# !!! THIS IS WIP (analyze the code structure at your own risk ^.^') # the scope of this is still undefined; we want to avoid premature generalization # - todo: separate the part on latency # based on ../whisper_scalability/whisper.py import matplotlib.pyplot as plt import numpy as np import math # Util and format functions #----------------------------------------------------------- class bcolors: HEADER = '\033[95m' OKBLUE = '\033[94m' OKGREEN = '\033[92m' WARNING = '\033[93m' FAIL = '\033[91m' ENDC = '\033[0m' BOLD = '\033[1m' UNDERLINE = '\033[4m' def sizeof_fmt(num): return "%.1f%s" % (num, "MB") def sizeof_fmt_kb(num): return "%.2f%s" % (num*1024, "KB") def magnitude_fmt(num): for x in ['','k','m']: if num < 1000: return "%2d%s" % (num, x) num /= 1000 # Color format based on daily bandwidth usage # <10mb/d = good, <30mb/d ok, <100mb/d bad, 100mb/d+ fail. def load_color_prefix(load): if load < (10): color_level = bcolors.OKBLUE elif load < (30): color_level = bcolors.OKGREEN elif load < (100): color_level = bcolors.WARNING else: color_level = bcolors.FAIL return color_level def load_color_fmt(load, string): return load_color_prefix(load) + string + bcolors.ENDC def print_header(string): print(bcolors.HEADER + string + bcolors.ENDC + "\n") def print_assumptions(xs): print("Assumptions/Simplifications:") for x in xs: print(x) print("") def usage_str(load_users_fn, n_users): load = load_users_fn(n_users) return load_color_fmt(load, "For " + magnitude_fmt(n_users) + " users, receiving bandwidth is " + sizeof_fmt(load_users_fn(n_users)) + "/hour") def print_usage(load_users): print(usage_str(load_users, 100)) print(usage_str(load_users, 100 * 100)) print(usage_str(load_users, 100 * 100 * 100)) print("") def latency_str(latency_users_fn, n_users, degree): latency = latency_users_fn(n_users, degree) return load_color_fmt(latency, "For " + magnitude_fmt(n_users) + " the average latency is " + ("%.3f" % latency_users_fn(n_users, degree)) + " s") def print_latency(latency_users): print(latency_str(latency_users, 100, average_node_degree)) print(latency_str(latency_users, 100 * 100, average_node_degree)) print(latency_str(latency_users, 100 * 100 * 100, average_node_degree)) print("") def num_edges_dregular(num_nodes, degree): # we assume and even d; d-regular graphs with both where both n and d are odd don't exist return num_nodes * (degree/2) def avg_node_distance_upper_bound(n_users, degree): return math.log(n_users, degree) # Assumptions #----------------------------------------------------------- # Users sent messages at a constant rate # The network topology is a d-regular graph (gossipsub aims at achieving this). # # Goal: # - reasonable bw and fetch time # ~1GB per month, ~ 30 MB per day, ~1 MB per hour average_node_degree = 6 # has to be even message_size = 0.002 # in MB (Mega Bytes) messages_sent_per_hour = 5 gossip_message_size = 0.00005 # 50Bytes in MB (see https://github.com/libp2p/specs/pull/413#discussion_r1018821589 ) d_lazy = 6 # gossip out degree 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) avg_ratio_gossip_replys = 0.01 # -> this is a wild guess! (todo: investigate) average_delay_per_hop = 0.1 #s # TODO: load case for status control messages (note: this also introduces messages by currently online, but not active users.) # TODO: spread in the latency distribution (the highest 10%ish of latencies might be too high) # Assumption strings (general/topology) a1 = "- A01. Message size (static): " + sizeof_fmt_kb(message_size) a2 = "- A02. Messages sent per node per hour (static) (assuming no spam; but also no rate limiting.): " + str(messages_sent_per_hour) a3 = "- A03. The network topology is a d-regular graph of degree (static): " + str(average_node_degree) a4 = "- A04. Messages outside of Waku Relay are not considered, e.g. store messages." a5 = "- A05. Messages are only sent once along an edge. (requires delays before sending)" a6 = "- A06. Messages are sent to all d-1 neighbours as soon as receiving a message (current operation)" # Thanks @Mmenduist # Assumption strings (store) a21 = "- A21. Store nodes do not store duplicate messages." # Assumption strings (gossip) a31 = "- A21. Gossip is not considered." a32 = "- A32. Gossip message size (IHAVE/IWANT) (static):" + sizeof_fmt_kb(gossip_message_size) a33 = "- A33. Ratio of IHAVEs followed-up by an IWANT (incl. the actual requested message):" + str(avg_ratio_gossip_replys) # Assumption strings (delay) a41 = "- A41. Delay is calculated based on an upper bound of the expected distance." a42 = "- A42. Average delay per hop (static): " + str(average_delay_per_hop) + "s." # Cases Load Per Node #----------------------------------------------------------- # Case 1 def load_case1(n_users): return message_size * messages_sent_per_hour * n_users def print_load_case1(): print_header("Load case 1 (store load)") print_assumptions([a1, a2, a3, a4, a21]) print_usage(load_case1) print("") print("------------------------------------------------------------") # Case 2 def load_case2(n_users): return message_size * messages_sent_per_hour * num_edges_dregular(n_users, average_node_degree) def print_load_case2(): print_header("Load case 2 (received load per node)") print("") print_assumptions([a1, a2, a3, a4, a5, a31]) print_usage(load_case2) print("") print("------------------------------------------------------------") # Case 3 def load_case3(n_users): return message_size * messages_sent_per_hour * n_users * (average_node_degree-1) def print_load_case3(): print_header("Load case 3 (received load per node)") print_assumptions([a1, a2, a3, a4, a6, a31]) print_usage(load_case3) print("") print("------------------------------------------------------------") # Case 4: def load_case4(n_users): messages_received_per_hour = messages_sent_per_hour * n_users * (average_node_degree-1) # see case 3 messages_load = message_size * messages_received_per_hour num_ihave = messages_received_per_hour * d_lazy * mcache_gossip ihave_load = num_ihave * gossip_message_size gossip_response_load = (num_ihave * (gossip_message_size + message_size)) * avg_ratio_gossip_replys # reply load contains both an IWANT (from requester to sender), and the actual wanted message (from sender to requester) gossip_total = ihave_load + gossip_response_load return messages_load + gossip_total def print_load_case4(): print_header("Load case 4 (received load per node incl. gossip)") print_assumptions([a1, a2, a3, a4, a6, a32, a33]) print_usage(load_case4) print("") print("------------------------------------------------------------") # Cases average latency #----------------------------------------------------------- def latency_case1(n_users, degree): return avg_node_distance_upper_bound(n_users, degree) * average_delay_per_hop def print_latency_case1(): print_header("Latency case 1 :: Topology: 6-regular graph. No gossip (note: gossip would help here)") print_assumptions([a3, a41, a42]) print_latency(latency_case1) print("") print("------------------------------------------------------------") # Run cases #----------------------------------------------------------- # Print goals print("") print(bcolors.HEADER + "Waku relay theoretical model (single shard). Attempts to encode characteristics of it." + bcolors.ENDC) print("Note: this analysis is concerned with currently active users.") print("The total number of users of an app using Waku relay could be factor 10 to 100 higher (estimated based on @Menduist Discord checks.)") print("") print("" + bcolors.ENDC) print_load_case1() print_load_case2() print_load_case3() print_load_case4() print_latency_case1() # Plot #----------------------------------------------------------- def plot(): n_users = np.logspace(2, 6, num=5) print(n_users) plt.xlim(100, 10**6) plt.ylim(1, 10**6) plt.plot(n_users, load_case1(n_users), label='case 1', linewidth=4, linestyle='dashed') plt.plot(n_users, load_case2(n_users), label='case 2', linewidth=4, linestyle='dashed') plt.plot(n_users, load_case3(n_users), label='case 3', linewidth=4, linestyle='dashed') plt.plot(n_users, load_case4(n_users), label='case 4', linewidth=4, linestyle='dashed') case1 = "Case 1. top: 6-regular; store load" case2 = "Case 2. top: 6-regular; receive load per node, send delay to reduce duplicates" case3 = "Case 3. top: 6-regular; receive load per node, current operation" case4 = "Case 4. top: 6-regular; receive load per node, current operation, incl. gossip" plt.xlabel('number of users (log)') plt.ylabel('mb/hour (log)') plt.legend([case1, case2, case3, case4], loc='upper left') plt.xscale('log') plt.yscale('log') plt.axhspan(0, 10, facecolor='0.2', alpha=0.2, color='blue') plt.axhspan(10, 30, facecolor='0.2', alpha=0.2, color='green') plt.axhspan(30, 100, facecolor='0.2', alpha=0.2, color='orange') plt.axhspan(100, 10**6, facecolor='0.2', alpha=0.2, color='red') # plt.show() figure = plt.gcf() # get current figure figure.set_size_inches(16, 9) # plt.savefig("waku_scaling_plot.svg") plt.savefig("waku_scaling_plot.png", dpi=300, orientation="landscape") plot()