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RFC 6687 - Performance Evaluation of the Routing Protocol for Lo


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Independent Submission                                  J. Tripathi, Ed.
Request for Comments: 6687                           J. de Oliveira, Ed.
Category: Informational                                Drexel University
ISSN: 2070-1721                                         JP. Vasseur, Ed.
                                                     Cisco Systems, Inc.
                                                            October 2012

                         Performance Evaluation
     of the Routing Protocol for Low-Power and Lossy Networks (RPL)

Abstract

   This document presents a performance evaluation of the Routing
   Protocol for Low-Power and Lossy Networks (RPL) for a small outdoor
   deployment of sensor nodes and for a large-scale smart meter network.
   Detailed simulations are carried out to produce several routing
   performance metrics using these real-life deployment scenarios.
   Please refer to the PDF version of this document, which includes
   several plots for the performance metrics not shown in the plain-text
   version.

Status of This Memo

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

   This is a contribution to the RFC Series, independently of any other
   RFC stream.  The RFC Editor has chosen to publish this document at
   its discretion and makes no statement about its value for
   implementation or deployment.  Documents approved for publication by
   the RFC Editor are not a candidate for any level of Internet
   Standard; see Section 2 of RFC 5741.

   Information about the current status of this document, any errata,
   and how to provide feedback on it may be obtained at
   http://www.rfc-editor.org/info/rfc6687.

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
   carefully, as they describe your rights and restrictions with respect
   to this document.

Table of Contents

   1. Introduction ....................................................2
   2. Terminology .....................................................3
   3. Methodology and Simulation Setup ................................4
   4. Performance Metrics .............................................7
      4.1. Common Assumptions .........................................7
      4.2. Path Quality ...............................................7
      4.3. Routing Table Size ........................................10
      4.4. Delay Bound for P2P Routing ...............................10
      4.5. Control Packet Overhead ...................................11
      4.6. Loss of Connectivity ......................................13
   5. RPL in a Building Automation Routing Scenario ..................18
      5.1. Path Quality ..............................................18
      5.2. Delay .....................................................19
   6. RPL in a Large-Scale Network ...................................19
      6.1. Path Quality ..............................................19
      6.2. Delay .....................................................21
      6.3. Control Packet Overhead ...................................21
   7. Scaling Property and Routing Stability .........................22
   8. Comments .......................................................24
   9. Security Considerations ........................................25
   10. Acknowledgements ..............................................25
   11. Informative References ........................................25

1.  Introduction

   Designing a routing protocol for Low-Power and Lossy Networks (LLNs)
   imposes great challenges, mainly due to low data rates, high
   probability of packet delivery failure, and strict energy constraints
   in the nodes.  The IETF ROLL Working Group took on this task and
   specified the Routing Protocol for Low-Power and Lossy Networks (RPL)
   in [RFC6550].

   RPL is designed to meet the core requirements specified in [RFC5826],
   [RFC5867], [RFC5673], and [RFC5548].

   This document's contribution is to provide a performance evaluation
   of RPL with respect to several metrics of interest.  This is
   accomplished using real data and topologies in a discrete event
   simulator developed to reproduce the protocol behavior.

   The following metrics are evaluated:

   o  Path quality metrics, such as ETX path cost, ETX path stretch, ETX
      fractional stretch, and hop distance stretch, as defined in
      Section 2 ("Terminology");

   o  Control plane overhead;

   o  End-to-end delay between nodes;

   o  Ability to cope with unstable situations (link churns, node
      dying);

   o  Required resource constraints on nodes (routing table size).

   Some of these metrics are mentioned in the aforementioned RFCs,
   whereas others have been introduced to consider the challenges and
   unique requirements of LLNs as discussed in [RFC6550].  For example,
   routing in a home automation deployment has strict time bounds on
   protocol convergence after any change in topology, as mentioned in
   Section 3.4 of [RFC5826].  [RFC5673] requires bounded and guaranteed
   end-to-end delay for routing in an industrial deployment, and
   [RFC5548] requires comparatively loose bounds on latency for end-to-
   end communication.  [RFC5548] mandates scalability in terms of
   protocol performance for a network of size ranging from 10^2 to 10^4
   nodes.

   Although simulation cannot prove formally that a protocol operates
   properly in all situations, it can give a good level of confidence in
   protocol behavior in highly stressful conditions, if and only if
   real-life data are used.  Simulation is particularly useful when
   theoretical model assumptions may not be applicable to such networks
   and scenarios.  In this document, real deployed network data traces
   have been used to model link behaviors and network topologies.

2.  Terminology

   Please refer to [ROLL-TERMS] and [RFC6550] for terminology.  In
   addition, the following terms are specified:

   PDR:  Packet Delivery Ratio.

   CDF:  Cumulative Distribution Function.

   Expected Transmission Count (ETX Metric):  The expected number of
      transmissions to reach the next hop is determined as the inverse
      of the link PDR.  Consequently, in every hop, if the link quality
      (PDR) is high, the expected number of transmissions to reach the
      next hop may be as low as 1.  However, if the PDR for the
      particular link is low, multiple transmissions may be needed.

   ETX Path Cost:  The ETX path cost metric is determined as the
      summation of the ETX value for each link on the route a packet
      takes towards the destination.

   ETX Path Cost Stretch:  The ETX path cost stretch is defined as the
      difference between the number of expected transmissions (ETX
      Metric) taken by a packet traveling from source to destination,
      following a route determined by RPL and a route determined by a
      hypothetical ideal shortest path routing protocol (using link ETX
      as the metric).

   ETX Fractional Stretch (fractional stretch factor of link ETX metric
      against ideal shortest path):  The fractional path stretch is the
      ratio of ETX path stretch to ETX path cost for the shortest path
      route for the source-destination pair.

   Hop Distance Stretch (stretch factor for node hop distance against
      ideal shortest path):  The hop distance stretch is defined as the
      difference between the number of hops taken by a packet traveling
      from source to destination, following a route determined by RPL
      and by a hypothetical ideal shortest path algorithm, both using
      ETX as the link cost.  The fractional hop distance stretch is
      computed as the ratio of path stretch to count value between a
      source-destination pair for the hypothetical shortest path route
      optimizing ETX path cost.

3.  Methodology and Simulation Setup

   In the context of this document, RPL has been simulated using OMNeT++
   [OMNeTpp], a well-known discrete event-based simulator written in C++
   and NEtwork Description (NED).  Castalia-2.2 [Castalia-2.2] has been
   used as a Wireless Sensor Network Simulator framework within OMNeT++.
   The output and events in the simulation are visualized with the help
   of the Network AniMator, or NAM, which is distributed with the NS
   (Network Simulator) [NS-2].

   Note that no versions of the NS itself are used in this simulation
   study.  Only the visualization tool was borrowed for verification
   purposes.

   In contrast with theoretical models, which may have assumptions not
   applicable to lossy links, real-life data was used for two aspects of
   the simulations:

   *  Link Failure Model: Derived from time-varying real network traces
      containing packet delivery probability for each link, over all
      channels, for both indoor network deployment and outdoor network
      deployment.

   *  Topology: Gathered from real-life deployment (traces mentioned
      above) as opposed to random topology simulations.

   A 45-node topology, deployed as an outdoor network and shown in
   Figure 1, and a 2442-node topology, gathered from a smart meter
   network deployment, were used in the simulations.  In Figure 1, links
   between a most preferred parent node and child nodes are shown in
   red.  Links that are shown in black are also part of the topology but
   are not between a preferred parent and child node.

   Figure 1 [See the PDF.]

             Figure 1: Outdoor Network Topology with 45 Nodes.

   Note that this is just a start to validate the simulation before
   using large-scale networks.

   A set of time-varying link quality data was gathered from a real
   network deployment to form a database used for the simulations.  Each
   link in the topology randomly 'picks up' a link model (trace) from
   the database.  Each link has a Packet Delivery Ratio (PDR) that
   varies with time (in the simulation, a new PDR is read from the
   database every 10 minutes) according to the gathered data.  Packets
   are dropped randomly from that link with probability (1 - PDR).  Each
   time a packet is about to be sent, the module generates a random
   number using the Mersenne Twister random number generation method.
   The random number is compared to the PDR to determine whether the
   packet should be dropped.  Note that each link uses a different
   random number generator to maintain true randomness in the simulator
   and to avoid correlation between links.  Also, the packet drop
   applies to all kinds of data and control packets (RPL), such as the
   DIO, DAO, and DIS packets defined in [RFC6550].  Figure 2 shows a
   typical temporal characteristic of links from the indoor network
   traces used in the simulations.  The figure shows several links with
   perfect connectivity, some links with a PDR as low as 10%, and
   several for which the PDR may vary from 30% to 80%, sharply changing
   back and forth between a high value (strong connectivity) and a low
   value (weak connectivity).

   Figure 2 [See the PDF.]

                Figure 2: Example of Link Characteristics.

   In the RPL simulator, the LBR (LLN Border Router) or the Directed
   Acyclic Graph (DAG) root first initiates sending out DIO messages,
   and the DAG is gradually constructed.  RPL makes use of trickle
   timers: the protocol sets a minimum time period with which the nodes
   start re-issuing DAOs, and this minimum period is denoted by the
   trickle parameter Imin.  RPL also sets an upper limit on how many
   times this time period can be doubled; this is denoted by the
   parameter DIOIntervalDoublings, as defined in [RFC6550].  For the
   simulation, Imin is initially set to 1 second and
   DIOIntervalDoublings is equal to 16, and therefore the maximum time
   between two consecutive DIO emissions by a node (under a steady
   network condition) is 18.2 hours.  The trickle time interval for
   emitting DIO messages assumes the initial value of 1 second and then
   changes over simulation time, as mentioned in [RFC6206].

   Another objective of this study is to give insight to the network
   administrator on how to tweak the trickle values.  These
   recommendations could then be used in applicability statement
   documents.

   Each node in the network, other than the LBR or DAG root, also emits
   DAO messages as specified in [RFC6550], to initially populate the
   routing tables with the prefixes received from children via the DAO
   messages to support Point-to-Point (P2P) and Point-to-Multipoint
   (P2MP) traffic in the "down" direction.  During these simulations, it
   is assumed that each node is capable of storing route information for
   other nodes in the network (storing mode of RPL).

   For nodes implementing RPL, as expected, the routing table memory
   requirement varies according to the position in the DODAG
   (Destination-Oriented DAG).  The (worst-case) assumption is made that
   there is no route summarization (aggregation) in the network.  Thus,
   a node closer to the DAG will have to store more entries in its
   routing table.  It is also assumed that all nodes have equal memory
   capacity to store the routing states.

   For simulations of the indoor network, each node sends traffic
   according to a Constant Bit Rate (CBR) to all other nodes in the
   network, over the simulation period.  Each node generates a new data
   packet every 10 seconds.  Each data packet has a size of 127 bytes
   including 802.15.4 PHY/MAC headers and RPL packet headers.  All
   control packets are also encapsulated with 802.15.4 PHY/MAC headers.
   To simulate a more realistic scenario, 80% of the packets generated
   by each node are destined to the root, and the remaining 20% of the

   packets are uniformly assigned as destined to nodes other than the
   root.  Therefore, the root receives a considerably larger amount of
   data than other nodes.  These values may be revised when studying P2P
   traffic so as to have a majority of traffic going to all nodes as
   opposed to the root.  In the later part of the simulation, a typical
   home/building routing scenario is also simulated, and different path
   quality metrics are computed for that traffic pattern.

   The packets are routed through the DODAG built by RPL according to
   the mechanisms specified in [RFC6550].

   A number of RPL parameters are varied (such as the packet rate from
   each source and the time period for emitting a new DAG sequence
   number) to observe their effect on the performance metric of
   interest.

4.  Performance Metrics

4.1.  Common Assumptions

   As the DAO messages are used to feed the routing tables in the
   network, they grow with time and size of the network.  Nevertheless,
   no constraint was imposed on the size of the routing table nor on how
   much information the node can store.  The routing table size is not
   expressed in terms of Kbytes of memory usage but measured in terms of
   the number of entries for each node.  Each entry has the next-hop
   node and path cost associated with the destination node.

   The link ETX (Expected Transmission Count) metric is used to build
   the DODAG and is specified in [RFC6551].

4.2.  Path Quality

   Hop Count:  For each source-destination pair, the number of hops for
      both RPL and shortest path routing is computed.  Shortest path
      routing refers to a hypothetical ideal routing protocol that would
      always provide the shortest path in terms of ETX path cost (or
      whichever metric is used) in the network.

   The Cumulative Distribution Function (CDF) of the hop count for all
   paths (n * (n - 1) in an n-node network) in the network with respect
   to the hop count is plotted in Figure 3 for both RPL and shortest
   path routing.  One can observe that the CDF corresponding to 4 hops
   is around 80% for RPL and 90% for shortest path routing.  In other
   words, for the given topology, 90% of the paths have a path length of
   4 hops or less with an ideal shortest path routing methodology,
   whereas in RPL P2P routing, 90% of the paths will have a length of no
   more than 5 hops.  This result indicates that despite having a

   non-optimized P2P routing scheme, the path quality of RPL is close to
   an optimized P2P routing mechanism for the topology under
   consideration.  Another reason for this may relate to the fact that
   the DAG root is at the center of the network; thus, routing through
   the DAG root is often close to an optimal (shortest path) routing.
   This result may be different in a topology where the DAG root is
   located at one end of the network.

   Figure 3 [See the PDF.]

               Figure 3: CDF of Hop Count versus Hop Count.

   ETX Path Cost:  In the simulation, the total ETX path cost (defined
      in the Terminology section) from source to destination for each
      packet is computed.

   Figure 4 shows the CDF of the total ETX path cost, both with RPL and
   shortest path routing.  Here also one can observe that the ETX path
   cost from all sources to all destinations is close to that of
   shortest path routing for the network.

   Figure 4 [See the PDF.]

   Figure 4: CDF of Total ETX Path Cost along Path versus ETX Path Cost.

   Path Stretch:  The path stretch metric encompasses the stretch factor
      for both hop distance and ETX path cost (as defined in the
      Terminology section).  The hop distance stretch, which is
      determined as the difference between the number of hops taken by a
      packet while following a route built via RPL and the number of
      hops taken by shortest path routing (using link ETX as the
      metric), is computed.  The ETX path cost stretch is also provided.

   The CDF of both path stretch metrics is plotted against the value of
   the corresponding path stretch over all packets in Figures 5 and 6,
   for hop distance stretch and ETX path stretch, respectively.  It can
   be observed that, for a few packets, the path built via RPL has fewer
   hops than the ideal shortest path where path ETX is minimized along
   the DAG.  This is because there are a few source-destination pairs
   where the total ETX path cost is equal to or less than that of the
   ideal shortest path when the packet takes a longer hop count.  As the
   RPL implementation ignores a 20% change in total ETX path cost before
   switching to a new parent or emitting a new DIO, it does not
   necessarily provide the shortest path in terms of total ETX path
   cost.  Thus, this implementation yields a few paths with smaller hop
   counts but larger (or equal) total ETX path cost.

   Figure 5 [See the PDF.]

               Figure 5: CDF of Hop Distance Stretch versus
                        Hop Distance Stretch Value.

   Figure 6 [See the PDF.]

     Figure 6: CDF of ETX Path Stretch versus ETX Path Stretch Value.

   The data for the CDF of the hop count and ETX path cost for the ideal
   shortest path (SP) and a path built via RPL, along with the CDF of
   the routing table size, is given below in Table 1.  Figures 3 to 7
   relate to the data in this table.

   +---------+--------+---------+-----------+------------+-------------+
   |   CDF   |   Hop  |   Hop   |  ETX Cost |  ETX Cost  |   Routing   |
   |  (%age) |  (SP)  |  (RPL)  |    (SP)   |    (RPL)   |  Table Size |
   +---------+--------+---------+-----------+------------+-------------+
   |     0   |   1.0  |   1.0   |     1     |    1.0     |      0      |
   |     5   |   1.0  |   1.03  |     1     |    1.242   |      1      |
   |    10   |   2.0  |   2.0   |     2     |    2.048   |      2      |
   |    15   |   2.0  |   2.01  |     2     |    2.171   |      2      |
   |    20   |   2.0  |   2.06  |     2     |    2.400   |      2      |
   |    25   |   2.0  |   2.11  |     2     |    2.662   |      3      |
   |    30   |   2.0  |   2.42  |     2     |    2.925   |      3      |
   |    35   |   2.0  |   2.90  |     3     |    3.082   |      3      |
   |    40   |   3.0  |   3.06  |     3     |    3.194   |      4      |
   |    45   |   3.0  |   3.1   |     3     |    3.41    |      4      |
   |    50   |   3.0  |   3.15  |     3     |    3.626   |      4      |
   |    55   |   3.0  |   3.31  |     3     |    3.823   |      5      |
   |    60   |   3.0  |   3.50  |     3     |    4.032   |      6      |
   |    65   |   3.0  |   3.66  |     3     |    4.208   |      7      |
   |    70   |   3.0  |   3.92  |     4     |    4.474   |      7      |
   |    75   |   4.0  |   4.16  |     4     |    4.694   |      7      |
   |    80   |   4.0  |   4.55  |     4     |    4.868   |      8      |
   |    85   |   4.0  |   4.70  |     4     |    5.091   |      9      |
   |    90   |   4.0  |   4.89  |     4     |    5.488   |     10      |
   |    95   |   4.0  |   5.65  |     5     |    5.923   |     12      |
   |   100   |   5.0  |   7.19  |     9     |   10.125   |     44      |
   +---------+--------+---------+-----------+------------+-------------+

                        Table 1: Path Quality CDFs.

   Overall, the path quality metrics give us important information about
   the protocol's performance when minimizing the ETX path cost is the
   objective to form the DAG.  The protocol, as explained, does not
   always provide an optimum path, especially for peer-to-peer
   communication.  However, it does end up reducing the control overhead

   cost, thereby reducing unnecessary parent selection and DIO message
   forwarding events, by choosing a non-optimized path.  Despite this
   specific implementation technique, around 30% of the packets travel
   the same number of hops as an ideal shortest path routing mechanism,
   and 20% of the packets experience the same number of attempted
   transmissions to reach the destination.  On average, this
   implementation costs only a few extra transmission attempts and saves
   a large number of control packet transmissions.

4.3.  Routing Table Size

   The objective of this metric is to observe the distribution of the
   number of entries per node.  Figure 7 shows the CDF of the number of
   routing table entries for all nodes.  Note that 90% of the nodes need
   to store less than 10 entries in their routing table for the topology
   under study.  The LBR does not have the same power or memory
   constraints as regular nodes do, and hence it can accommodate entries
   for all the nodes in the network.  The requirement to accommodate
   devices with low storage capacity has been mandated in [RFC5673],
   [RFC5826], and [RFC5867].  However, when RPL is implemented in
   storing mode, some nodes closer to the LBR or DAG root will require
   more memory to store larger routing tables.

   Figure 7 [See the PDF.]

   Figure 7: CDF of Routing Table Size with Respect to Number of Nodes.

4.4.  Delay Bound for P2P Routing

   For delay-sensitive applications, such as home and building
   automation, it is critical to optimize the end-to-end delay.
   Figure 8 shows the upper bound and distributions of delay for paths
   between any two given nodes for different hop counts between the
   source and destination.  Here, the hop count refers to the number of
   hops a packet travels to reach the destination when using RPL paths.
   This hop distance does not correspond to the shortest path distance
   between two nodes.  Note that each packet has a length of 127 bytes,
   with a 240-kbps radio, which makes the transmission delay
   approximately 4 milliseconds (ms).

   Figure 8 [See the PDF.]

    Figure 8: Comparison of Packet Latency, for Different Path Lengths,
                          Expressed in Hop Count.

   RFCs 5673 [RFC5673] and 5548 [RFC5548] mention a requirement for the
   end-to-end delivery delay to remain within a bounded latency.  For
   instance, according to the industrial routing requirement,

   non-critical closed-loop applications may have a latency requirement
   that can be as low as 100 ms, whereas monitoring services may
   tolerate a delay in the order of seconds.  The results show that
   about 99% of the end-to-end communication (where the maximum hop
   count is 7 hops) is bounded within the 100-ms requirement, for the
   topology under study.  It should be noted that due to poor link
   condition, there may be packet drops triggering retransmission, which
   may cause larger end-to-end delivery delays.  Nodes in the proximity
   of the LBR may become congested at high traffic loads, which can also
   lead to higher end-to-end delay.

4.5.  Control Packet Overhead

   The control plane overhead is an important routing characteristic in
   LLNs.  It is imperative to bound the control plane overhead.  One of
   the distinctive characteristics of RPL is that it makes use of
   trickle timers so as to reduce the number of control plane packets by
   eliminating redundant messages.  The aim of this performance metric
   is thus to analyze the control plane overhead both in stable
   conditions (no network element failure overhead) and in the presence
   of failures.

   Data and control plane traffic comparison for each node:  Figure 9
      shows the comparison between the amount of data packets
      transmitted (including forwarded packets) and control packets (DIO
      and DAO messages) transmitted for all individual nodes when link
      ETX is used to optimize the DAG.  As mentioned earlier, each node
      generates a new data packet every 10 seconds.  Here one can
      observe that a considerable amount of traffic is routed through
      the DAG root itself.  The x axis indicates the node ID in the
      network.  Also, as expected, the nodes that are closer to the DAG
      root and that act as routers (as opposed to leaves) handle much
      more data traffic than other nodes.  Nodes 12, 36, and 38 are
      examples of nodes next to the DAG root, taking part in routing
      most of the data packets and hence having many more data packet
      transmissions than other nodes, as observed in Figure 9.  We can
      also observe that the proportion of control traffic is negligible
      for those nodes.  This result also reinforces the fact that the
      amount of control plane traffic generated by RPL is negligible on
      these topologies.  Leaf nodes have comparable amounts of data and
      control packet transmissions (they do not take part in routing the
      data).

   Figure 9 [See the PDF.]

     Figure 9: Amount of Data and Control Packets Transmitted against
                 Node Id Using Link ETX as Routing Metric.

   Data and control packet transmission with respect to time:  In
      Figures 10, 11, and 12, the amount of data and control packets
      transmitted for node 12 (low rank in DAG, closer to the root),
      node 43 (in the middle), and node 31 (leaf node) are shown,
      respectively.  These values stand for the number of data and
      control packets transmitted for each 10-minute interval for the
      particular node, to help understand what the ratio is between data
      and control packets exchanged in the network.  One can observe
      that nodes closer to the DAG root have a higher proportion of data
      packets (as expected), and the proportion of control traffic is
      negligible in comparison with the data traffic.  Also, the amount
      of data traffic handled by a node within a given interval varies
      largely over time for a node closer to the DAG root, because in
      each interval the destination of the packets from the same source
      changes, while 20% of the packets are destined to the DAG root.
      As a result, the pattern of the traffic that is handled changes
      widely in each interval for the nodes closer to the DAG root.  For
      the nodes that are farther away from the DAG root, the ratio of
      data traffic to control traffic is smaller, since the amount of
      data traffic is greatly reduced.

   The control traffic load exhibits a wave-like pattern.  The amount of
   control packets for each node drops quickly as the DODAG stabilizes,
   due to the effect of trickle timers.  However, when a new DODAG
   sequence is advertised (global repair of the DODAG), the trickle
   timers are reset and the nodes start emitting DIOs frequently again
   to rebuild the DODAG.  For a node closer to the DAG root, the amount
   of data packets is much larger than that of control packets and
   somewhat oscillatory around a mean value.  The amount of control
   packets exhibits a 'saw-tooth' behavior.  In the case where the ETX
   link metric is used, when the PDR changes, the ETX link metric for a
   node to its child changes, which may lead to choosing a new parent
   and changing the DAG rank of the child.  This event resets the
   trickle timer and triggers the emission of a new DIO.  Also, the
   issue of a new DODAG sequence number triggers DODAG re-computation
   and resets the trickle timers.  Therefore, one can observe that the
   number of control packets attains a high value for one interval and
   comes down to lower values for subsequent intervals.  The interval
   with a high number of control packets denotes the interval where the
   timers to emit a new DIO are reset more frequently.  As the network
   stabilizes, the control packets are less dense in volume.  For leaf
   nodes, the amount of control packets is comparable to that of data
   packets, as leaf nodes are more prone to face changes in their DODAG
   rank as opposed to nodes closer to the DAG root when the link ETX
   value in the topology changes dynamically.

   Figure 10 [See the PDF.]

         Figure 10: Amount of Data and Control Packets Transmitted
                               for Node 12.

   Figure 11 [See the PDF.]

         Figure 11: Amount of Data and Control Packets Transmitted
                               for Node 43.

   Figure 12 [See the PDF.]

         Figure 12: Amount of Data and Control Packets Transmitted
                               for Node 31.

4.6.  Loss of Connectivity

   Upon link failures, a node may lose its parents -- preferred and
   backup (if any) -- thus leading to a loss of connectivity (no path to
   the DAG root).  RPL specifies two mechanisms for DODAG repairs,
   referred to as global repair and local repair.  In this document,
   simulation results are presented to evaluate the amount of time data
   packets are dropped due to a loss of connectivity for the following
   two cases: a) when only using global repair (i.e., the DODAG is
   rebuilt thanks to the emission of new DODAG sequence numbers by the
   DAG root), and b) when using local repair (poisoning the sub-DAG in
   case of loss of connectivity) in addition to global repair.  The idea
   is to tune the frequency at which new DODAG sequence numbers are
   generated by the DAG root, and also to observe the effect of varying
   the frequency for global repair and the concurrent use of global and
   local repair.  It is expected that more frequent increments of DODAG
   sequence numbers will lead to a shorter duration of connectivity loss
   at a price of a higher rate of control packets in the network.  For
   the use of both global and local repair, the simulation results show
   the trade-off in amount of time that a node may remain without
   service and total number of control packets.

   Figure 13 shows the CDF of time spent by any node without service,
   when the data packet rate is one packet every 10 seconds and a new
   DODAG sequence number is generated every 10 minutes.  This plot
   reflects the property of global repair without any local repair
   scheme.  When all the parents are temporarily unreachable from a
   node, the time before it hears a DIO from another node is recorded,
   which gives the time without service.  We define the DAG repair timer
   as the interval at which the LBR increments the DAG sequence number,

   thus triggering a global re-optimization.  In some cases, this value
   might go up to the DAG repair timer value, because until a DIO is
   heard, the node does not have a parent and hence no route to the LBR
   or other nodes not in its own sub-DAG.  Clearly, this situation
   indicates a lack of connectivity and loss of service for the node.

   Figure 13 [See the PDF.]

         Figure 13: CDF: Loss of Connectivity with Global Repair.

   The effect of the DAG repair timer on time without service is plotted
   in Figure 14, where the source rate is 20 seconds/packet and in
   Figure 15, where the source sends a packet every 10 seconds.

   Figure 14 [See the PDF.]

            Figure 14: CDF: Loss of Connectivity for Different
           Global Repair Period, Source Rate 20 Seconds/Packet.

   Figure 15 [See the PDF.]

            Figure 15: CDF: Loss of Connectivity for Different
           Global Repair Period, Source Rate 10 Seconds/Packet.

   The data for Figures 13 and 15 can be found in Table 2.  The table
   shows how the CDF of time without connectivity to the LBR increases
   while we increase the time period to emit new DAG sequence numbers,
   when the nodes generate a packet every 10 seconds.

   +---------+------------------+------------------+-------------------+
   |   CDF   |  Repair Period   |  Repair Period   |   Repair Period   |
   |  (%age) |   10 Minutes     |   30 Minutes     |    60 Minutes     |
   +---------+------------------+------------------+-------------------+
   |     0   |       0.464      |       0.045      |       0.027       |
   |     5   |       0.609      |       0.424      |       0.396       |
   |    10   |       1.040      |       1.451      |       0.396       |
   |    15   |       1.406      |       3.035      |       0.714       |
   |    20   |       1.934      |       3.521      |       0.714       |
   |    25   |       2.113      |       5.461      |       1.856       |
   |    30   |       3.152      |       5.555      |       1.856       |
   |    35   |       3.363      |       7.756      |       6.173       |
   |    40   |       4.9078     |       8.604      |       6.173       |
   |    45   |       8.575      |       9.181      |      14.751       |
   |    50   |       9.788      |      21.974      |      14.751       |
   |    55   |      13.230      |      30.017      |      14.751       |
   |    60   |      17.681      |      31.749      |      16.166       |
   |    65   |      29.356      |      68.709      |      16.166       |
   |    70   |      34.019      |      92.974      |     302.459       |
   |    75   |      49.444      |     117.869      |     302.459       |
   |    80   |      75.737      |     133.653      |     488.602       |
   |    85   |     150.089      |     167.828      |     488.602       |
   |    90   |     180.505      |     271.884      |     488.602       |
   |    95   |     242.247      |     464.047      |     488.602       |
   |   100   |     273.808      |     464.047      |     488.602       |
   +---------+------------------+------------------+-------------------+

   Table 2: Loss of Connectivity Time, Data Rate - 10 Seconds / Packet.

   The data for Figure 14 can be found in Table 3.  The table shows how
   the CDF of time without connectivity to the LBR increases while we
   increase the time period to emit new DAG sequence numbers, when the
   nodes generate a packet every 20 seconds.

   +---------+------------------+------------------+-------------------+
   |   CDF   |   Repair Period  |   Repair Period  |   Repair Period   |
   |  (%age) |    10 Minutes    |    30 Minutes    |    60 Minutes     |
   +---------+------------------+------------------+-------------------+
   |     0   |       0.071      |       0.955      |       0.167       |
   |     5   |       0.126      |       2.280      |       1.377       |
   |    10   |       0.403      |       2.926      |       1.409       |
   |    15   |       0.902      |       3.269      |       1.409       |
   |    20   |       1.281      |      16.623      |       3.054       |
   |    25   |       2.322      |      21.438      |       5.175       |
   |    30   |       2.860      |      48.479      |       5.175       |
   |    35   |       3.316      |      49.495      |      10.30        |
   |    40   |       3.420      |      93.700      |      25.406       |
   |    45   |       6.363      |     117.594      |      25.406       |
   |    50   |      11.500      |     243.429      |      34.379       |
   |    55   |      19.703      |     277.039      |     102.141       |
   |    60   |      22.216      |     284.660      |     102.141       |
   |    65   |      39.211      |     285.101      |     328.293       |
   |    70   |      63.197      |     376.549      |     556.296       |
   |    75   |      88.986      |     443.450      |     556.296       |
   |    80   |     147.509      |     452.883      |    1701.52        |
   |    85   |     154.26       |     653.420      |    2076.41        |
   |    90   |     244.241      |     720.032      |    2076.41        |
   |    95   |     518.835      |    1760.47       |    2076.41        |
   |   100   |     555.57       |    1760.47       |    2076.41        |
   +---------+------------------+------------------+-------------------+

   Table 3: Loss of Connectivity Time, Data Rate - 20 Seconds / Packet.

   Figure 16 shows the effect of the DAG global repair timer period on
   control traffic.  As expected, as the frequency at which new DAG
   sequence numbers are generated increases, the amount of control
   traffic decreases because DIO messages are sent less frequently to
   rebuild the DODAG.  However, reducing the control traffic comes at a
   price of increased loss of connectivity when only global repair is
   used.

   Figure 16 [See the PDF.]

            Figure 16: Amount of Control Traffic for Different
                          Global Repair Periods.

   From the above results, it is clear that the time the protocol takes
   to re-establish routes and to converge, after an unexpected link or
   device failure happens, is fairly long.  [RFC5826] mandates that "the
   routing protocol MUST converge within 0.5 seconds if no nodes have
   moved".  Clearly, implementation of a repair mechanism based on new
   DAG sequence numbers alone would not meet the requirements.  Hence, a
   local repair mechanism, in the form of poisoning the sub-DAG and
   issuing a DIS, has been adopted.

   The effect of the DAG repair timer on time without service when local
   repair is activated is now observed and plotted in Figure 17, where
   the source rate is 20 seconds/packet.  A comparison of the CDF of
   loss of connectivity for the global repair mechanism and the global +
   local repair mechanism is shown in Figures 18 and 19 (semi-log plots,
   x axis in logarithmic scale and y axis in linear scale), where the
   source generates a packet every 10 seconds and 20 seconds,
   respectively.  For these plots, the x axis shows time in log scale,
   and the y axis denotes the corresponding CDF in linear scale.  One
   can observe that using local repair (with poisoning of the sub-DAG)
   greatly reduces loss of connectivity.

   Figure 17 [See the PDF.]

    Figure 17: CDF: Loss of Connectivity for Different DAG Repair Timer
      Values for Global+Local Repair, Source Rate 20 Seconds/Packet.

   Figure 18 [See the PDF.]

        Figure 18: CDF: Loss of Connectivity for Global Repair and
            Global+Local Repair, Source Rate 10 Seconds/Packet.

   Figure 19 [See the PDF.]

        Figure 19: CDF: Loss of Connectivity for Global Repair and
            Global+Local Repair, Source Rate 20 Seconds/Packet.

   A comparison between the amount of control plane overhead used for
   global repair only and for the global plus local repair mechanism is
   shown in Figure 20, which highlights the improved performance of RPL
   in terms of convergence time at very little extra overhead.  From
   Figure 19, in 85% of the cases the protocol finds connectivity to the
   LBR for the concerned nodes within a fraction of seconds when local
   repair is employed.  Using only global repair leads to repair periods
   of 150-154 seconds, as observed in Figures 13 and 14.

   Figure 20 [See the PDF.]

            Figure 20: Number of Control Packets for Different
            DAG Sequence Number Period, for Both Global Repair
                         and Global+Local Repair.

5.  RPL in a Building Automation Routing Scenario

   Unlike the previous traffic pattern, where a majority of the total
   traffic generated by any node is destined to the root, this section
   considers a different traffic pattern, which is more prominent in a
   home or building routing scenario.  In the simulations shown below,
   the nodes send 60% of their total generated traffic to the physically
   1-hop distant node and 20% of traffic to a 2-hop distant node; the
   other 20% of traffic is distributed among other nodes in the network.
   The CDF of path quality metrics such as hop count, ETX path cost,
   average hop distance stretch, ETX path stretch, and delay for P2P
   routing for all pairs of nodes is calculated.  Maintaining a low
   delay bound for P2P traffic is of high importance, as applications in
   home and building routing typically have low delay tolerance.

5.1.  Path Quality

   Figure 21 shows the CDF of the hop count for both RPL and ideal
   shortest path routing for the traffic pattern described above.
   Figure 22 shows the CDF of the expected number of transmissions (ETX)
   for each packet to reach its destination.  Figures 23 and 24 show the
   CDF of the stretch factor for these two metrics.  To illustrate the
   stretch factor, an example from Figure 24 will be given next.  For
   all paths built by RPL, 85% of the time, the path cost is less than
   the path cost for the ideal shortest path plus one.

   Figure 21 [See the PDF.]

            Figure 21: CDF of End-to-End Hop Count for RPL and
                   Ideal Shortest Path in Home Routing.

   Figure 22 [See the PDF.]

            Figure 22: CDF of ETX Path Cost Metric for RPL and
                   Ideal Shortest Path in Home Routing.

   Figure 23 [See the PDF.]

     Figure 23: CDF of Hop Distance Stretch from Ideal Shortest Path.

   Figure 24 [See the PDF.]

      Figure 24: CDF of ETX Metric Stretch from Ideal Shortest Path.

5.2.  Delay

   To get an idea of maximum observable delay in the above-mentioned
   traffic pattern, the delay for different numbers of hops to the
   destination for RPL is considered.  Figure 25 shows how the end-to-
   end packet latency is distributed for different packets with
   different hop counts in the network.

   Figure 25 [See the PDF.]

        Figure 25: Packet Latency for Different Hop Counts in RPL.

   For this deployment scenario, 60% of the traffic has been restricted
   to a 1-hop neighborhood.  Hence, intuitively, the protocol is
   expected to yield path qualities that are close to those of ideal
   shortest path routing for most of the paths.  From the CDF of the hop
   count and ETX path cost, it is clear that peer-to-peer paths are more
   often closer to an ideal shortest path.  The end-to-end delay for
   distances within 2 hops is less than 60 ms for 99% of the delivered
   packets, while packets traversing 5 hops or more are delivered within
   100 ms 99% of the time.  These results demonstrate that for a normal
   routing scenario of an LLN deployment in a building, RPL performs
   fairly well without incurring much control plane overhead, and it can
   be applied for delay-critical applications as well.

6.  RPL in a Large-Scale Network

   In this section, we focus on simulating RPL in a large network and
   study its scalability by focusing on a few performance metrics: the
   latency and path cost stretch, and the amount of control packets.
   The 2442-node smart meter network with its corresponding link traces
   was used in this scalability study.  To simulate a more realistic
   scenario for a smart meter network, 100% of the packets generated by
   each node are destined to the root.  Therefore, no traffic is
   destined to nodes other than the root.

6.1.  Path Quality

   To investigate RPL's scalability, the CDF of the ETX path cost in the
   large-scale smart meter network is compared to a hypothetical ideal
   shortest path routing protocol that minimizes the total ETX path cost
   (Figure 26).  In this simulation, the path stretch is also calculated
   for each packet that traverses the network.  The path stretch is
   determined as the difference between the path cost taken by a packet

   while following a route built via RPL and a path computed using an
   ideal shortest path routing protocol.  The CDF of the ETX fractional
   stretch, which is determined as the ETX metric stretch value over the
   ETX path cost of an ideal shortest path, is plotted in Figure 27.

   The fractional hop distance stretch value, as defined in the
   Terminology section, is shown in Figure 28.

   Looking at the path quality plots, it is obvious that RPL works in a
   non-optimal fashion in this deployment scenario as well.  However, on
   average, for each source-destination pair, the ETX fractional stretch
   is limited to 30% of the ideal shortest path cost.  This fraction is
   higher for paths with shorter distances and lower for paths where the
   source and destination are far apart.  The negative stretch factor
   for the hop count is an interesting feature of this deployment and is
   due to RPL's decision to not switch to another parent where the
   improvement in path quality is not significant.  As mentioned
   previously, in this implementation, a node will only switch to a new
   parent if the advertised ETX path cost to the LBR through the new
   candidate parent is 20% better than the old one.  The nodes tend to
   hear DIOs from a smaller hop count first, and later do not always
   shift to a larger hop count and smaller ETX path cost.  As the
   traffic is mostly to the DAG root, some P2P paths built via RPL do
   yield a smaller hop count from source to destination, albeit at a
   larger ETX path cost.

   As observed in Figure 26, 90% of the packets transmitted during the
   simulation have a (shortest) ETX path cost to destination less than
   or equal to 12.  However, via RPL, 90% of the packets will follow
   paths that have a total ETX path cost of up to 14.  Though all
   packets are destined to the LBR, it is to be noted that this
   implementation ignores a change of up to 20% in total ETX path cost.
   Figures 27 and 28 indicate that all paths have a very low ETX
   fractional stretch factor as far as the total ETX path cost is
   concerned, and some of the paths have lower hop counts to the LBR or
   DAG root as well when compared to the hop count of the ideal shortest
   path.

   Figure 26 [See the PDF.]

        Figure 26: CDF of Total ETX Path Cost versus ETX Path Cost.

   Figure 27 [See the PDF.]

              Figure 27: CDF of ETX Fractional Stretch versus
                       ETX Fractional Stretch Value.

   Figure 28 [See the PDF.]

              Figure 28: CDF of Fractional Hop Count Stretch.

6.2.  Delay

   Figure 29 shows how end-to-end packet latency is distributed for
   different hop counts in the network.  According to [RFC5548], Urban
   LLNs (U-LLNs) are delay tolerant, and the information, except for
   critical alarms, should arrive within a fraction of the reporting
   interval (within a few seconds).  The packet generation for this
   deployment has been set higher than usual to incur high traffic
   volume, and nodes generate data once every 30 seconds.  However, the
   end-to-end latency for most of the packets is condensed between
   500 ms and 1 s, where the upper limit corresponds to packets
   traversing longer (greater than or equal to 6 hops) paths.

   Figure 29 [See the PDF.]

               Figure 29: End-to-End Packet Delivery Latency
                         for Different Hop Counts.

6.3.  Control Packet Overhead

   Figure 30 shows the comparison between data packets (originated and
   forwarded) and control packets (DIO and DAO messages) transmitted by
   each node (link ETX is used as the routing metric).  Here one can
   observe that in spite of the large scale of the network, the amount
   of control traffic in the protocol is negligible in comparison to
   data packet transmission.  The smaller node ID for this network
   actually indicates closer proximity to the DAG root, and nodes with
   high ID numbers are actually farther away from the DAG root.  Also,
   as expected, we can observe in Figures 31, 32, and 33 that the
   (non-leaf) nodes closer to the DAG root have many more data packet
   transmissions than other nodes.  The leaf nodes have comparable
   amounts of data and control packet transmissions, as they do not take
   part in routing the data.  As seen before, the data traffic for a
   child node has much less variation than the nodes that are closer to
   the DAG root.  This variation decreases with increase in DAG depth.
   In this topology, Nodes 1, 2, and 3, etc., are direct children of
   the LBR.

   Figure 30 [See the PDF.]

              Figure 30: Data and Control Packet Comparison.

   Figure 31 [See the PDF.]

         Figure 31: Data and Control Packets over Time for Node 1.

   Figure 32 [See the PDF.]

        Figure 32: Data and Control Packets over Time for Node 78.

   Figure 33 [See the PDF.]

        Figure 33: Data and Control Packets over Time for Node 300.

   In Figure 34, the effect of the global repair period timer on control
   packet overhead is shown.

   Figure 34 [See the PDF.]

            Figure 34: Numbers of Control Packets for Different
                       Global Repair Timer Periods.

7.  Scaling Property and Routing Stability

   An important metric of interest is the maximum load experienced by
   any node (CPU usage) in terms of the number of control packets
   transmitted by the node.  Also, to get an idea of scaling properties
   of RPL in large-scale networks, it is also key to analyze the number
   of packets handled by the RPL nodes for networks of different sizes.

   In these simulations, at any given interval, the node with maximum
   control overhead load is identified.  The amount of maximum control
   overhead processed by that node is plotted against time for three
   different networks under study.  The first one is Network 'A', which
   has 45 nodes and is shown in Figure 1 (Section 3); the second is
   Network 'B', which is another deployed outdoor network with 86 nodes;
   and the third is Network 'C', which is the large deployed smart meter
   network with 2442 nodes as noted previously in this document.

   In Figure 35, the comparison of maximum control loads is shown for
   different network sizes.  For the network with 45 nodes, the maximum
   number of control packets in the network stays within a limit of
   50 packets (per 1-minute interval), where for the networks with 86
   and 2442 nodes, this limit stretches to 100 and 2 * 10^3 packets per
   1-minute interval, respectively.

   Figure 35 [See the PDF.]

          Figure 35: Scaling Property of Maximum Control Packets
                     Processed by Any Node over Time.

   For a network built with low-power devices interconnected by lossy
   links, it is of the utmost importance to ensure that routing packets
   are not flooded in the entire network and that the routing topology
   stays as stable as possible.  Any change in routing information,
   especially parent-child relationships, would reset the timer, leading
   to emitting new DIOs, and would hence change the node's path metric
   to reach the root.  This change will trigger a series of control
   plane messages (RPL packets) in the DODAG.  Therefore, it is
   important to carefully control the triggering of DIO control packets
   via the use of thresholds.

   In this study, the effect of the tolerance value that is considered
   before emitting a DIO reflecting a new path cost is analyzed.  Four
   cases are considered:

   o  No change in DAG depth of a node is ignored;

   o  The implementation ignores a 10% change in the ETX path cost to
      the DAG root.  That is, if the change in total path cost to the
      root/LBR -- due to DIO reception from the most preferred parent or
      due to shifting to another parent -- is less than 10%, the node
      will not advertise the new metric to the root;

   o  The implementation ignores a 20% change in ETX path cost to the
      DAG root for any node before deciding to advertise a new depth;

   o  The implementation ignores a 30% change in the total ETX path cost
      to the DAG root of a node before deciding to advertise a new
      depth.

   This decision does affect the optimum path quality to the DAG root.
   As observed in Figure 36, for 0% tolerance, 95% of paths used have an
   ETX fractional stretch factor of less than 10%.  Similarly, for 10%
   and 20% tolerance levels, 95% of paths will have a 15% and 20% ETX
   fractional path stretch.  However, the increased routing stability
   and decreased control overhead are the profit gained from the 10%
   extra increase in path length or ETX path cost, whichever is used as
   the metric to optimize the DAG.

   Figure 36 [See the PDF.]

                 Figure 36: ETX Fractional Stretch Factor
                      for Different Tolerance Levels.

   As the above-mentioned threshold also affects the path taken by a
   packet, this study also demonstrates the effect of the threshold on
   routing stability (number of times P2P paths change between a source
   and a destination).  For Network 'A' (shown in Figure 1) and the

   large smart meter network 'C', the CDF of path change is plotted in
   Figures 37 and 38, respectively, against the fraction of path change
   for different thresholds (triggering the emission of a new DIO upon
   path cost change).

   If X packets are transferred from source A to destination B, and out
   of X times, Y times the path between this source-destination pair is
   changed, then we compute the fraction of path change as Y/X * 100%.
   This metric is computed over all source-destination pairs, and the
   CDF is plotted in the y axis.

   Figure 37 [See the PDF.]

     Figure 37: Distribution of Fraction of Path Change for Network A.

   Figure 38 [See the PDF.]

            Figure 38: Distribution of Fraction of Path Change
                           for Large Network C.

   This document also compares the CDF of the fraction of path change
   for three different networks -- A, B, and C.  Figure 39 shows how the
   three networks exhibit a change of P2P path when a 30% change in
   metric cost to the root is ignored before shifting to a new parent.

   Figure 39 [See the PDF.]

     Figure 39: Comparison of Distribution of Fraction of Path Change.

8.  Comments

   All the simulation results presented in this document corroborate the
   expected protocol behavior for the topologies and traffic model used
   in the study.  For the particular discussed scenarios, the protocol
   is shown to meet the desired delay and convergency requirements and
   to exhibit self-healing properties without external intervention,
   incurring negligible control overhead (only a small fraction of data
   traffic).  RPL provided near-optimum path quality for most of the
   packets in the scenarios considered here and is able to trade off
   control overhead for path quality via configurable parameters (such
   as decisions on when to switch to a new parent), as per the
   application and device requirements; thus, RPL can trade off routing
   stability for control overhead as well.  Finally, as per the
   requirement of urban LLN deployments, the protocol is shown to scale
   to larger topologies (several thousand nodes), for the topologies
   considered in this implementation.

9.  Security Considerations

   This document describes investigations performed in the Castalia
   wireless sensor network simulator; it does not consider packets on
   the Internet.  [RFC6550] describes security considerations for RPL
   networks.

10.  Acknowledgements

   The authors would like to acknowledge Jerald P. Martocci, Mukul
   Goyal, Emmanuel Monnerie, Philip Levis, Omprakash Gnawali, and Craig
   Partridge for their valuable and helpful suggestions over metrics to
   include and overall feedback.

11.  Informative References

   [Castalia-2.2]
              Boulis, A., "Castalia: Revealing pitfalls in designing
              distributed algorithms in WSN", Proceedings of the 5th
              international conference on Embedded networked sensor
              systems (SenSys'07), pp. 407-408, 2007.

   [NS-2]     "The Network Simulator version 2 (ns-2)",
              <http://www.isi.edu/nsnam/ns/>.

   [OMNeTpp]  Varga, A., "The OMNeT++ Discrete Event Simulation System",
              Proceedings of the European Simulation
              Multiconference (ESM'2001), June 2001.

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

   [RFC5673]  Pister, K., Ed., Thubert, P., Ed., 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.

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

   [RFC6206]  Levis, P., Clausen, T., Hui, J., Gnawali, O., and J. Ko,
              "The Trickle Algorithm", RFC 6206, March 2011.

   [RFC6550]  Winter, T., Ed., Thubert, P., Ed., Brandt, A., Hui, J.,
              Kelsey, R., Levis, P., Pister, K., Struik, R., Vasseur,
              JP., and R. Alexander, "RPL: IPv6 Routing Protocol for
              Low-Power and Lossy Networks", RFC 6550, March 2012.

   [RFC6551]  Vasseur, JP., Ed., Kim, M., Ed., Pister, K., Dejean, N.,
              and D. Barthel, "Routing Metrics Used for Path Calculation
              in Low-Power and Lossy Networks", RFC 6551, March 2012.

   [ROLL-TERMS]
              Vasseur, JP., "Terminology in Low power And Lossy
              Networks", Work in Progress, September 2011.

Authors' Addresses

   Joydeep Tripathi (editor)
   Drexel University
   3141 Chestnut Street 7-313
   Philadelphia, PA  19104
   USA

   EMail: jt369@drexel.edu

   Jaudelice C. de Oliveira (editor)
   Drexel University
   3141 Chestnut Street 7-313
   Philadelphia, PA  19104
   USA

   EMail: jau@coe.drexel.edu

   JP. Vasseur (editor)
   Cisco Systems, Inc.
   11, Rue Camille Desmoulins
   Issy Les Moulineaux  92782
   France

   EMail: jpv@cisco.com

 

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