also be defined as multiplicative
   (metric operator) with '>' as a metric order relation. The same
   remark applies to Link Color metric.

3  Applicability to RPL

   According to [I-D.ietf-roll-rpl], Objective Function (OF) defines how
   routing metrics, optimization objectives and related functions are
   used to compute Rank. Furthermore, OF dictates how parents in the
   DODAG are selected and thus the DODAG formation is defined by OF.

   On the other hand, Rank defines the node's individual position
   relative to other nodes with respect to a DODAG root. Rank strictly
   increases in the Down direction (towards leaf nodes) and strictly
   decreases in the Up direction (towards root node). The exact way Rank
   is computed, depends on the DAG's OF, as mentioned earlier.

   Furthermore, according to [I-D.ietf-roll-rpl], minHopRankIncrease
   value is defined as the minimum increase in Rank between a node and
   any of its DODAG parents, while maxRankIncrease is defined as the
   maximum value increase that a given node can advertise within the
   same DODAG version.

   There are two distinct approaches to follow, regarding the usability
   of multiple basic or derived routing metrics into one composite
   metric in RPL routing protocol, namely the lexical metric composition
   and the additive metric composition.
 


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3.1  Lexical Metric Composition

   According to the lexical metric composition approach, when comparing
   two composite metric values, the node will select as a DODAG parent
   the node with the lower (or greater, respectively) value of the first
   composition metric, and if the first component values are equal (or
   differ less than a predefined threshold) then it will select the one
   with the lower (or greater, respectively) value of the second
   composition metric. Some examples of well-known composite lexical
   metrics used in IP networks are 'widest-shortest' path, that selects
   the widest path among the set of shortest paths between the source
   and the destination node, and 'most reliable-shortest' path, that
   selects the most reliable path among the set of shortest paths.

   This is totally in line with the "Prec" field carried within the DAG
   Metric Container Object defined in [I-D.ietf-roll-rpl] and [I-
   D.ietf.roll-routing-metrics] that indicates the precedence of each
   routing metric (or constraint) present in the Objective Function.

3.2  Additive Metric Composition

   According to the additive metric composition, the Rank is evaluated
   based on a defined OF (composition function) and advertised through
   the DIO message. Moreover, the values of the basic metrics are
   aggregated along the path and are included in the DAG Metric
   Container Object.

   This approach is also compatible with RPL specifications, since
   according to [I-D.ietf-roll-routing-metrics], in this case the
   relevant flags of the DAG Metric Container Object must be: C = 0, O =
   0, A = 0x00, and R = 0.

4  Composition Metrics Requirements

   As discussed in the previous section, the selection of the basic
   routing metrics for designing a composite metric is not
   straightforward for the routing solution to fulfil routing protocol
   requirements (convergence, optimality, loop-freeness). In this
   section the composition metrics requirements will be examined,
   followed by explanatory text or representative examples, to guide
   prospective routing protocol designs and implementations.

4.1  Metrics MUST be well-defined. 

   For applying an efficient composite metric, all basic or derived
   metrics must be well-defined. The use of new or not thoroughly tested
   basic metrics SHALL be avoided.

 


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4.2  Metrics MUST reflect the basic characteristics of LLNs.

   Each network has its own unique characteristics. As an example, a
   fundamental concern in ad-hoc networks consists on link reliability
   and node mobility, while in IP networks, bandwidth and latency are of
   great importance. In LLNs, the resource constraints of nodes demand
   primarily for energy conservation, link stability and traffic load
   balance. Thus, the basic metrics selected for defining a composite
   metric must be analyzed towards capturing the fundamental
   characteristics of LLNs. In the following, two simple examples are
   analyzed, where the composite metric consists of Hop-Count (HP) and
   ETX metric. 

   +-------------------------------------------------------------------+
   |                                (A) <0 , 1.0>                      |
   |                                / \                                |
   |                               /   \                               |
   |                              /     \                              |
   |                         1.3 /       \ 1.2                         |
   |                            /         \                            |
   |                           /           \                           |
   |                          /             \                          |
   |              <1 , 1.3> (B)             (C) <1 , 1.2>              |
   |                         |\_          _/ |                         |
   |                         |  \_      _/   |                         |
   |                         | 1.5\_  _/1.6  |                         |
   |                     1.3 |      \/       | 1.3                     |
   |                         |     _/\_      |                         |
   |                         |   _/    \_    |                         |
   |                         | _/        \_  |                         |
   |                        (D)             (E)                        |
   |      w(A,B,D) = <2 , 3.6>               w(A,C,E) = <2 , 3.5>      |
   |      w(A,C,D) = <2 , 3.8>               w(A,B,E) = <2 , 3.8>      |
   +-------------------------------------------------------------------+
   Figure 2: Example of a simple composite metric consisting of HP and
   ETX metrics.

   Example 1: Consider the LLN depicted in Figure 2, where the metrics
   taken into account are HP and ETX, as described above. Both metrics
   are added along the path and these values are advertised through DIO
   messages. The parentheses present the HP and ETX values,
   respectively.

   It is evident that if one applies an OF based on the lexical
   composition of these two metrics (either 'shortest-most reliable' or
   'most reliable-shortest'), node D will select node B as its parent,
   while node E will select node C as its parent in both lexical cases.

 


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   Similarly, by using the additive metric composition approach in the
   form of w=(a1*HP)+(a2*ETX), node D will select B as its parent and
   node E will select C for any combination of a1 and a2 values (given
   that 0<=a1,a2<=1 and a1+a2=1). 

   Example 2: As a second example, consider the (slightly) more complex
   LLN depicted in Figure 3. Again, consider applying HP and ETX
   metrics, added along the traversed paths. This example demonstrates
   the dependency of the parent selection process dictated by the OF
   composition function.

   +-------------------------------------------------------------------+
   |                                (A) <0 , 1.0>                      |
   |                                / \                                |
   |                               /   \                               |
   |                              /     \                              |
   |                         1.2 /       \ 1.2                         |
   |                            /         \                            |
   |                           /           \                           |
   |                          /             \                          |
   |              <1 , 1.2> (B)             (C) <1 , 1.2>              |
   |                          \              |                         |
   |                           \             | 1.1                     |
   |                            \            |                         |
   |                         2.8 \          (E) <2 , 2.3>              |
   |                              \        /                           |
   |                               \     _/ 1.1                        |
   |                                \  /                               |
   |                                 (D)                               |
   |                         w(A,B,D) = <2 , 5.0>                      |
   |                       w(A,C,E,D) = <3 , 4.4>                      |
   +-------------------------------------------------------------------+
   Figure 3: Dependency of routing process dictated by different OF's.

   If the 'shortest-most reliable' lexical metric composition is chosen,
   then node D will select node E as its parent, although the traversed
   path is not the shortest one. On the contrary, if the 'most reliable-
   shortest' lexical metric composition approach is chosen, then node D
   will select node B as its parent, although the traversed path is not
   the most reliable.

   Accordingly, following the additive metric composition of the form
   (a1*HP)+(a2*ETX) implies that if (a1,a2)=(0.8,0.2), then node D will
   select node B as its parent, while in case that (a1,a2)=(0.2,0.8),
   node D will select node E as its parent.



 


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4.3  Metrics MUST be orthogonal and not antagonistic. 

   Orthogonality means that no redundant information is carried within
   different basic metrics. As an example, the use of RSSI and LQL for
   metric composition is not a wise option, since they capture the same
   LLN characteristic; link reliability. In this way, less computational
   burden (and possibly fewer message exchange) will be achieved.

   Moreover, the utilization of antagonistic metrics must be avoided. As
   antagonistic metrics can be defined those metrics that eliminate the
   effects of one another. As an example, by definition Hop-Count
   includes a sense of 'greediness', while LQL partially eliminates this
   characteristic, since it promotes the most stable links. Assuming
   that all nodes use the same transmission power level, then a node,
   based on RSSI metric, will (most probably) select as parent node the
   neighbor closer to it.

4.4  Metrics MUST exhibit continuity.

   That is, small variations in metric values, MUST result in small
   variations in the composite metric value. This requirement is more
   related to derived metrics. Special attention must be paid so that
   the derived metrics do not produce either instabilities or
   inconsistencies.

4.5  Metrics MUST be scalable.

   A composite metric must be able to scale to large LLNs (or even
   Internet). This requirement is relevant to path computation
   complexity, since the complexity of the path computation is
   determined by the composition rules of the metric. Especially in
   LLNs, this requirement is of great importance, taking into account
   that the computational power of LLN nodes is constrained.

4.6  Metrics must have known and identified sources of inaccuracies and
   measurement uncertainties.

   Most of the basic metrics are prone to inaccuracies. A representative
   example is LQL, as defined in [I-D.ietf-roll-routing-metrics],
   defined in [0,7] domain. Only seven discrete values are used for LQL
   quantification (0 is excluded). Thus, a range of link quality values
   will be represented by the same LQL value. In other words, when such
   metrics are used, the sources of inaccuracies must be, at least,
   identified.




 


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4.7  Metrics MUST follow the same properties and rules.

   As described above, the combination of metrics retaining different
   properties and rules may lead to routing instabilities and selection
   of non-optimal paths. So, the basic routing metrics with different
   properties must be transformed to derived metrics holding the same
   properties in order to be used for metric composition. For example,
   in case that ETX ([1,512], '+', '<') is used in conjunction to the
   node remaining energy percentage (RE) ([0,1], '*', '>'), then a
   derived metric must be used for the remaining energy (e.g. 1/RE).
   With this transformation, both metrics are defined at the same
   domain, they are additive, and are using '<' as the order relation.

   Example 3: Consider the LLN depicted in Figure 4, where the metrics
   taken into consideration are ETX and Remaining Energy percentage,
   shown as <ETX, RE>. Also, each node has a remaining energy
   percentage, as shown in the parenthesis next to each node, e.g. node
   B has a remaining energy percentage value of 0.8, while node C has a
   remaining energy percentage value equal to 1.0.

   +-------------------------------------------------------------------+
   |                           (1.0)(A) <1.0 , 1.0>                    |
   |                                / \                                |
   |                               /   \                               |
   |                              /     \                              |
   |                         1.2 /       \ 1.1                         |
   |                            /         \                            |
   |                           /           \                           |
   |                          /             \                          |
   |             <2.2 , 0.8> (B)(0.8)   (1.0)(C) <2.1 , 1.0>           |
   |                          \              |                         |
   |                           \             | 1.2                     |
   |                            \            |                         |
   |                         2.2 \     (0.6)(E) <3.3 , 0.6>            |
   |                              \        /                           |
   |                               \   ___/ 1.2                        |
   |                                \ /                                |
   |                                (D)(0.7)                           |
   |                         w(A,B,D) = <4.4 , 0.56> (4.4+0.56=4.96)   |
   |                       w(A,C,E,D) = <4.5 , 0.42> (4.5+0.42=4.92)   |
   +-------------------------------------------------------------------+
   Figure 4: Composition of metrics with different properties and rules.

   Applying the two lexical metric composition approaches (ETX or RE
   precedence), node D will select node B as its parent in both cases.

   Furthermore, consider that one applies the additive metric
   composition rule ETX+RE and selects the parent based on the '<' order
 


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   relation. In this case, node D will select node E as its parent,
   since w(A,B,D)=4.4+0.56=4.96 > w(A,C,E,D)=4.5+0.42=4.92. This results
   in from the different properties and rules governing these two basic
   metrics.

   A possible solution might be the transformation of RE metric in such
   a way that metric range, operator and order relation of the derived
   RE metric coincides with ETX's. This can be achieved by defining the
   derived RE metric, denoted as dRE, as the inverse of RE (1/RE),
   defined in the range [1.935*10^-3,1]. In this way, dRE shares the
   same metric range with ETX, namely [1, 512]. Furthermore, the dRE
   order relation is '<' and the metric operator is '+'.

   By applying dRE at the composition function and calculating Rank at
   node D, it is evident that node B will be selected as node D's parent
   since (w(A,B,D)=4.4+(1/0.56)=6.1857 <
   w(A,C,E,D)=4.5+(1/0.42)=6.881).

4.8  Frequent metric values alterations SHALL NOT lead to routing
   inconsistencies.

   This requirement applies mostly to dynamic metrics. In case that
   dynamic metrics are participating in the OF, then frequent routing
   alterations may result in, which is undesirable since it may lead to
   routing instabilities or loops. As a solution, a hysteresis factor
   can be used in this case in order to reduce frequent routing path
   alterations due to dynamic metric values.

   +-------------------------------------------------------------------+
   |                           (1.0)(A) <0 , 1.0>                      |
   |                                / \                                |
   |                               /   \                               |
   |                              /     \                              |
   |                             /       \                             |
   |                            /         \                            |
   |                           /           \                           |
   |                          /             \                          |
   |              <1 , 0.8> (B)(0.8)  (0.79)(C) <1 , 0.79>             |
   |                          \             /                          |
   |                           \           /                           |
   |                            \         /                            |
   |                             \       /                             |
   |                              \     /                              |
   |                               \   /                               |
   |                                \ /                                |
   |                                (D)(0.7)                           |
   +-------------------------------------------------------------------+
   Figure 5: Implication of dynamic metric inclusion in a composite
 


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   lexical approach.

   Example 4: Consider the simple LLN topology depicted in Figure 5,
   where the OF consists of HP and RE metrics, following the lexical
   metric composition approach (HP, RE).

   In this case, node D will select node B as its parent to forward
   traffic data packets, since w(A,B,D)>w(A,C,D). Furthermore,
   considering that the cost of forwarding a data packet reduces the RE
   percentage by 0.02, then the metric values at the next DIO
   transmission of node B will be <1, 0.78>, while the next DIO
   transmission of node C will be <1,0.79>. These advertised values will
   lead node D to select node C as its parent node and thus forward next
   traffic data packet through node C.

   Apparently, node D alters its parent selection on a per-packet basis,
   which may lead to routing inconsistencies (viewed in a larger scale).
   One solution to this issue MIGHT be the introduction of the
   hysteresis factor, where the node will switch to another parent only
   if its path value exceeds the minimum path value by a predefined
   threshold, as described in [I-D.ietf-roll-minrank-hysteresis-of].

   Example 5: As a second example, consider the LLN depicted in Figure
   6. The applied composite metric uses ETX and RE.

   +-------------------------------------------------------------------+
   |                           (1.0)(A) <1.0 , 1.0>                    |
   |                                / \                                |
   |                               /   \                               |
   |                              /     \                              |
   |                       (1.3) /       \ (1.3)                       |
   |                            /         \                            |
   |                           /           \                           |
   |                          /             \                          |
   |            <2.3 , 0.8> (B)(0.8)  (0.79)(C) <2.3 , 0.79>           |
   |                          \             /                          |
   |                           \           /                           |
   |                            \         /                            |
   |                       (1.4) \       / (1.3)                       |
   |                              \     /                              |
   |                               \   /                               |
   |                                \ /                                |
   |                                (D)(0.7)                           |
   |                        w(A,B,D) = <3.7 , 0.56>                    |
   |                        w(A,C,D) = <3.6 , 0.55>                    |
   +-------------------------------------------------------------------+
   Figure 6: An advantage of additive metric composition compared to
   lexical metric composition approach.
 


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   This example will demonstrate an advantage of additive metric
   composition compared to lexical metric composition.

   Consider applying lexical metric composition of the precedence vector
   (ETX, RE). Assuming that ETX values do not change, then node D is
   always selecting node B as its DODAG parent, leading node B to energy
   depletion.

   On the contrary, setting proper values in the additive metric
   composition function of the form (a1*ETX)+(a2*RE), remaining energy
   percentage value is taken into consideration and after a number of
   interactions (data traffic forwarding) with node B, node D will
   switch to node C as its parent. Obviously, the frequency of this
   switching process is directly proportional to the values of a1 and
   a2.

4.9  Composite metric MUST hold properties of isotonicity and
   monotonicity.

   Monotonicity means that the path weight increases when prefixed or
   suffixed by another path (or link). A routing metric is monotonic if
   and only if w(a)<=w(a&b) and w(a)<=w(c&a) (where '&' denotes the
   metric operator) for any paths a,b,c. Moreover, the routing metric is
   right-monotonic if only the former inequality holds, and left-
   monotonic if only the latter inequality holds. Finally, a routing
   metric is defined as strictly monotonicity if both w(a)<w(a&b) and
   w(a)<w(c&a) hold. If the routing metric is monotonic, then
   convergence and loop-freeness of the routing protocol is ensured.

   Moreover, the isotonicity property essentially means that a routing
   metric should ensure that the order of the weights of two paths is
   preserved if they are appended or prefixed by a common third path. In
   mathematical form, a routing metric is isotonic if and only if
   w(a)<=w(b) implies both w(a&c)<=w(b&c) and w(c&a)<=w(c&b) for all
   paths a,b,c. In accordance to monotonicity, left-, right- and strict
   isotonicity can be defined, respectively. If the algebra is isotonic,
   then the paths onto which routing protocols converge are optimal.

   According to [Yang], RPL, as a distance vector based, hop-by-hop
   routing protocol must be left-monotonic and left-isotonic in order to
   fulfil the routing algebra requirements of convergence, optimality
   and loop-freeness.

   Example 6: Consider the LLN topology, as shown in Figure 7. The basic
   metrics taken into consideration are Latency and Throughput.

   Latency metric (L) is defined as the sum of the transmission
   latencies along the path to the root node for a fixed-size packet.
 


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   The source node selects as its parent the node advertising path with
   minimum latency value. In other words, the metric operator is '+' and
   the metric order relation is '<'.

   Throughput metric (T) is defined as the minimum throughput value
   along the path to the root. The source node will select as its parent
   the node advertising the maximum value of path throughput. Thus, for
   this metric: the metric operator is 'min' and the metric order
   relation is 'max'.

   In this example, the composite metric is defined as (L + T) with '<'
   as the composite metric order relation.

   Since the contribution of any path increases the non-negative
   composite metric value and one is minimizing along the non-decreasing
   paths, the metric satisfies the property of monotonicity.

   On the contrary, isotonicity does not hold for this composite metric.
   

   +-------------------------------------------------------------------+
   |                                (A) <1 , 10>                       |
   |                                / \                                |
   |                               /   \                               |
   |                              /     \                              |
   |                             /       \                             |
   |                            /         \                            |
   |                           /           \                           |
   |                          /             \                          |
   |                <3 , 2> (B)             (C) <2 , 9>                |
   |                          \             /                          |
   |                           \           /                           |
   |                            \         /                            |
   |                             \       /                             |
   |                              \     /                              |
   |                               \   /                               |
   |                                \ /                                |
   |                        <2 , 8> (D) w(A,B,D) = <6 , 2> = 8         |
   |                                 |  w(A,C,D) = <5 , 8> = 13        |
   |                                 |                                 |
   |                                 |                                 |
   |                        <6 , 2> (E) w(A,B,D,E) = <12 , 2> = 14     |
   |                                    w(A,C,D,E) = <11 , 2> = 13     |
   +-------------------------------------------------------------------+
   Figure 7: Non-isotonic routing metric leads to non-optimal paths
   selection.

   Calculating path values, it is straightforward that node D will
 


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   select node B as its parent node, since w(A,B,D)<w(A,C,D). Adding
   link D-E, then w(A,B,D,E)>w(A,C,D,E). Thus isotonicity does not hold
   for the composite metric (L + T) as defined in this example. The
   implication of this can be seen from the following example: The
   optimal path for the pair of source-destination A-D is A-B-D, while
   the optimal path for the pair of A-E is A-C-D-E, according to
   composite metric under examination. Thus, optimality of traversed
   paths is not guaranteed.

4.10  Metrics MUST be normalized.

   In case that an additive composite metric is used in conjunction with
   weighting factors for providing better QoS characteristics according
   to different applications, normalization of basic or derived metrics
   MUST take place. Considering a composite metric consisting of ETX and
   RE, the normalization process yields that a composition function can
   be defined as: a1*(1-(1/ETX))+a2*(1-RE). In this case, both metrics
   are defined in [0,1], are additive and 'minimizable'.Furthermore, if
   RSSI participates in the composite metric, then RSSI must become an
   additive metric by applying the logarithmic properties and then used
   in the form of the following derived metric: a3*(1/log(RSSI)).

5  Conclusion

   As explained in this document, the composition of several basic or
   derived routing metrics into a composite routing metric is a
   challenging problem.

   Thus, the goal of this document is to describe the framework for
   routing metrics composition properties and mechanisms, providing
   guidelines for the proper selection and composition of basic metrics
   into composite metrics for applicability to RPL routing protocol.

   This has been achieved by examining issues related to composing a
   routing metric, subject to multiple basic and derived metrics.

6  Security Considerations

   No new considerations are raised  this document.

7  IANA Considerations

   This document includes no request to IANA.

8  Acknowledgement

   The work presented in this I-D is partially supported by the EU-
   funded FP7-ICT-257245 VITRO project. Apart form this, the European
 


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   Commission has no responsibility for the content of this document.

9  References

9.1  Normative References


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

   [I-D.ietf-roll-routing-metrics] Vasseur, J., Kim, M., Pister, K.,
              Dejean, N., and D. Barthel, "Routing Metrics used for Path
              Calculation in Low Power and Lossy Networks", draft-ietf-
              roll-routing-metrics-19, March 2011.

   [I-D.ietf-roll-rpl]  Winter, T., Thubert, P., Brandt, A., Clausen,
              T., Hui, J., Kelsey, R., Levis, P., Pister, K., Struik,
              R., and JP. Vasseur, "RPL: IPv6 Routing Protocol for Low
              Power and Lossy Networks", draft-ietf-roll-rpl-19, March
              2011.

   [I-D.ietf-roll-of0]  Thubert, P., "RPL Objective Function 0", draft-
              ietf-roll-of0-07, March 2011.

   [I-D.ietf-roll-minrank-hysteresis-of]  Gnawali, O., and P. Levis,
              "The Minimum Rank Objective Function with Hysteresis",
              draft-ietf-roll-minrank-hysteresis-of-02, September 2010.

9.2  Informative References


   [I-D.ietf-roll-terminology]  Vasseur, J., "Terminology in Low Power
              and Lossy Networks", draft-ietf-roll-terminology-04 (work
              in progress), September 2010.

   [RFC2330]  Paxson, V., Almes, G., Mahdavi, J., and M. Mathis,
              "Framework for IP Performance Metrics", RFC2330, May 1998.

   [RFC5548]  Dohler, M., Watteyne, T., Winter, T., and D. Barthel,
              "Routing Requirements for Urban Low-Power and Lossy
              Networks", RFC 5548, May 2009.

   [RFC5673]  Pister, K., Thubert, P., Dwars, S., and T. Phinney,
              "Industrial Routing Requirements in Low-Power and Lossy
              Networks", RFC 5673, October 2009.

   [RFC5826]  Brandt, A., Buron, J., and G. Porcu, "Home Automation
              Routing Requirements in Low-Power and Lossy Networks", RFC
 


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              5826, April 2010.

   [RFC5835]  Morton, A., and S. Van der Berghe, "Framework for Metric
              Composition", RFC5835, April 2010.

   [RFC5867]  Martocci, J., De Mil, P., Riou, N., and W. Vermeylen,
              "Building Automation Routing Requirements in Low-Power and
              Lossy Networks", RFC 5867, June 2010.

   [RFC6049]  Morton, A., and E. Stephan, "Spatial Composition of
              Metrics", RFC 6049, January 2011.

   [Sobrinho] J. Sobrinho, "Network Routing with Path Vector Protocols:
              Theory and Applications", ACM SIGCOMM, 2003, pp. 49-60.

   [Yang]     Yang, Y., and J. Wang, "Design Guidelines for Routing
              Metrics in Multihop Wireless Networks", IEEE INFOCOM 2008,
              pp. 1615-1623.

Authors' Addresses

   Theodore Zahariadis (editor)
   Technological Educational Institute of Halkida (TEIHAL)
   Psachna, Evia, 34400, Greece.

   EMail: zahariad@teihal.gr


   Panos Trakadas (editor)
   Hellenic Authority for Communications Security and Privacy (ADAE)
   3, Ierou Lochou, str, 15125, Greece.

   EMail: trakadasp@adae.gr


















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