+++ /dev/null
-
-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 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 = loaders.xmlfile(util.sibling("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(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
projects / tahoe-lafs / tahoe-lafs.git / commitdiff