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* equations/discussion for latency, bandwidth and duplicates added. some equations corrected! * some minor adjustments in formulas * updated theoratical waku latency/bandwidth computations * Update waku_scalability/waku_scaling.md typo fix Co-authored-by: Alberto Soutullo <alberto.soutullo639@gmail.com> * corrected latency description --------- Co-authored-by: Alberto Soutullo <alberto.soutullo639@gmail.com>
86 lines
5.0 KiB
Python
86 lines
5.0 KiB
Python
# Assumptions
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# -----------------------------------------------------------
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# Users sent messages at a constant rate
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# The network topology is a d-regular graph (gossipsub aims at achieving this).
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# general / topology
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from utils import sizeof_fmt_kb
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average_node_degree = 6 # has to be even
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message_size = 0.002 # in MB (Mega Bytes)
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messages_sent_per_hour = 5 # ona a single pubsub topic / shard
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# Here we've chosen assumptions that keep the average message size the same.
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# (big_message_size * ratio_of_big_messages) + (small_message_size * (1-ratio_of_big_messages)) == message_size
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small_message_size = 0.001
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big_message_size = 0.006 # in MB (Mega Bytes)
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ratio_of_big_messages = .2 # ratio of number of big messages / number of other messages
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idontwant_too_late = 0.6 # ratio of number of big messages that are sent to a node after that node has received them
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# gossip
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gossip_message_size = (
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0.00005 # 50Bytes in MB (see https://github.com/libp2p/specs/pull/413#discussion_r1018821589 )
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)
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idontwant_message_size = 0.00005
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d_lazy = 6 # gossip out degree
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mcache_gossip = 3 # Number of history windows to use when emitting gossip (see https://github.com/libp2p/specs/blob/master/pubsub/gossipsub/gossipsub-v1.0.md)
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avg_ratio_gossip_replys = 0.01 # -> this is a wild guess! (todo: investigate)
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# multi shard
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avg_nodes_per_shard = 10000 # average number of nodes that a part of a single shard
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avg_shards_per_node = 3 # average number of shards a given node is part of
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# latency
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average_delay_per_hop = 0.1 # s
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# peer bandwidth
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average_peer_bandwidth = 30 # Mbps
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# TODO: load case for status control messages (note: this also introduces messages by currently online, but not active users.)
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# TODO: spread in the latency distribution (the highest 10%ish of latencies might be too high)
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# Assumption strings (general/topology)
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a1 = "- A01. Message size (static): " + sizeof_fmt_kb(message_size)
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a2 = "- A02. Messages sent per node per hour (static) (assuming no spam; but also no rate limiting.): " + str(messages_sent_per_hour)
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a3 = "- A03. The network topology is a d-regular graph of degree (static): " + str(average_node_degree)
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a16 = "- A16. There exists at most one peer edge between any two nodes."
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a17 = "- A17. The peer network is connected."
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a4 = "- A04. Messages outside of Waku Relay are not considered, e.g. store messages."
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a5 = "- A05. Messages are only sent once along an edge. (requires delays before sending)"
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a6 = "- A06. Messages are sent to all d-1 neighbours as soon as receiving a message (current operation)" # Thanks @Mmenduist
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a7 = "- A07. Single shard (i.e. single pubsub mesh)"
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a8 = "- A08. Multiple shards; mapping of content topic (multicast group) to shard is 1 to 1"
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a9 = "- A09. Max number of nodes per shard (static) " + str(avg_nodes_per_shard)
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a10 = "- A10. Number of shards a given node is part of (static) " + str(avg_shards_per_node)
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a11 = "- A11. Number of nodes in the network is variable.\n\
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These nodes are distributed evenly over " + str(avg_shards_per_node) + " shards.\n\
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Once all of these shards have " + str(avg_nodes_per_shard) + " nodes, new shards are spawned.\n\
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These new shards have no influcene on this model, because the nodes we look at are not part of these new shards."
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a12 = "- A12. Including 1:1 chat. Messages sent to a given user are sent into a 1:1 shard associated with that user's node.\n\
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Effectively, 1:1 chat adds a receive load corresponding to one additional shard a given node has to be part of."
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a13 = "- A13. 1:1 chat messages sent per node per hour (static): " + str(messages_sent_per_hour) # could introduce a separate variable here
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a14 = "- A14. 1:1 chat shards are filled one by one (not evenly distributed over the shards).\n\
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This acts as an upper bound and overestimates the 1:1 load for lower node counts."
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a15 = "- A15. Naive light node. Requests all messages in shards that have (large) 1:1 mapped multicast groups the light node is interested in."
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# Assumption strings (store)
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a21 = "- A21. Store nodes do not store duplicate messages."
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# Assumption strings (gossip)
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a31 = "- A31. Gossip is not considered."
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a32 = "- A32. Gossip message size (IHAVE/IWANT) (static):" + sizeof_fmt_kb(gossip_message_size)
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a33 = "- A33. Ratio of IHAVEs followed-up by an IWANT (incl. the actual requested message):" + str(avg_ratio_gossip_replys)
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a34 = "- A34. Gossip message size for IDONTWANT (static): " + sizeof_fmt_kb(idontwant_message_size)
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a35 = "- A35. Ratio of messages that are big enough to trigger a IDONTWANT response: " + str(ratio_of_big_messages)
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a36 = "- A36. Ratio of big messages that are avoided due to IDONTWANT: " + str(1/idontwant_too_late)
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a37 = "- A37. Size of messages large enough to trigger IDONTWANT (static): " + sizeof_fmt_kb(big_message_size)
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# Assumption strings (delay)
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a41 = "- A41. Delay is calculated based on an upper bound of the expected distance."
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a42 = "- A42. Average delay per hop (static): " + str(average_delay_per_hop) + "s."
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a43 = "- A43. Average peer bandwidth (static): " + str(average_peer_bandwidth) + "Mbps."
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