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tahoe-lafs/misc/operations_helpers/provisioning/provisioning.py

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resurrect provisioning.py It looks like commit 916d26e7103208fa207259d62ce453a5a8b9acd0, in addition to making a one-line fix for #1681, also deleted misc/operations_helpers/provisioning/provisioning.py entirely. This brings it back.
2013-03-26 00:57:01 +00:00
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):
More passing tests on Python 3.
2021-01-22 20:07:03 +00:00
if req.method != b"POST":
resurrect provisioning.py It looks like commit 916d26e7103208fa207259d62ce453a5a8b9acd0, in addition to making a one-line fix for #1681, also deleted misc/operations_helpers/provisioning/provisioning.py entirely. This brings it back.
2013-03-26 00:57:01 +00:00
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
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