mirror of
https://github.com/tahoe-lafs/tahoe-lafs.git
synced 2024-12-23 23:02:25 +00:00
80b43b409f
It looks like commit 916d26e710, in
addition to making a one-line fix for #1681, also deleted
misc/operations_helpers/provisioning/provisioning.py entirely. This
brings it back.
777 lines
36 KiB
Python
777 lines
36 KiB
Python
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from nevow import inevow, rend, loaders, tags as T
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import math
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import util
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# factorial and binomial copied from
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# http://mail.python.org/pipermail/python-list/2007-April/435718.html
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def div_ceil(n, d):
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"""
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The smallest integer k such that k*d >= n.
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"""
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return (n/d) + (n%d != 0)
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def factorial(n):
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"""factorial(n): return the factorial of the integer n.
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factorial(0) = 1
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factorial(n) with n<0 is -factorial(abs(n))
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"""
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result = 1
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for i in xrange(1, abs(n)+1):
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result *= i
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assert n >= 0
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return result
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def binomial(n, k):
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assert 0 <= k <= n
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if k == 0 or k == n:
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return 1
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# calculate n!/k! as one product, avoiding factors that
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# just get canceled
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P = k+1
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for i in xrange(k+2, n+1):
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P *= i
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# if you are paranoid:
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# C, rem = divmod(P, factorial(n-k))
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# assert rem == 0
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# return C
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return P//factorial(n-k)
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class ProvisioningTool(rend.Page):
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addSlash = True
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docFactory = loaders.xmlfile(util.sibling("provisioning.xhtml"))
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def render_forms(self, ctx, data):
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req = inevow.IRequest(ctx)
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def getarg(name, astype=int):
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if req.method != "POST":
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return None
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if name in req.fields:
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return astype(req.fields[name].value)
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return None
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return self.do_forms(getarg)
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def do_forms(self, getarg):
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filled = getarg("filled", bool)
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def get_and_set(name, options, default=None, astype=int):
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current_value = getarg(name, astype)
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i_select = T.select(name=name)
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for (count, description) in options:
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count = astype(count)
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if ((current_value is not None and count == current_value) or
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(current_value is None and count == default)):
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o = T.option(value=str(count), selected="true")[description]
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else:
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o = T.option(value=str(count))[description]
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i_select = i_select[o]
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if current_value is None:
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current_value = default
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return current_value, i_select
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sections = {}
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def add_input(section, text, entry):
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if section not in sections:
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sections[section] = []
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sections[section].extend([T.div[text, ": ", entry], "\n"])
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def add_output(section, entry):
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if section not in sections:
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sections[section] = []
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sections[section].extend([entry, "\n"])
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def build_section(section):
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return T.fieldset[T.legend[section], sections[section]]
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def number(value, suffix=""):
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scaling = 1
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if value < 1:
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fmt = "%1.2g%s"
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elif value < 100:
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fmt = "%.1f%s"
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elif value < 1000:
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fmt = "%d%s"
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elif value < 1e6:
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fmt = "%.2fk%s"; scaling = 1e3
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elif value < 1e9:
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fmt = "%.2fM%s"; scaling = 1e6
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elif value < 1e12:
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fmt = "%.2fG%s"; scaling = 1e9
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elif value < 1e15:
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fmt = "%.2fT%s"; scaling = 1e12
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elif value < 1e18:
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fmt = "%.2fP%s"; scaling = 1e15
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else:
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fmt = "huge! %g%s"
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return fmt % (value / scaling, suffix)
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user_counts = [(5, "5 users"),
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(50, "50 users"),
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(200, "200 users"),
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(1000, "1k users"),
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(10000, "10k users"),
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(50000, "50k users"),
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(100000, "100k users"),
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(500000, "500k users"),
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(1000000, "1M users"),
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]
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num_users, i_num_users = get_and_set("num_users", user_counts, 50000)
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add_input("Users",
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"How many users are on this network?", i_num_users)
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files_per_user_counts = [(100, "100 files"),
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(1000, "1k files"),
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(10000, "10k files"),
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(100000, "100k files"),
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(1e6, "1M files"),
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]
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files_per_user, i_files_per_user = get_and_set("files_per_user",
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files_per_user_counts,
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1000)
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add_input("Users",
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"How many files for each user? (avg)",
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i_files_per_user)
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space_per_user_sizes = [(1e6, "1MB"),
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(10e6, "10MB"),
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(100e6, "100MB"),
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(200e6, "200MB"),
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(1e9, "1GB"),
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(2e9, "2GB"),
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(5e9, "5GB"),
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(10e9, "10GB"),
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(100e9, "100GB"),
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(1e12, "1TB"),
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(2e12, "2TB"),
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(5e12, "5TB"),
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]
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# Estimate ~5gb per user as a more realistic case
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space_per_user, i_space_per_user = get_and_set("space_per_user",
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space_per_user_sizes,
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5e9)
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add_input("Users",
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"How much data for each user? (avg)",
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i_space_per_user)
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sharing_ratios = [(1.0, "1.0x"),
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(1.1, "1.1x"),
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(2.0, "2.0x"),
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]
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sharing_ratio, i_sharing_ratio = get_and_set("sharing_ratio",
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sharing_ratios, 1.0,
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float)
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add_input("Users",
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"What is the sharing ratio? (1.0x is no-sharing and"
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" no convergence)", i_sharing_ratio)
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# Encoding parameters
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encoding_choices = [("3-of-10-5", "3.3x (3-of-10, repair below 5)"),
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("3-of-10-8", "3.3x (3-of-10, repair below 8)"),
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("5-of-10-7", "2x (5-of-10, repair below 7)"),
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("8-of-10-9", "1.25x (8-of-10, repair below 9)"),
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("27-of-30-28", "1.1x (27-of-30, repair below 28"),
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("25-of-100-50", "4x (25-of-100, repair below 50)"),
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]
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encoding_parameters, i_encoding_parameters = \
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get_and_set("encoding_parameters",
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encoding_choices, "3-of-10-5", str)
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encoding_pieces = encoding_parameters.split("-")
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k = int(encoding_pieces[0])
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assert encoding_pieces[1] == "of"
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n = int(encoding_pieces[2])
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# we repair the file when the number of available shares drops below
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# this value
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repair_threshold = int(encoding_pieces[3])
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add_input("Servers",
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"What are the default encoding parameters?",
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i_encoding_parameters)
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# Server info
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num_server_choices = [ (5, "5 servers"),
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(10, "10 servers"),
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(15, "15 servers"),
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(30, "30 servers"),
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(50, "50 servers"),
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(100, "100 servers"),
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(200, "200 servers"),
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(300, "300 servers"),
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(500, "500 servers"),
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(1000, "1k servers"),
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(2000, "2k servers"),
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(5000, "5k servers"),
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(10e3, "10k servers"),
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(100e3, "100k servers"),
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(1e6, "1M servers"),
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]
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num_servers, i_num_servers = \
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get_and_set("num_servers", num_server_choices, 30, int)
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add_input("Servers",
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"How many servers are there?", i_num_servers)
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# availability is measured in dBA = -dBF, where 0dBF is 100% failure,
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# 10dBF is 10% failure, 20dBF is 1% failure, etc
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server_dBA_choices = [ (10, "90% [10dBA] (2.4hr/day)"),
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(13, "95% [13dBA] (1.2hr/day)"),
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(20, "99% [20dBA] (14min/day or 3.5days/year)"),
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(23, "99.5% [23dBA] (7min/day or 1.75days/year)"),
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(30, "99.9% [30dBA] (87sec/day or 9hours/year)"),
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(40, "99.99% [40dBA] (60sec/week or 53min/year)"),
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(50, "99.999% [50dBA] (5min per year)"),
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]
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server_dBA, i_server_availability = \
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get_and_set("server_availability",
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server_dBA_choices,
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20, int)
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add_input("Servers",
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"What is the server availability?", i_server_availability)
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drive_MTBF_choices = [ (40, "40,000 Hours"),
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]
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drive_MTBF, i_drive_MTBF = \
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get_and_set("drive_MTBF", drive_MTBF_choices, 40, int)
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add_input("Drives",
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"What is the hard drive MTBF?", i_drive_MTBF)
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# http://www.tgdaily.com/content/view/30990/113/
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# http://labs.google.com/papers/disk_failures.pdf
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# google sees:
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# 1.7% of the drives they replaced were 0-1 years old
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# 8% of the drives they repalced were 1-2 years old
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# 8.6% were 2-3 years old
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# 6% were 3-4 years old, about 8% were 4-5 years old
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drive_size_choices = [ (100, "100 GB"),
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(250, "250 GB"),
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(500, "500 GB"),
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(750, "750 GB"),
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(1000, "1000 GB"),
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(2000, "2000 GB"),
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(3000, "3000 GB"),
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]
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drive_size, i_drive_size = \
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get_and_set("drive_size", drive_size_choices, 3000, int)
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drive_size = drive_size * 1e9
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add_input("Drives",
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"What is the capacity of each hard drive?", i_drive_size)
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drive_failure_model_choices = [ ("E", "Exponential"),
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("U", "Uniform"),
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]
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drive_failure_model, i_drive_failure_model = \
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get_and_set("drive_failure_model",
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drive_failure_model_choices,
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"E", str)
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add_input("Drives",
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"How should we model drive failures?", i_drive_failure_model)
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# drive_failure_rate is in failures per second
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if drive_failure_model == "E":
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drive_failure_rate = 1.0 / (drive_MTBF * 1000 * 3600)
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else:
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drive_failure_rate = 0.5 / (drive_MTBF * 1000 * 3600)
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# deletion/gc/ownership mode
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ownership_choices = [ ("A", "no deletion, no gc, no owners"),
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("B", "deletion, no gc, no owners"),
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("C", "deletion, share timers, no owners"),
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("D", "deletion, no gc, yes owners"),
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("E", "deletion, owner timers"),
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]
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ownership_mode, i_ownership_mode = \
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get_and_set("ownership_mode", ownership_choices,
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"A", str)
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add_input("Servers",
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"What is the ownership mode?", i_ownership_mode)
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# client access behavior
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access_rates = [ (1, "one file per day"),
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(10, "10 files per day"),
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(100, "100 files per day"),
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(1000, "1k files per day"),
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(10e3, "10k files per day"),
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(100e3, "100k files per day"),
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]
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download_files_per_day, i_download_rate = \
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get_and_set("download_rate", access_rates,
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100, int)
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add_input("Users",
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"How many files are downloaded per day?", i_download_rate)
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download_rate = 1.0 * download_files_per_day / (24*60*60)
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upload_files_per_day, i_upload_rate = \
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get_and_set("upload_rate", access_rates,
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10, int)
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add_input("Users",
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"How many files are uploaded per day?", i_upload_rate)
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upload_rate = 1.0 * upload_files_per_day / (24*60*60)
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delete_files_per_day, i_delete_rate = \
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get_and_set("delete_rate", access_rates,
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10, int)
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add_input("Users",
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"How many files are deleted per day?", i_delete_rate)
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delete_rate = 1.0 * delete_files_per_day / (24*60*60)
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# the value is in days
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lease_timers = [ (1, "one refresh per day"),
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(7, "one refresh per week"),
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]
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lease_timer, i_lease = \
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get_and_set("lease_timer", lease_timers,
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7, int)
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add_input("Users",
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"How frequently do clients refresh files or accounts? "
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"(if necessary)",
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i_lease)
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seconds_per_lease = 24*60*60*lease_timer
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check_timer_choices = [ (1, "every week"),
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(4, "every month"),
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(8, "every two months"),
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(16, "every four months"),
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]
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check_timer, i_check_timer = \
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get_and_set("check_timer", check_timer_choices, 4, int)
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add_input("Users",
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"How frequently should we check on each file?",
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i_check_timer)
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file_check_interval = check_timer * 7 * 24 * 3600
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if filled:
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add_output("Users", T.div["Total users: %s" % number(num_users)])
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add_output("Users",
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T.div["Files per user: %s" % number(files_per_user)])
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file_size = 1.0 * space_per_user / files_per_user
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add_output("Users",
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T.div["Average file size: ", number(file_size)])
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total_files = num_users * files_per_user / sharing_ratio
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add_output("Grid",
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T.div["Total number of files in grid: ",
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number(total_files)])
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total_space = num_users * space_per_user / sharing_ratio
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add_output("Grid",
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T.div["Total volume of plaintext in grid: ",
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number(total_space, "B")])
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total_shares = n * total_files
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add_output("Grid",
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T.div["Total shares in grid: ", number(total_shares)])
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expansion = float(n) / float(k)
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total_usage = expansion * total_space
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add_output("Grid",
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T.div["Share data in grid: ", number(total_usage, "B")])
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if n > num_servers:
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# silly configuration, causes Tahoe2 to wrap and put multiple
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# shares on some servers.
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add_output("Servers",
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T.div["non-ideal: more shares than servers"
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" (n=%d, servers=%d)" % (n, num_servers)])
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# every file has at least one share on every server
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buckets_per_server = total_files
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shares_per_server = total_files * ((1.0 * n) / num_servers)
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else:
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# if nobody is full, then no lease requests will be turned
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# down for lack of space, and no two shares for the same file
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# will share a server. Therefore the chance that any given
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# file has a share on any given server is n/num_servers.
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buckets_per_server = total_files * ((1.0 * n) / num_servers)
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# since each such represented file only puts one share on a
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# server, the total number of shares per server is the same.
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shares_per_server = buckets_per_server
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add_output("Servers",
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T.div["Buckets per server: ",
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number(buckets_per_server)])
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add_output("Servers",
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T.div["Shares per server: ",
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number(shares_per_server)])
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# how much space is used on the storage servers for the shares?
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# the share data itself
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share_data_per_server = total_usage / num_servers
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add_output("Servers",
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T.div["Share data per server: ",
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number(share_data_per_server, "B")])
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# this is determined empirically. H=hashsize=32, for a one-segment
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# file and 3-of-10 encoding
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share_validation_per_server = 266 * shares_per_server
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# this could be 423*buckets_per_server, if we moved the URI
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# extension into a separate file, but that would actually consume
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# *more* space (minimum filesize is 4KiB), unless we moved all
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# shares for a given bucket into a single file.
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share_uri_extension_per_server = 423 * shares_per_server
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# ownership mode adds per-bucket data
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H = 32 # depends upon the desired security of delete/refresh caps
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# bucket_lease_size is the amount of data needed to keep track of
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# the delete/refresh caps for each bucket.
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bucket_lease_size = 0
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client_bucket_refresh_rate = 0
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owner_table_size = 0
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if ownership_mode in ("B", "C", "D", "E"):
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bucket_lease_size = sharing_ratio * 1.0 * H
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if ownership_mode in ("B", "C"):
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# refreshes per second per client
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client_bucket_refresh_rate = (1.0 * n * files_per_user /
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seconds_per_lease)
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add_output("Users",
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T.div["Client share refresh rate (outbound): ",
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number(client_bucket_refresh_rate, "Hz")])
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server_bucket_refresh_rate = (client_bucket_refresh_rate *
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num_users / num_servers)
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add_output("Servers",
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T.div["Server share refresh rate (inbound): ",
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number(server_bucket_refresh_rate, "Hz")])
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if ownership_mode in ("D", "E"):
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# each server must maintain a bidirectional mapping from
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# buckets to owners. One way to implement this would be to
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# put a list of four-byte owner numbers into each bucket, and
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# a list of four-byte share numbers into each owner (although
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# of course we'd really just throw it into a database and let
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# the experts take care of the details).
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owner_table_size = 2*(buckets_per_server * sharing_ratio * 4)
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if ownership_mode in ("E",):
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# in this mode, clients must refresh one timer per server
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client_account_refresh_rate = (1.0 * num_servers /
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seconds_per_lease)
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add_output("Users",
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T.div["Client account refresh rate (outbound): ",
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number(client_account_refresh_rate, "Hz")])
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server_account_refresh_rate = (client_account_refresh_rate *
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num_users / num_servers)
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add_output("Servers",
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T.div["Server account refresh rate (inbound): ",
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number(server_account_refresh_rate, "Hz")])
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# TODO: buckets vs shares here is a bit wonky, but in
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# non-wrapping grids it shouldn't matter
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share_lease_per_server = bucket_lease_size * buckets_per_server
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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
|