Internet DRAFT - draft-zahariadis-roll-metrics-composition
draft-zahariadis-roll-metrics-composition
ROLL Th. Zahariadis, Ed.
Internet Draft TEIHAL
Intended Status: Informational P. Trakadas, Ed.
Expires: May 27, 2013 ADAE
November 23, 2012
Design Guidelines for Routing Metrics Composition in LLN
draft-zahariadis-roll-metrics-composition-04
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.
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carefully, as they describe your rights and restrictions with respect
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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 Trust-Aware Routing Metric . . . . . . . . . . . . . . . . . . 7
3.1 Packets Forwarding Indication . . . . . . . . . . . . . . . 8
4 Applicability to RPL . . . . . . . . . . . . . . . . . . . . . 8
4.1 Lexical Metric Composition . . . . . . . . . . . . . . . . 9
4.2 Additive Metric Composition . . . . . . . . . . . . . . . . 9
5 Composition Metrics Requirements . . . . . . . . . . . . . . . 9
5.1 Metrics MUST be well-defined. . . . . . . . . . . . . . . . 10
5.2 Metrics MUST reflect the basic characteristics of LLNs. . . 10
5.3 Metrics MUST be orthogonal and not antagonistic. . . . . . 12
5.4 Metrics MUST exhibit continuity. . . . . . . . . . . . . . 12
5.5 Metrics MUST be scalable. . . . . . . . . . . . . . . . . . 12
5.6 Metrics must have known and identified sources of
inaccuracies and measurement uncertainties. . . . . . . . . 12
5.7 Metrics MUST follow the same properties and rules. . . . . 13
5.8 Frequent metric values alterations SHALL NOT lead to
routing inconsistencies. . . . . . . . . . . . . . . . . . 14
5.9 Composite metric MUST hold properties of isotonicity and
monotonicity. . . . . . . . . . . . . . . . . . . . . . . . 16
6. Generic Rules for Metrics Composition . . . . . . . . . . . . . 18
7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 19
8 Security Considerations . . . . . . . . . . . . . . . . . . . . 20
9 IANA Considerations . . . . . . . . . . . . . . . . . . . . . . 20
10 Acknowledgement . . . . . . . . . . . . . . . . . . . . . . . 20
11 References . . . . . . . . . . . . . . . . . . . . . . . . . . 20
11.1 Normative References . . . . . . . . . . . . . . . . . . . 20
11.2 Informative References . . . . . . . . . . . . . . . . . . 21
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 22
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1 Introduction
Low Power and Lossy Networks (LLNs) have specific routing
requirements, as described in [RFC5548], [RFC5673], [RFC5826],
[RFC5867], and [I-D.ietf-roll-applicability-ami]. 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 [RFC6551], consisting
of link/node, qualitative/quantitative, static/dynamic metrics and
constraints. According to [RFC6550], 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 [RFC6552], 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 [RFC6551].
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 [RFC6550] and [RFC6551].
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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
defined as a metric operator.
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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], [RFC5867], and [I-D.ietf-roll-applicability-ami] 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 [RFC6552], [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 metrics 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 [RFC6551], a metric can either be recorded or aggregated
along the path. In the latter case, the metric can be of maximum type
(A=0x01), minimum type (A=0x02), 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 Throughput and
Bandwidth are representative examples of concave metrics.
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.
In Figure 1, the properties and rules for some well-known basic
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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 | additive | < |
| Throughput | 32-bit integer | concave (min.) | > |
| RSSI | [0,255] | additive | > |
| 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 [RFC6551]. 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 additive (metric operator) with '>' as a metric
order relation. The same remark applies to Link Color metric.
Moreover, some of the abovementioned link or node metrics may also be
used by RPL as constraints. In such cases, if a link or a node does
not satisfy a required constraint, it is excluded from the candidate
neighbor set, leading to a constrained shortest path (NP-complete
problem). However, this draft mainly focuses on setting the
requirements for optimal path selection, among several paths
satisfying all supplied constraints (if any).
3 Trust-Aware Routing Metric
Cooperation among nodes in LLNs raises high concerns regarding
security issues. Most solutions available in the literature try to
secure networking operations using traditional security techniques,
such as encryption and key management. However, the implementation of
such security measures comes at a high cost, since it requires
significant memory and processing resources, increasing at the same
time the energy consumption. To defend against a number of routing
attacks, an alternative but rather efficient approach is trust
management. Following this approach, LLN nodes establish trust
relations based on their expectation that their neighbors will
sincerely cooperate on particular tasks (data forwarding). This
concept allows one to define and utilize a trust-aware routing metric
for the selection of the routing path.
Although this issue has been extensively discussed in the literature,
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no attention has been paid on the definition of a trust-aware metric
for LLNs, that can be directly and efficiently combined with other
metrics, fulfilling routing metrics properties and thus ensuring
routing protocol requirements, as discussed above.
3.1 Packets Forwarding Indication
Packets Forwarding Indication (PFI) is defined as an effective trust-
aware routing metric, capable of capturing the forwarding willingness
of the neighboring nodes. Following the concept of ETX, PFI is
defined as the inverse probability that node B will forward a packet
received coming from node A and is expressed as PFI(A,B)=Ns/Nt, where
Ns is the number of successfully forwarded packets (originating from
node A) by node B, and Nt is the total number of packets that node A
sent to node B for further forwarding. Thus, PFI expresses the
expected number of transmissions required for a packet to reach its
destination (edge router) when denial of forwarding occurs (e.g.
black-hole, grey-hole attack). As a result, PFI calculated for a path
is subject to the reaction of a node's perception in terms of a
neighbor's forwarding willingness. Specifically, PFI path weights
depend on the capability of re-transmitting every packet that has not
been further forwarded.
According to the analysis presented in [Velivasaki], PFI can be
considered either as an additive routing metric, defined in [1,+inf],
or as a multiplicative metric that fulfills the routing algebra
requirements for strict isotonicity and strict monotonicity and thus
can be combined with other routing metrics as will be discussed
below.
4 Applicability to RPL
According to [RFC6550], 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 [RFC6550], 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.
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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.
4.1 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 [RFC6550] and [RFC6551] that
indicates the precedence of each routing metric (or constraint)
present in the Objective Function.
4.2 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 [RFC6551], in this case the relevant flags of the DAG
Metric Container Object must be: C = 0, O = 0, A = 0x00, and R = 0.
5 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.
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5.1 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.
5.2 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) <1 , 1.0> |
| / \ |
| / \ |
| / \ |
| 1.3 / \ 1.2 |
| / \ |
| / \ |
| / \ |
| <2 , 1.3> (B) (C) <2 , 1.2> |
| |\_ _/ | |
| | \_ _/ | |
| | 1.5\_ _/1.6 | |
| 1.3 | \/ | 1.3 |
| | _/\_ | |
| | _/ \_ | |
| | _/ \_ | |
| (D) (E) |
| w(A,B,D) = <3 , 3.6> w(A,C,E) = <3 , 3.5> |
| w(A,C,D) = <3 , 3.8> w(A,B,E) = <3 , 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.
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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.
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) <1 , 1.0> |
| / \ |
| / \ |
| / \ |
| 1.2 / \ 1.2 |
| / \ |
| / \ |
| / \ |
| <2 , 1.2> (B) (C) <2 , 1.2> |
| \ | |
| \ | 1.1 |
| \ | |
| 2.8 \ (E) <3 , 2.3> |
| \ / |
| \ _/ 1.1 |
| \ / |
| (D) |
| w(A,B,D) = <3 , 5.0> |
| w(A,C,E,D) = <4 , 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
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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.
5.3 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 RSSI 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.
5.4 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.
5.5 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.
5.6 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 [RFC6551], 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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5.7 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).
5.8 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.
Example 4: Consider the simple LLN topology depicted in Figure 5,
where the OF consists of HP and (concave) 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 <2 , 0.78>, while the next DIO
transmission of node C will be <2 , 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].
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+-------------------------------------------------------------------+
| (1.0)(A) <1 , 1.0> |
| / \ |
| / \ |
| / \ |
| / \ |
| / \ |
| / \ |
| / \ |
| <2 , 0.8> (B)(0.8) (0.79)(C) <2 , 0.79> |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| (D)(0.7) |
+-------------------------------------------------------------------+
Figure 5: Implication of dynamic metric inclusion in a composite
lexical approach.
Example 5: As a second example, consider the LLN depicted in Figure
6. The applied composite metric uses ETX and RE.
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.
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+-------------------------------------------------------------------+
| (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.
5.9 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 monotonic 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
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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.
Thus, each node selects as its parent the node advertising path with
minimum aggregated 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. Under this metric, each 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 + (1/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.
Calculating path values, it is straightforward that node D selects
node B as its parent node, since w(A,B,D)<w(A,C,D), sending (via DIO
Metric Container) the pair of values <6 , 0.8> to node E. Having node
D as its only potential parent, node E will recalculate Latency and
Throughput values and transmit the pair of path values <11 , 0.3>,
although it can be computed that w(A,B,D,E)>w(A,C,D,E). Finally,
comparing the pair of values received by nodes E and G, node H will
select node G as its parent and route traffic through the path H-G-F-
A. However, according to this composite metric the optimal path is
the one traversing H-E-D-C-A. This stems from the fact that the
optimal path for the pair of source-destination nodes A-D is A-B-D,
while the optimal path for the pair of A-E is A-C-D-E.
This example proves that utilizing a composite metric that does not
satisfy the property of isotonicity (L + (1/T) in this case) may lead
to the selection of a non-optimal path.
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+-------------------------------------------------------------------+
| -------------(A) <1 , 1.0> |
| / / \ |
| / / \ |
| (6 , 0.9)/ (3 , 0.8)/ \(2 , 0.3) |
| / / \ |
| / / \ |
| / / \ |
| / / \ |
| <6 , 0.9>(F) <4 , 0.8>(B) (C) <3 , 0.3> |
| | \ / |
| (5 , 0.6)| \ / |
| | (2 , 0.8)\ /(2 , 0.8) |
| | \ / |
|<12 , 0.6>(G) \ / |
| | \ / |
| | \ / |
| | (D) w(A,B,D) = <6 , 0.8> = 7.25 |
| | | w(A,C,D) = <5 , 0.3> = 8.33 |
| \ (5 , 0.3)| |
| \ | |
| \ <6 , 2> (E) w(A,B,D,E) = <11 , 0.3> = 14.33|
| \ ----------/ w(A,C,D,E) = <10 , 0.3> = 13.33|
| (2 , 0.8)\ /(2 , 0.8) |
| \ / |
| (H) w(A,F,G,H) = <14 , 0.6> = 15.66 |
| w(A,B,D,E,H) = <13 , 0.3> = 16.33 |
| w(A,C,D,E,H) = <12 , 0.3> = 15.33 |
| |
+-------------------------------------------------------------------+
Figure 7: Adoption of a non-isotonic routing metric leads to non-
optimal paths selection.
6. Generic Rules for Metrics Composition
Taking into consideration the composition metrics requirements
discussed above, this section provides generic composition rules that
must be used during combination of basic or derived metrics to
achieve convergence, optimality and loop-freeness for the RPL routing
protocol.
1. Any two basic or derived metrics can be combined in the lexical
approach given that the metric to be used first in this composition
is strictly isotonic. As an example, HP and ETX can be used in any
precedence to define a composite metric that guarantees routing
algebra requirements (monotonicity and isotonicity). Moreover,
latency and packet loss percentage (being additive and multiplicative
metrics, respectively) can be combined in a lexical composition
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function.
2. Two additive routing metrics can be composed in an additive
manner, given that they follow the same properties and rules (namely
metric operator and metric order relation). A simple example could be
the utilization of a composition function of the form a1*HP+a2*ETX.
The question arising is whether multiplicative metrics can also be
used in such an approach. Consider, for example, a reliability metric
such as packet loss percentage. By applying logarithmic function to
this basic metric, one can define a derived metric that follows the
additive metric operator and share the same order relation with ETX.
By properly modifying the metric domain of the newly derived metric,
a combination with ETX can be achieved under the additive metric
composition.
From the abovementioned rules, it is obvious that lexical approach is
less restrictive, offering combinations among a plethora of additive,
multiplicative and concave metrics, according to user or application-
specific requirements. On the other hand, combining routing metrics
in an additive manner is more demanding in terms of mathematical
formulation. However, achieving to define a composite routing metric
under the additive approach is advantageous since it offers the
flexibility to set proper values to the weighting factors of the
composed metrics and thus satisfy quality of service requirements
according to user demand. On the contrary, following the lexical
approach, such flexibility is not possible since the metric used
first in lexical approach is dominating over the second metric.
Concluding, as a general rule of thumb, in cases where maximization
in terms of a specific metric is required while the second metric is
used only as a tie-break, lexical approach is to be used. On the
contrary, in cases where two link or node characteristics must be
captured in a more balanced manner, the utilization of the additive
composition approach is advantageous.
7 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.
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8 Security Considerations
No new considerations are raised this document.
9 IANA Considerations
This document includes no request to IANA.
10 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
Commission has no responsibility for the content of this document.
11 References
11.1 Normative References
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119, March 1997.
[RFC6550] 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", March 2012.
[RFC6552] Thubert, P., "RPL Objective Function 0", draft-ietf-roll-
of0-20 (work in progress), March 2012.
[RFC6551] Vasseur, J., Kim, M., Pister, K., Dejean, N., and D.
Barthel, "Routing Metrics used for Path Calculation in Low
Power and Lossy Networks", March 2012.
[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-10 (work in
progress), April 2012.
[I-D.ietf-roll-applicability-ami] Popa, D., Jetcheva, J., Dejean,
N., Salazar, R., Hui, J., and K. Monden, "Applicability
Statement for the Routing Protocol for Low Power and Lossy
Networks (RPL) in AMI Networks", draft-ietf-roll-
applicability-ami-06 (work in progress), April 2012.
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11.2 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
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.
[Velivasaki] Velivasaki, T-H. N., Karkazis, P., Zahariadis, Th. V.,
Trakadas, P. T., Capsalis, C. N., "Trust-Aware and Link-
Reliable Routing Metric Composition for Wireless Sensor
Networks", Transactions on Emerging Telecommunications
Technologies,
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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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