| Internet-Draft | BE Multicast Simulation | April 2023 |
| Chen, et al. | Expires 25 October 2023 | [Page] |
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.¶
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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:¶
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.¶
The following acronyms are used in this document:¶
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.¶
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.¶
For simulating Stateless Best Effort Multicast Using MRH (BEM-MRH) defined in [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.¶
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).¶
Figure 1 shows the results of simulating the BEM-MRH and BIER for every tree size for network size 4096.¶
+======+=========================+=========================+ | | 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 | +======+==========+==============+==========+==============+
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.¶
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.¶
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.¶
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).¶
Figure 2 shows the results of simulating the BEM-MRH and BIER for every tree size for network size 8192.¶
+======+=========================+=========================+ | | 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 | +======+==========+==============+==========+==============+
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.¶
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.¶
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.¶
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).¶
Figure 3 shows the results of simulating the BEM-MRH and BIER for every tree size for network size 16384.¶
+======+=========================+=========================+ | | 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 | +======+==========+==============+==========+==============+
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.¶
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.¶
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.¶
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).¶
No IANA is requested.¶
TBD¶