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<rfc category="std"
     docName="draft-chen-pim-be-mrh-simu-04"
     ipr="trust200902"
     xmlns:xi="http://www.w3.org/2001/XInclude"
>
  <front>
    <title abbrev="BE Multicast Simulation">
    Stateless Best Effort Multicast Simulations</title>
    
     <author initials="H" surname="Chen" fullname="Huaimo Chen">
      <organization>Independent</organization>
      <address>
        <postal>
          <street></street>
          <city>Boston, MA</city>
          <region></region>
          <code></code>
          <country>USA</country>
        </postal>
        <email>hchen.ietf@gmail.com</email>
      </address>
    </author>

    <author fullname="Donald E. Eastlake 3rd" initials="D" surname="Eastlake">
      <organization>Independent</organization>
      <address>
        <postal>
          <street>2386 Panoramic Circle</street>
          <city>Apopka, FL</city>
          <region></region>
          <code>32703</code>
          <country>USA</country>
        </postal>
        <phone>+1-508-333-2270</phone>
        <email>d3e3e3@gmail.com</email>
      </address>
    </author>

    <author fullname="Mike McBride" initials="M" surname="McBride">
      <organization>Futurewei</organization>
      <address>
        <email>michael.mcbride@futurewei.com</email>
      </address>
    </author>

   <author initials="Y" fullname="Yanhe Fan" 
            surname="Fan">
      <organization>Casa Systems</organization>
      <address>
        <postal>
          <street></street>
          <city></city>
          <region></region>
          <code></code>
          <country>USA</country>
        </postal>
        <email>yfan@casa-systems.com</email>
      </address>
    </author>

    <author fullname="Gyan S. Mishra" initials="G" surname="Mishra">
      <organization>Verizon</organization>
      <address>
        <postal>
          <street>13101 Columbia Pike</street>
          <city>Silver Spring</city>
          <code>MD 20904</code>
          <country>USA</country>
        </postal>
        <phone> 301 502-1347</phone>
        <email>gyan.s.mishra@verizon.com</email>
      </address>
    </author>

  <author fullname="Yisong Liu" initials="Y" surname="Liu">
   <organization>China Mobile</organization>
   <address>
        <postal>
          <street></street>
          <city></city>
          <region></region>
          <code></code>
          <country></country>
        </postal>
    <email>liuyisong@chinamobile.com</email>
   </address>
  </author>

     <author initials="A" fullname="Aijun Wang" 
            surname="Wang">
      <organization>China Telecom</organization>
      <address>
        <postal>
          <street>Beiqijia Town, Changping District</street>
          <city>Beijing</city>
          <region> </region>
          <code>102209</code>
          <country>China</country>
        </postal>
        <email>wangaj3@chinatelecom.cn</email>
      </address>
    </author>

   <author initials="X" fullname="Xufeng Liu" 
            surname="Liu">
      <organization>IBM Corporation</organization>
      <address>
        <postal>
          <street> </street>
          <city> </city>
          <region> </region>
          <code></code>
          <country>USA</country>
        </postal>
        <email>xufeng.liu.ietf@gmail.com</email>
      </address>
    </author>

   <author initials="L" fullname="Lei Liu" 
            surname="Liu">
      <organization>Fujitsu</organization>
      <address>
        <postal>
          <street> </street>
          <city> </city>
          <region></region>
          <code></code>
          <country>USA</country>
        </postal>
        <email>liulei.kddi@gmail.com</email>
      </address>
    </author>

    <date year="2024" month="september" day="24"/>

    <abstract>
      <t>This document describes simulations of 
         stateless best effort Multicasts and lists 
         a set of simulation results for 
         different large network sizes and different tree sizes. 
      </t>

      <t/>
    </abstract>

    <note title="Requirements Language">
      <t>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 <xref
      target="RFC2119"></xref> <xref target="RFC8174"></xref>
      when, and only when, they appear in all
      capitals, as shown here.</t>
    </note>
  </front>

  <middle>
    <section title="Introduction">	

     <t>For a tree given by its root/ingress and leaves/egresses,
        a few of solutions are proposed to multicast 
        data from the ingress to the egresses 
        using the shortest IGP paths to the egresses.
        They include:

        <list style="hanging">
          <t hangText="o BEM-MRH:">Stateless Best Effort Multicast Using MRH 
            <xref target = "I-D.chen-pim-be-mrh"/>.</t>
          <t hangText="o BIER:">Multicast Using Bit Index Explicit Replication
            <xref target = "RFC8279"/>.</t>
          <t hangText="o RGB:">RGB (Replication through Global Bitstring) Segment 
             for Multicast Source Routing over IPv6 
            <xref target = "I-D.lx-msr6-rgb-segment"/>.</t>
        </list>
     </t>

      <t>This document describes simulations of 
         stateless best effort Multicasts and lists 
         a set of simulation results for 
         different large network sizes and different tree sizes. 
      </t>

    <section title="Acronyms">
      <t>The following acronyms are used in this document:
        <list style="hanging">
          <t hangText="CE:">Customer edge/equipment.</t>
          <t hangText="MRH:">Multicast Routing Header.</t>
          <t hangText="P2MP:">Point 2 Multi-Point.</t>
          <t hangText="PE:">Provider Edge.</t>
        </list>
      </t>

    </section>

    </section> <!-- Introduction -->


    <section title="Simulations of BE Multicasts">
    <t>A simulation of a BE Multicast means 
       a computation of the encoding of a tree in a given network
       according to the BE Multicast.
       The tree has a number of egresses/leaves, 
       which is the size of the tree.
       The network has a number of nodes,
       which is the size of the network.
    </t>

    <t>For a given network size (i.e., a number of nodes in the network),
       we assume that half of the nodes are PEs.
       For a given tree size (i.e., a number of leaves/egresses) T, 
       we select T egress nodes from the PEs randomly first.
       And then we compute the encoding of the tree with these T 
       selected egress nodes. 
       The computation results include the total size of the encoding 
       of the tree and the number of packet copies that the ingress/root
       of the tree will encapsulate and send.
    </t>
      
    <t>For simulating Stateless Best Effort Multicast Using MRH (BEM-MRH)
      defined in <xref target = "I-D.chen-pim-be-mrh"/>, 
      we compute the encoding according to BE-MRH
      for each of the trees with different tree sizes in
      each of the networks with different network sizes.
    </t>

    </section> <!-- Simulations of BE Multicasts -->


    <section title="Some Simulation Results">
      <t>Suppose that we have a set of network sizes 
         netSizes = {4096, 8192, 16384} and a set of tree sizes
         treeSizes = {16, 24, 32, 48, 64, 80, 96, 128}.
         We simulate the BEM-MRH and BIER for each tree size in treeSizes 
         for each network size in netSizes. 
         For BIER, we use BitString length 256 (bits).</t>

      <t><xref target = "simu-netsize-4096"/> 
         shows the results of simulating the BEM-MRH and BIER for 
         every tree size for network size 4096.
      </t>

    <t>
<figure anchor="simu-netsize-4096" 
 title="Results of simulating BEM-MRH and BIER for network with 4096 nodes">
  <artwork  align="center"> <![CDATA[
+======+=========================+=========================+
|      |       BEM-MRH           |        BIER             | 
| Tree | Encoding |Number of     | Encoding |Number of     |
| Size | Size     |Packet Copies | Size     |Packet Copies |
+======+==========+==============+==========+==============+
|  16  |    32    |      1       |    224   |       7      |
+------+----------+--------------+----------+--------------+
|  24  |    47    |      1       |    256   |       8      |
+------+----------+--------------+----------+--------------+
|  32  |    62    |      1       |    256   |       8      |
+------+----------+--------------+----------+--------------+
|  48  |    93    |      1       |    256   |       8      |
+------+----------+--------------+----------+--------------+
|  64  |   128    |      1       |    256   |       8      |
+------+----------+--------------+----------+--------------+
|  80  |   154    |      1       |    256   |       8      |
+------+----------+--------------+----------+--------------+
|  96  |   164    |      1       |    256   |       8      |
+------+----------+--------------+----------+--------------+
| 128  |   196    |      1       |    256   |       8      |
+======+==========+==============+==========+==============+]]></artwork>
</figure>
</t>
     <t>From the simulation results of BEM-MRH in the figure, 
        we see that the number of packet copies is 1 for any tree size
        (refer to the third column of the table).

        This indicates that 
        after receiving a multicast packet from a traffic source       
        such as a CE, the ingress/root of the tree can encapsulate 
        one packet copy and send the packet to the egress/leaf 
        nodes of the tree through using BEM-MRH. 
     </t>

     <t>From the simulation results of BIER in the figure, 
        we see that the number of packet copies is 7 for tree size 16 
        and 8 for any other tree size
        (refer to the last column of the table).

        This indicates that 
        after receiving a multicast packet from a traffic source       
        such as a CE, the ingress/root of the tree need to make 
        7/8 packet copies, encapsulate each of the copies 
        and send the packet copies to the egress/leaf 
        nodes of the tree through using BIER. 
     </t>

     <t>From the simulation results of BEM-MRH in the figure, 
        we see that the total size of the encoding tree is 
        32 (bytes) for a tree with 16 leaves/egresses,
        47 (bytes) for a tree with 24 leaves/egresses,
        ..., 
        196 (bytes) for a tree with 128 leaves/egresses
        (refer to the second column of the table).

        The total size of the encoding tree is always less than
        or equal to two times the tree size. 
     </t>

     <t>From the simulation results of BIER in the figure, 
        we see that the total size of the encoding tree is 
        224 (bytes) for a tree with 16 leaves/egresses,
        and 256 (bytes) for any other tree size
        (refer to the fourth column of the table). 
     </t>

      <t><xref target = "simu-netsize-8192"/> 
         shows the results of simulating the BEM-MRH and BIER for 
         every tree size for network size 8192.
      </t>

    <t>
<figure anchor="simu-netsize-8192" 
 title="Results of simulating BEM-MRH and BIER for network with 8192 nodes">
  <artwork  align="center"> <![CDATA[
+======+=========================+=========================+
|      |       BEM-MRH           |        BIER             | 
| Tree | Encoding |Number of     | Encoding |Number of     |
| Size | Size     |Packet Copies | Size     |Packet Copies |
+======+==========+==============+==========+==============+
|  16  |    32    |      1       |    320   |      10      |
+------+----------+--------------+----------+--------------+
|  24  |    48    |      1       |    352   |      11      |
+------+----------+--------------+----------+--------------+
|  32  |    64    |      1       |    416   |      13      |
+------+----------+--------------+----------+--------------+
|  48  |    96    |      1       |    448   |      14      |
+------+----------+--------------+----------+--------------+
|  64  |   124    |      1       |    512   |      16      |
+------+----------+--------------+----------+--------------+
|  80  |   159    |      1       |    512   |      16      |
+------+----------+--------------+----------+--------------+
|  96  |   187    |      1       |    512   |      16      |
+------+----------+--------------+----------+--------------+
| 128  |   235    |      1       |    512   |      16      |
+======+==========+==============+==========+==============+]]></artwork>
</figure>
</t>

     <t>From the simulation results of BEM-MRH in the figure, 
        we see that the number of packet copies is 1 for any tree size
        (refer to the third column of the table).

        This indicates that 
        after receiving a multicast packet from a traffic source       
        such as a CE, the ingress/root of the tree can encapsulate 
        one packet copy and send the packet to the egress/leaf 
        nodes of the tree through using BEM-MRH. 
     </t>

     <t>From the simulation results of BIER in the figure, 
        we see that the number of packet copies is from 10 to 16 for tree size 
        from 16 to 128
        (refer to the last column of the table).

        This indicates that 
        after receiving a multicast packet from a traffic source       
        such as a CE, the ingress/root of the tree need to make 
        10 to 16 packet copies, encapsulate each of the copies 
        and send the packet copies to the egress/leaf 
        nodes of the tree through using BIER. 
     </t>

     <t>From the simulation results of BEM-MRH in the figure, 
        we see that the total size of the encoding tree is 
        32 (bytes) for a tree with 16 leaves/egresses,
        48 (bytes) for a tree with 24 leaves/egresses,
        ..., 
        235 (bytes) for a tree with 128 leaves/egresses
        (refer to the second column of the table).

        The total size of the encoding tree is always less than
        or equal to two times the tree size. 
     </t>

     <t>From the simulation results of BIER in the figure, 
        we see that the total size of the encoding tree is 
        from 320 to 512 (bytes) for a tree with size from 16 to 128 
        (leaves/egresses)
        (refer to the fourth column of the table). 
     </t>

      <t><xref target = "simu-netsize-16384"/> 
         shows the results of simulating the BEM-MRH and BIER for 
         every tree size for network size 16384.
      </t>

    <t>
<figure anchor="simu-netsize-16384" 
 title="Results of simulating BEM-MRH and BIER for network with 16384 nodes">
  <artwork  align="center"> <![CDATA[
+======+=========================+=========================+
|      |       BEM-MRH           |        BIER             | 
| Tree | Encoding |Number of     | Encoding |Number of     |
| Size | Size     |Packet Copies | Size     |Packet Copies |
+======+==========+==============+==========+==============+
|  16  |    32    |      1       |    384   |      12      |
+------+----------+--------------+----------+--------------+
|  24  |    48    |      1       |    480   |      15      |
+------+----------+--------------+----------+--------------+
|  32  |    64    |      1       |    704   |      22      |
+------+----------+--------------+----------+--------------+
|  48  |    96    |      1       |    800   |      25      |
+------+----------+--------------+----------+--------------+
|  64  |   126    |      1       |    896   |      28      |
+------+----------+--------------+----------+--------------+
|  80  |   158    |      1       |    928   |      29      |
+------+----------+--------------+----------+--------------+
|  96  |   192    |      1       |    992   |      31      |
+------+----------+--------------+----------+--------------+
| 128  |   256    |      1       |   1024   |      32      |
+======+==========+==============+==========+==============+]]></artwork>
</figure>
</t>

     <t>From the simulation results of BEM-MRH in the figure, 
        we see that the number of packet copies is 1 for any tree size
        (refer to the third column of the table).

        This indicates that 
        after receiving a multicast packet from a traffic source       
        such as a CE, the ingress/root of the tree can encapsulate 
        one packet copy and send the packet to the egress/leaf 
        nodes of the tree through using BEM-MRH. 
     </t>

     <t>From the simulation results of BIER in the figure, 
        we see that the number of packet copies is from 12 to 32 for tree size
        from 16 to 128
        (refer to the last column of the table).

        This indicates that 
        after receiving a multicast packet from a traffic source       
        such as a CE, the ingress/root of the tree need to make 
        12 to 32 packet copies, encapsulate each of the copies 
        and send the packet copies to the egress/leaf 
        nodes of the tree through using BIER. 
     </t>

     <t>From the simulation results of BEM-MRH in the figure, 
        we see that the total size of the encoding tree is 
        32 (bytes) for a tree with 16 leaves/egresses,
        48 (bytes) for a tree with 24 leaves/egresses,
        ..., 
        256 (bytes) for a tree with 128 leaves/egresses
        (refer to the second column of the table).

        The total size of the encoding tree is always less than
        or equal to two times the tree size. 
     </t>

     <t>From the simulation results of BIER in the figure, 
        we see that the total size of the encoding tree is 
        from 384 to 1024 (bytes) for a tree with size from 16 to 128 
        (leaves/egresses)
        (refer to the fourth column of the table). 
     </t>

    </section> <!-- Some Simulation Results --> 


     <section anchor="Security" title="Security Considerations">
      <t>No.</t>
    </section>

    <section anchor="IANA" title="IANA Considerations">
     <t>No IANA is requested.</t>
    </section> <!-- IANA Considerations -->

    <section anchor="Acknowledgements" title="Acknowledgements">
      <t>TBD</t>
    </section>
  </middle>

  <back>
    <references title="Normative References">
<xi:include
    href="https://www.rfc-editor.org/refs/bibxml/reference.RFC.2119.xml"/>
<xi:include
    href="https://www.rfc-editor.org/refs/bibxml/reference.RFC.8174.xml"/>
<xi:include
    href="https://www.rfc-editor.org/refs/bibxml/reference.RFC.8279.xml"/>
<!--      <?rfc include="reference.RFC.2119"?>
      <?rfc include="reference.RFC.8174"?>
      <?rfc include="reference.RFC.8200"?>
      <?rfc include="reference.RFC.8279"?>-->
      <?rfc include="reference.I-D.chen-pim-be-mrh"?>
      <?rfc include="reference.I-D.lx-msr6-rgb-segment"?>
    </references>

<!--    <references title="Informative References">
      <?rfc include="reference.I-D.chen-pim-srv6-p2mp-path"?>
      <?rfc include="reference.I-D.ietf-pim-sr-p2mp-policy"?>
    </references>-->


  </back>

</rfc>
