+
+from nevow import inevow, rend, tags as T
+import math
+from allmydata.util import mathutil
+from allmydata.web.common import getxmlfile
+
+# factorial and binomial copied from
+# http://mail.python.org/pipermail/python-list/2007-April/435718.html
+
+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 xrange(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 xrange(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 = getxmlfile("provisioning.xhtml")
+
+ def render_forms(self, ctx, data):
+ req = inevow.IRequest(ctx)
+
+ def getarg(name, astype=int):
+ if req.method != "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(mathutil.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 = mathutil.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 = mathutil.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
projects / tahoe-lafs / tahoe-lafs.git / commitdiff