from nevow import inevow, rend, loaders, tags as T import math import util # factorial and binomial copied from # http://mail.python.org/pipermail/python-list/2007-April/435718.html def div_ceil(n, d): """ The smallest integer k such that k*d >= n. """ return (n/d) + (n%d != 0) def factorial(n): """factorial(n): return the factorial of the integer n. factorial(0) = 1 factorial(n) with n<0 is -factorial(abs(n)) """ result = 1 for i in range(1, abs(n)+1): result *= i assert n >= 0 return result def binomial(n, k): assert 0 <= k <= n if k == 0 or k == n: return 1 # calculate n!/k! as one product, avoiding factors that # just get canceled P = k+1 for i in range(k+2, n+1): P *= i # if you are paranoid: # C, rem = divmod(P, factorial(n-k)) # assert rem == 0 # return C return P//factorial(n-k) class ProvisioningTool(rend.Page): addSlash = True docFactory = loaders.xmlfile(util.sibling("provisioning.xhtml")) def render_forms(self, ctx, data): req = inevow.IRequest(ctx) def getarg(name, astype=int): if req.method != b"POST": return None if name in req.fields: return astype(req.fields[name].value) return None return self.do_forms(getarg) def do_forms(self, getarg): filled = getarg("filled", bool) def get_and_set(name, options, default=None, astype=int): current_value = getarg(name, astype) i_select = T.select(name=name) for (count, description) in options: count = astype(count) if ((current_value is not None and count == current_value) or (current_value is None and count == default)): o = T.option(value=str(count), selected="true")[description] else: o = T.option(value=str(count))[description] i_select = i_select[o] if current_value is None: current_value = default return current_value, i_select sections = {} def add_input(section, text, entry): if section not in sections: sections[section] = [] sections[section].extend([T.div[text, ": ", entry], "\n"]) def add_output(section, entry): if section not in sections: sections[section] = [] sections[section].extend([entry, "\n"]) def build_section(section): return T.fieldset[T.legend[section], sections[section]] def number(value, suffix=""): scaling = 1 if value < 1: fmt = "%1.2g%s" elif value < 100: fmt = "%.1f%s" elif value < 1000: fmt = "%d%s" elif value < 1e6: fmt = "%.2fk%s"; scaling = 1e3 elif value < 1e9: fmt = "%.2fM%s"; scaling = 1e6 elif value < 1e12: fmt = "%.2fG%s"; scaling = 1e9 elif value < 1e15: fmt = "%.2fT%s"; scaling = 1e12 elif value < 1e18: fmt = "%.2fP%s"; scaling = 1e15 else: fmt = "huge! %g%s" return fmt % (value / scaling, suffix) user_counts = [(5, "5 users"), (50, "50 users"), (200, "200 users"), (1000, "1k users"), (10000, "10k users"), (50000, "50k users"), (100000, "100k users"), (500000, "500k users"), (1000000, "1M users"), ] num_users, i_num_users = get_and_set("num_users", user_counts, 50000) add_input("Users", "How many users are on this network?", i_num_users) files_per_user_counts = [(100, "100 files"), (1000, "1k files"), (10000, "10k files"), (100000, "100k files"), (1e6, "1M files"), ] files_per_user, i_files_per_user = get_and_set("files_per_user", files_per_user_counts, 1000) add_input("Users", "How many files for each user? (avg)", i_files_per_user) space_per_user_sizes = [(1e6, "1MB"), (10e6, "10MB"), (100e6, "100MB"), (200e6, "200MB"), (1e9, "1GB"), (2e9, "2GB"), (5e9, "5GB"), (10e9, "10GB"), (100e9, "100GB"), (1e12, "1TB"), (2e12, "2TB"), (5e12, "5TB"), ] # Estimate ~5gb per user as a more realistic case space_per_user, i_space_per_user = get_and_set("space_per_user", space_per_user_sizes, 5e9) add_input("Users", "How much data for each user? (avg)", i_space_per_user) sharing_ratios = [(1.0, "1.0x"), (1.1, "1.1x"), (2.0, "2.0x"), ] sharing_ratio, i_sharing_ratio = get_and_set("sharing_ratio", sharing_ratios, 1.0, float) add_input("Users", "What is the sharing ratio? (1.0x is no-sharing and" " no convergence)", i_sharing_ratio) # Encoding parameters encoding_choices = [("3-of-10-5", "3.3x (3-of-10, repair below 5)"), ("3-of-10-8", "3.3x (3-of-10, repair below 8)"), ("5-of-10-7", "2x (5-of-10, repair below 7)"), ("8-of-10-9", "1.25x (8-of-10, repair below 9)"), ("27-of-30-28", "1.1x (27-of-30, repair below 28"), ("25-of-100-50", "4x (25-of-100, repair below 50)"), ] encoding_parameters, i_encoding_parameters = \ get_and_set("encoding_parameters", encoding_choices, "3-of-10-5", str) encoding_pieces = encoding_parameters.split("-") k = int(encoding_pieces[0]) assert encoding_pieces[1] == "of" n = int(encoding_pieces[2]) # we repair the file when the number of available shares drops below # this value repair_threshold = int(encoding_pieces[3]) add_input("Servers", "What are the default encoding parameters?", i_encoding_parameters) # Server info num_server_choices = [ (5, "5 servers"), (10, "10 servers"), (15, "15 servers"), (30, "30 servers"), (50, "50 servers"), (100, "100 servers"), (200, "200 servers"), (300, "300 servers"), (500, "500 servers"), (1000, "1k servers"), (2000, "2k servers"), (5000, "5k servers"), (10e3, "10k servers"), (100e3, "100k servers"), (1e6, "1M servers"), ] num_servers, i_num_servers = \ get_and_set("num_servers", num_server_choices, 30, int) add_input("Servers", "How many servers are there?", i_num_servers) # availability is measured in dBA = -dBF, where 0dBF is 100% failure, # 10dBF is 10% failure, 20dBF is 1% failure, etc server_dBA_choices = [ (10, "90% [10dBA] (2.4hr/day)"), (13, "95% [13dBA] (1.2hr/day)"), (20, "99% [20dBA] (14min/day or 3.5days/year)"), (23, "99.5% [23dBA] (7min/day or 1.75days/year)"), (30, "99.9% [30dBA] (87sec/day or 9hours/year)"), (40, "99.99% [40dBA] (60sec/week or 53min/year)"), (50, "99.999% [50dBA] (5min per year)"), ] server_dBA, i_server_availability = \ get_and_set("server_availability", server_dBA_choices, 20, int) add_input("Servers", "What is the server availability?", i_server_availability) drive_MTBF_choices = [ (40, "40,000 Hours"), ] drive_MTBF, i_drive_MTBF = \ get_and_set("drive_MTBF", drive_MTBF_choices, 40, int) add_input("Drives", "What is the hard drive MTBF?", i_drive_MTBF) # http://www.tgdaily.com/content/view/30990/113/ # http://labs.google.com/papers/disk_failures.pdf # google sees: # 1.7% of the drives they replaced were 0-1 years old # 8% of the drives they repalced were 1-2 years old # 8.6% were 2-3 years old # 6% were 3-4 years old, about 8% were 4-5 years old drive_size_choices = [ (100, "100 GB"), (250, "250 GB"), (500, "500 GB"), (750, "750 GB"), (1000, "1000 GB"), (2000, "2000 GB"), (3000, "3000 GB"), ] drive_size, i_drive_size = \ get_and_set("drive_size", drive_size_choices, 3000, int) drive_size = drive_size * 1e9 add_input("Drives", "What is the capacity of each hard drive?", i_drive_size) drive_failure_model_choices = [ ("E", "Exponential"), ("U", "Uniform"), ] drive_failure_model, i_drive_failure_model = \ get_and_set("drive_failure_model", drive_failure_model_choices, "E", str) add_input("Drives", "How should we model drive failures?", i_drive_failure_model) # drive_failure_rate is in failures per second if drive_failure_model == "E": drive_failure_rate = 1.0 / (drive_MTBF * 1000 * 3600) else: drive_failure_rate = 0.5 / (drive_MTBF * 1000 * 3600) # deletion/gc/ownership mode ownership_choices = [ ("A", "no deletion, no gc, no owners"), ("B", "deletion, no gc, no owners"), ("C", "deletion, share timers, no owners"), ("D", "deletion, no gc, yes owners"), ("E", "deletion, owner timers"), ] ownership_mode, i_ownership_mode = \ get_and_set("ownership_mode", ownership_choices, "A", str) add_input("Servers", "What is the ownership mode?", i_ownership_mode) # client access behavior access_rates = [ (1, "one file per day"), (10, "10 files per day"), (100, "100 files per day"), (1000, "1k files per day"), (10e3, "10k files per day"), (100e3, "100k files per day"), ] download_files_per_day, i_download_rate = \ get_and_set("download_rate", access_rates, 100, int) add_input("Users", "How many files are downloaded per day?", i_download_rate) download_rate = 1.0 * download_files_per_day / (24*60*60) upload_files_per_day, i_upload_rate = \ get_and_set("upload_rate", access_rates, 10, int) add_input("Users", "How many files are uploaded per day?", i_upload_rate) upload_rate = 1.0 * upload_files_per_day / (24*60*60) delete_files_per_day, i_delete_rate = \ get_and_set("delete_rate", access_rates, 10, int) add_input("Users", "How many files are deleted per day?", i_delete_rate) delete_rate = 1.0 * delete_files_per_day / (24*60*60) # the value is in days lease_timers = [ (1, "one refresh per day"), (7, "one refresh per week"), ] lease_timer, i_lease = \ get_and_set("lease_timer", lease_timers, 7, int) add_input("Users", "How frequently do clients refresh files or accounts? " "(if necessary)", i_lease) seconds_per_lease = 24*60*60*lease_timer check_timer_choices = [ (1, "every week"), (4, "every month"), (8, "every two months"), (16, "every four months"), ] check_timer, i_check_timer = \ get_and_set("check_timer", check_timer_choices, 4, int) add_input("Users", "How frequently should we check on each file?", i_check_timer) file_check_interval = check_timer * 7 * 24 * 3600 if filled: add_output("Users", T.div["Total users: %s" % number(num_users)]) add_output("Users", T.div["Files per user: %s" % number(files_per_user)]) file_size = 1.0 * space_per_user / files_per_user add_output("Users", T.div["Average file size: ", number(file_size)]) total_files = num_users * files_per_user / sharing_ratio add_output("Grid", T.div["Total number of files in grid: ", number(total_files)]) total_space = num_users * space_per_user / sharing_ratio add_output("Grid", T.div["Total volume of plaintext in grid: ", number(total_space, "B")]) total_shares = n * total_files add_output("Grid", T.div["Total shares in grid: ", number(total_shares)]) expansion = float(n) / float(k) total_usage = expansion * total_space add_output("Grid", T.div["Share data in grid: ", number(total_usage, "B")]) if n > num_servers: # silly configuration, causes Tahoe2 to wrap and put multiple # shares on some servers. add_output("Servers", T.div["non-ideal: more shares than servers" " (n=%d, servers=%d)" % (n, num_servers)]) # every file has at least one share on every server buckets_per_server = total_files shares_per_server = total_files * ((1.0 * n) / num_servers) else: # if nobody is full, then no lease requests will be turned # down for lack of space, and no two shares for the same file # will share a server. Therefore the chance that any given # file has a share on any given server is n/num_servers. buckets_per_server = total_files * ((1.0 * n) / num_servers) # since each such represented file only puts one share on a # server, the total number of shares per server is the same. shares_per_server = buckets_per_server add_output("Servers", T.div["Buckets per server: ", number(buckets_per_server)]) add_output("Servers", T.div["Shares per server: ", number(shares_per_server)]) # how much space is used on the storage servers for the shares? # the share data itself share_data_per_server = total_usage / num_servers add_output("Servers", T.div["Share data per server: ", number(share_data_per_server, "B")]) # this is determined empirically. H=hashsize=32, for a one-segment # file and 3-of-10 encoding share_validation_per_server = 266 * shares_per_server # this could be 423*buckets_per_server, if we moved the URI # extension into a separate file, but that would actually consume # *more* space (minimum filesize is 4KiB), unless we moved all # shares for a given bucket into a single file. share_uri_extension_per_server = 423 * shares_per_server # ownership mode adds per-bucket data H = 32 # depends upon the desired security of delete/refresh caps # bucket_lease_size is the amount of data needed to keep track of # the delete/refresh caps for each bucket. bucket_lease_size = 0 client_bucket_refresh_rate = 0 owner_table_size = 0 if ownership_mode in ("B", "C", "D", "E"): bucket_lease_size = sharing_ratio * 1.0 * H if ownership_mode in ("B", "C"): # refreshes per second per client client_bucket_refresh_rate = (1.0 * n * files_per_user / seconds_per_lease) add_output("Users", T.div["Client share refresh rate (outbound): ", number(client_bucket_refresh_rate, "Hz")]) server_bucket_refresh_rate = (client_bucket_refresh_rate * num_users / num_servers) add_output("Servers", T.div["Server share refresh rate (inbound): ", number(server_bucket_refresh_rate, "Hz")]) if ownership_mode in ("D", "E"): # each server must maintain a bidirectional mapping from # buckets to owners. One way to implement this would be to # put a list of four-byte owner numbers into each bucket, and # a list of four-byte share numbers into each owner (although # of course we'd really just throw it into a database and let # the experts take care of the details). owner_table_size = 2*(buckets_per_server * sharing_ratio * 4) if ownership_mode in ("E",): # in this mode, clients must refresh one timer per server client_account_refresh_rate = (1.0 * num_servers / seconds_per_lease) add_output("Users", T.div["Client account refresh rate (outbound): ", number(client_account_refresh_rate, "Hz")]) server_account_refresh_rate = (client_account_refresh_rate * num_users / num_servers) add_output("Servers", T.div["Server account refresh rate (inbound): ", number(server_account_refresh_rate, "Hz")]) # TODO: buckets vs shares here is a bit wonky, but in # non-wrapping grids it shouldn't matter share_lease_per_server = bucket_lease_size * buckets_per_server share_ownertable_per_server = owner_table_size share_space_per_server = (share_data_per_server + share_validation_per_server + share_uri_extension_per_server + share_lease_per_server + share_ownertable_per_server) add_output("Servers", T.div["Share space per server: ", number(share_space_per_server, "B"), " (data ", number(share_data_per_server, "B"), ", validation ", number(share_validation_per_server, "B"), ", UEB ", number(share_uri_extension_per_server, "B"), ", lease ", number(share_lease_per_server, "B"), ", ownertable ", number(share_ownertable_per_server, "B"), ")", ]) # rates client_download_share_rate = download_rate * k client_download_byte_rate = download_rate * file_size add_output("Users", T.div["download rate: shares = ", number(client_download_share_rate, "Hz"), " , bytes = ", number(client_download_byte_rate, "Bps"), ]) total_file_check_rate = 1.0 * total_files / file_check_interval client_check_share_rate = total_file_check_rate / num_users add_output("Users", T.div["file check rate: shares = ", number(client_check_share_rate, "Hz"), " (interval = %s)" % number(1 / client_check_share_rate, "s"), ]) client_upload_share_rate = upload_rate * n # TODO: doesn't include overhead client_upload_byte_rate = upload_rate * file_size * expansion add_output("Users", T.div["upload rate: shares = ", number(client_upload_share_rate, "Hz"), " , bytes = ", number(client_upload_byte_rate, "Bps"), ]) client_delete_share_rate = delete_rate * n server_inbound_share_rate = (client_upload_share_rate * num_users / num_servers) server_inbound_byte_rate = (client_upload_byte_rate * num_users / num_servers) add_output("Servers", T.div["upload rate (inbound): shares = ", number(server_inbound_share_rate, "Hz"), " , bytes = ", number(server_inbound_byte_rate, "Bps"), ]) add_output("Servers", T.div["share check rate (inbound): ", number(total_file_check_rate * n / num_servers, "Hz"), ]) server_share_modify_rate = ((client_upload_share_rate + client_delete_share_rate) * num_users / num_servers) add_output("Servers", T.div["share modify rate: shares = ", number(server_share_modify_rate, "Hz"), ]) server_outbound_share_rate = (client_download_share_rate * num_users / num_servers) server_outbound_byte_rate = (client_download_byte_rate * num_users / num_servers) add_output("Servers", T.div["download rate (outbound): shares = ", number(server_outbound_share_rate, "Hz"), " , bytes = ", number(server_outbound_byte_rate, "Bps"), ]) total_share_space = num_servers * share_space_per_server add_output("Grid", T.div["Share space consumed: ", number(total_share_space, "B")]) add_output("Grid", T.div[" %% validation: %.2f%%" % (100.0 * share_validation_per_server / share_space_per_server)]) add_output("Grid", T.div[" %% uri-extension: %.2f%%" % (100.0 * share_uri_extension_per_server / share_space_per_server)]) add_output("Grid", T.div[" %% lease data: %.2f%%" % (100.0 * share_lease_per_server / share_space_per_server)]) add_output("Grid", T.div[" %% owner data: %.2f%%" % (100.0 * share_ownertable_per_server / share_space_per_server)]) add_output("Grid", T.div[" %% share data: %.2f%%" % (100.0 * share_data_per_server / share_space_per_server)]) add_output("Grid", T.div["file check rate: ", number(total_file_check_rate, "Hz")]) total_drives = max(div_ceil(int(total_share_space), int(drive_size)), num_servers) add_output("Drives", T.div["Total drives: ", number(total_drives), " drives"]) drives_per_server = div_ceil(total_drives, num_servers) add_output("Servers", T.div["Drives per server: ", drives_per_server]) # costs if drive_size == 3000 * 1e9: add_output("Servers", T.div["3000GB drive: $250 each"]) drive_cost = 250 else: add_output("Servers", T.div[T.b["unknown cost per drive, assuming $100"]]) drive_cost = 100 if drives_per_server <= 4: add_output("Servers", T.div["1U box with <= 4 drives: $1500"]) server_cost = 1500 # typical 1U box elif drives_per_server <= 12: add_output("Servers", T.div["2U box with <= 12 drives: $2500"]) server_cost = 2500 # 2U box else: add_output("Servers", T.div[T.b["Note: too many drives per server, " "assuming $3000"]]) server_cost = 3000 server_capital_cost = (server_cost + drives_per_server * drive_cost) total_server_cost = float(num_servers * server_capital_cost) add_output("Servers", T.div["Capital cost per server: $", server_capital_cost]) add_output("Grid", T.div["Capital cost for all servers: $", number(total_server_cost)]) # $70/Mbps/mo # $44/server/mo power+space server_bandwidth = max(server_inbound_byte_rate, server_outbound_byte_rate) server_bandwidth_mbps = div_ceil(int(server_bandwidth*8), int(1e6)) server_monthly_cost = 70*server_bandwidth_mbps + 44 add_output("Servers", T.div["Monthly cost per server: $", server_monthly_cost]) add_output("Users", T.div["Capital cost per user: $", number(total_server_cost / num_users)]) # reliability any_drive_failure_rate = total_drives * drive_failure_rate any_drive_MTBF = 1 // any_drive_failure_rate # in seconds any_drive_MTBF_days = any_drive_MTBF / 86400 add_output("Drives", T.div["MTBF (any drive): ", number(any_drive_MTBF_days), " days"]) drive_replacement_monthly_cost = (float(drive_cost) * any_drive_failure_rate *30*86400) add_output("Grid", T.div["Monthly cost of replacing drives: $", number(drive_replacement_monthly_cost)]) total_server_monthly_cost = float(num_servers * server_monthly_cost + drive_replacement_monthly_cost) add_output("Grid", T.div["Monthly cost for all servers: $", number(total_server_monthly_cost)]) add_output("Users", T.div["Monthly cost per user: $", number(total_server_monthly_cost / num_users)]) # availability file_dBA = self.file_availability(k, n, server_dBA) user_files_dBA = self.many_files_availability(file_dBA, files_per_user) all_files_dBA = self.many_files_availability(file_dBA, total_files) add_output("Users", T.div["availability of: ", "arbitrary file = %d dBA, " % file_dBA, "all files of user1 = %d dBA, " % user_files_dBA, "all files in grid = %d dBA" % all_files_dBA, ], ) time_until_files_lost = (n-k+1) / any_drive_failure_rate add_output("Grid", T.div["avg time until files are lost: ", number(time_until_files_lost, "s"), ", ", number(time_until_files_lost/86400, " days"), ]) share_data_loss_rate = any_drive_failure_rate * drive_size add_output("Grid", T.div["share data loss rate: ", number(share_data_loss_rate,"Bps")]) # the worst-case survival numbers occur when we do a file check # and the file is just above the threshold for repair (so we # decide to not repair it). The question is then: what is the # chance that the file will decay so badly before the next check # that we can't recover it? The resulting probability is per # check interval. # Note that the chances of us getting into this situation are low. P_disk_failure_during_interval = (drive_failure_rate * file_check_interval) disk_failure_dBF = 10*math.log10(P_disk_failure_during_interval) disk_failure_dBA = -disk_failure_dBF file_survives_dBA = self.file_availability(k, repair_threshold, disk_failure_dBA) user_files_survives_dBA = self.many_files_availability( \ file_survives_dBA, files_per_user) all_files_survives_dBA = self.many_files_availability( \ file_survives_dBA, total_files) add_output("Users", T.div["survival of: ", "arbitrary file = %d dBA, " % file_survives_dBA, "all files of user1 = %d dBA, " % user_files_survives_dBA, "all files in grid = %d dBA" % all_files_survives_dBA, " (per worst-case check interval)", ]) all_sections = [] all_sections.append(build_section("Users")) all_sections.append(build_section("Servers")) all_sections.append(build_section("Drives")) if "Grid" in sections: all_sections.append(build_section("Grid")) f = T.form(action=".", method="post", enctype="multipart/form-data") if filled: action = "Recompute" else: action = "Compute" f = f[T.input(type="hidden", name="filled", value="true"), T.input(type="submit", value=action), all_sections, ] try: from allmydata import reliability # we import this just to test to see if the page is available _hush_pyflakes = reliability del _hush_pyflakes f = [T.div[T.a(href="../reliability")["Reliability Math"]], f] except ImportError: pass return f def file_availability(self, k, n, server_dBA): """ The full formula for the availability of a specific file is:: 1 - sum([choose(N,i) * p**i * (1-p)**(N-i)] for i in range(k)]) Where choose(N,i) = N! / ( i! * (N-i)! ) . Note that each term of this summation is the probability that there are exactly 'i' servers available, and what we're doing is adding up the cases where i is too low. This is a nuisance to calculate at all accurately, especially once N gets large, and when p is close to unity. So we make an engineering approximation: if (1-p) is very small, then each [i] term is much larger than the [i-1] term, and the sum is dominated by the i=k-1 term. This only works for (1-p) < 10%, and when the choose() function doesn't rise fast enough to compensate. For high-expansion encodings (3-of-10, 25-of-100), the choose() function is rising at the same time as the (1-p)**(N-i) term, so that's not an issue. For low-expansion encodings (7-of-10, 75-of-100) the two values are moving in opposite directions, so more care must be taken. Note that the p**i term has only a minor effect as long as (1-p)*N is small, and even then the effect is attenuated by the 1-p term. """ assert server_dBA > 9 # >=90% availability to use the approximation factor = binomial(n, k-1) factor_dBA = 10 * math.log10(factor) exponent = n - k + 1 file_dBA = server_dBA * exponent - factor_dBA return file_dBA def many_files_availability(self, file_dBA, num_files): """The probability that 'num_files' independent bernoulli trials will succeed (i.e. we can recover all files in the grid at any given moment) is p**num_files . Since p is close to unity, we express in p in dBA instead, so we can get useful precision on q (=1-p), and then the formula becomes:: P_some_files_unavailable = 1 - (1 - q)**num_files That (1-q)**n expands with the usual binomial sequence, 1 - nq + Xq**2 ... + Xq**n . We use the same approximation as before, since we know q is close to zero, and we get to ignore all the terms past -nq. """ many_files_dBA = file_dBA - 10 * math.log10(num_files) return many_files_dBA