695 lines
27 KiB
Python
695 lines
27 KiB
Python
from . import distribution
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from . import geometry
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from .distribution import Distribution
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from .expr import Expr, Node
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from .geometry import Point, Segment
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from typing import *
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import collections
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import datetime
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import itertools
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import numpy as np
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import pulp
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T = TypeVar('T')
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LOAD = 'load'
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NETWORK = 'network'
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LATENCY = 'latency'
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# TODO(mwhittaker): Add some other non-optimal strategies.
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# TODO(mwhittaker): Make it easy to make arbitrary strategies.
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class NoStrategyFoundError(ValueError):
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pass
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class QuorumSystem(Generic[T]):
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def __init__(self, reads: Optional[Expr[T]] = None,
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writes: Optional[Expr[T]] = None) -> None:
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if reads is not None and writes is not None:
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optimal_writes = reads.dual()
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if not all(optimal_writes.is_quorum(wq) for wq in writes.quorums()):
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raise ValueError(
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'Not all read quorums intersect all write quorums')
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self.reads = reads
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self.writes = writes
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elif reads is not None and writes is None:
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self.reads = reads
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self.writes = reads.dual()
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elif reads is None and writes is not None:
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self.reads = writes.dual()
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self.writes = writes
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else:
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raise ValueError('A QuorumSystem must be instantiated with a set '
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'of read quorums or a set of write quorums')
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self.x_to_node = {node.x: node for node in self.nodes()}
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def __repr__(self) -> str:
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return f'QuorumSystem(reads={self.reads}, writes={self.writes})'
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def read_quorums(self) -> Iterator[Set[T]]:
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return self.reads.quorums()
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def write_quorums(self) -> Iterator[Set[T]]:
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return self.writes.quorums()
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def is_read_quorum(self, xs: Set[T]) -> bool:
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return self.reads.is_quorum(xs)
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def is_write_quorum(self, xs: Set[T]) -> bool:
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return self.writes.is_quorum(xs)
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def node(self, x: T) -> Node[T]:
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return self.x_to_node[x]
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def nodes(self) -> Set[Node[T]]:
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return self.reads.nodes() | self.writes.nodes()
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def elements(self) -> Set[T]:
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return {node.x for node in self.nodes()}
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def resilience(self) -> int:
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return min(self.read_resilience(), self.write_resilience())
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def read_resilience(self) -> int:
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return self.reads.resilience()
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def write_resilience(self) -> int:
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return self.writes.resilience()
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def dup_free(self) -> bool:
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return self.reads.dup_free() and self.writes.dup_free()
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def load(self,
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optimize: str = LOAD,
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load_limit: Optional[float] = None,
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network_limit: Optional[float] = None,
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latency_limit: Optional[datetime.timedelta] = None,
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read_fraction: Optional[Distribution] = None,
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write_fraction: Optional[Distribution] = None,
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f: int = 0) -> float:
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return self.strategy(
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optimize,
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load_limit,
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network_limit,
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latency_limit,
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read_fraction,
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write_fraction,
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f
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).load(read_fraction, write_fraction)
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def capacity(self,
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optimize: str = LOAD,
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load_limit: Optional[float] = None,
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network_limit: Optional[float] = None,
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latency_limit: Optional[datetime.timedelta] = None,
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read_fraction: Optional[Distribution] = None,
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write_fraction: Optional[Distribution] = None,
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f: int = 0) -> float:
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return self.strategy(
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optimize,
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load_limit,
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network_limit,
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latency_limit,
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read_fraction,
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write_fraction,
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f
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).capacity(read_fraction, write_fraction)
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def network_load(self,
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optimize: str = LOAD,
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load_limit: Optional[float] = None,
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network_limit: Optional[float] = None,
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latency_limit: Optional[datetime.timedelta] = None,
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read_fraction: Optional[Distribution] = None,
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write_fraction: Optional[Distribution] = None,
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f: int = 0) -> float:
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return self.strategy(
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optimize,
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load_limit,
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network_limit,
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latency_limit,
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read_fraction,
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write_fraction,
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f
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).network_load(read_fraction, write_fraction)
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def latency(self,
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optimize: str = LOAD,
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load_limit: Optional[float] = None,
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network_limit: Optional[float] = None,
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latency_limit: Optional[datetime.timedelta] = None,
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read_fraction: Optional[Distribution] = None,
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write_fraction: Optional[Distribution] = None,
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f: int = 0) -> float:
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return self.strategy(
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optimize,
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load_limit,
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network_limit,
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latency_limit,
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read_fraction,
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write_fraction,
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f
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).latency(read_fraction, write_fraction)
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def uniform_strategy(self, f: int = 0) -> 'Strategy[T]':
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"""
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uniform_strategy(f) returns a uniform strategy over the minimal
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f-resilient quorums. That is, every minimal f-resilient quorum is
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equally likely to be chosen.
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"""
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if f < 0:
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raise ValueError('f must be >= 0')
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elif f == 0:
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read_quorums = list(self.read_quorums())
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write_quorums = list(self.write_quorums())
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else:
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xs = list(self.elements())
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read_quorums = list(self._f_resilient_quorums(f, xs, self.reads))
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write_quorums = list(self._f_resilient_quorums(f, xs, self.reads))
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if len(read_quorums) == 0:
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raise NoStrategyFoundError(
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f'There are no {f}-resilient read quorums')
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if len(write_quorums) == 0:
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raise NoStrategyFoundError(
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f'There are no {f}-resilient write quorums')
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read_quorums = self._minimize(read_quorums)
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write_quorums = self._minimize(write_quorums)
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sigma_r = {frozenset(rq): 1 / len(rq) for rq in read_quorums}
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sigma_w = {frozenset(wq): 1 / len(wq) for wq in write_quorums}
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return Strategy(self, sigma_r, sigma_w)
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def strategy(self,
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optimize: str = LOAD,
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load_limit: Optional[float] = None,
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network_limit: Optional[float] = None,
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latency_limit: Optional[datetime.timedelta] = None,
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read_fraction: Optional[Distribution] = None,
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write_fraction: Optional[Distribution] = None,
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f: int = 0) -> 'Strategy[T]':
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if optimize not in {LOAD, NETWORK, LATENCY}:
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raise ValueError(
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f'optimize must be one of {LOAD}, {NETWORK}, or {LATENCY}')
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if optimize == LOAD and load_limit is not None:
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raise ValueError(
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'a load limit cannot be set when optimizing for load')
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if optimize == NETWORK and network_limit is not None:
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raise ValueError(
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'a network limit cannot be set when optimizing for network')
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if optimize == LATENCY and latency_limit is not None:
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raise ValueError(
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'a latency limit cannot be set when optimizing for latency')
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if f < 0:
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raise ValueError('f must be >= 0')
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d = distribution.canonicalize_rw(read_fraction, write_fraction)
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if f == 0:
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return self._load_optimal_strategy(
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list(self.read_quorums()),
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list(self.write_quorums()),
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d,
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optimize=optimize,
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load_limit=load_limit,
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network_limit=network_limit,
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latency_limit=latency_limit)
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else:
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xs = list(self.elements())
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read_quorums = list(self._f_resilient_quorums(f, xs, self.reads))
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write_quorums = list(self._f_resilient_quorums(f, xs, self.reads))
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if len(read_quorums) == 0:
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raise NoStrategyFoundError(
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f'There are no {f}-resilient read quorums')
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if len(write_quorums) == 0:
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raise NoStrategyFoundError(
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f'There are no {f}-resilient write quorums')
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return self._load_optimal_strategy(
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read_quorums,
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write_quorums,
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d,
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optimize=optimize,
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load_limit=load_limit,
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network_limit=network_limit,
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latency_limit=latency_limit)
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def _minimize(self, sets: List[Set[T]]) -> List[Set[T]]:
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sets = sorted(sets, key=lambda s: len(s))
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minimal_elements: List[Set[T]] = []
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for x in sets:
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if not any(x >= y for y in minimal_elements):
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minimal_elements.append(x)
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return minimal_elements
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def _f_resilient_quorums(self,
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f: int,
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xs: List[T],
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e: Expr) -> Iterator[Set[T]]:
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"""
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Consider a set X of elements in xs. We say X is f-resilient if, despite
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removing an arbitrary set of f elements from X, X is a quorum in e.
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_f_resilient_quorums returns the set of all f-resilient quorums.
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"""
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assert f >= 1
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def helper(s: Set[T], i: int) -> Iterator[Set[T]]:
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if all(e.is_quorum(s - set(failure))
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for failure in itertools.combinations(s, min(f, len(s)))):
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yield set(s)
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return
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for j in range(i, len(xs)):
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s.add(xs[j])
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yield from helper(s, j + 1)
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s.remove(xs[j])
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return helper(set(), 0)
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def _read_quorum_latency(self, quorum: Set[Node[T]]) -> datetime.timedelta:
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return self._quorum_latency(quorum, self.is_read_quorum)
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def _write_quorum_latency(self, quorum: Set[Node[T]]) -> datetime.timedelta:
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return self._quorum_latency(quorum, self.is_write_quorum)
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def _quorum_latency(self,
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quorum: Set[Node[T]],
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is_quorum: Callable[[Set[T]], bool]) \
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-> datetime.timedelta:
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nodes = list(quorum)
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nodes.sort(key=lambda node: node.latency)
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for i in range(len(quorum)):
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if is_quorum({node.x for node in nodes[:i+1]}):
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return nodes[i].latency
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raise ValueError('_quorum_latency called on a non-quorum')
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def _load_optimal_strategy(
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self,
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read_quorums: List[Set[T]],
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write_quorums: List[Set[T]],
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read_fraction: Dict[float, float],
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optimize: str = LOAD,
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load_limit: Optional[float] = None,
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network_limit: Optional[float] = None,
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latency_limit: Optional[datetime.timedelta] = None) -> 'Strategy[T]':
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"""
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Consider the following 2x2 grid quorum system.
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a b
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c d
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with
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read_quorums = [{a, b}, {c, d}]
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write_quorums = [{a, c}, {a, d}, {b, c}, {b, d}]
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We want to find the strategy that is optimal with respect to load,
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network load, or latency that satisfies the provided load, network
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load, or latency constraints.
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We can find the optimal strategy using linear programming. First, we
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create a variable ri for every read quorum i and a variable wi for
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every write quorum i. ri represents the probabilty of selecting the ith
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read quorum, and wi represents the probabilty of selecting the ith
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write quorum.
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We now explain how to represent load, network load, and latency as
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linear expressions.
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Load
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====
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Assume a read fraction fr and write fraction fw. The load of a node a is
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load(a) = (fr * rprob(a) / rcap(a)) + (fw * wprob(a) / wcap(a))
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where prob_r(a) and prob_w(a) are the probabilities that a is selected
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as part of a read or write quorum respectively; and rcap(a) and wcap(a)
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are the read and write capacities of a. We can express prob_r(a) and
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prob_w(a) as follows:
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rprob(a) = sum({ri | a is in read quorum i})
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wprob(a) = sum({wi | a is in write quorum i})
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Using the example grid quorum above, we have:
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rprob(a) = r0 wprob(a) = w0 + w1
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rprob(b) = r0 wprob(b) = w2 + w3
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rprob(c) = r1 wprob(c) = w0 + w2
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rprob(d) = r1 wprob(d) = w1 + w3
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The load of a strategy is the maximum load on any node. We can compute
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this by minimizing a new variable l and constraining the load of every
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node to be less than l. Using the example above, we have
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min l subject to
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fr * r0 * rcap(a) + fw * (w0 + w1) * wcap(a) <= l
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fr * r0 * rcap(b) + fw * (w2 + w3) * wcap(b) <= l
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fr * r1 * rcap(c) + fw * (w0 + w2) * wcap(c) <= l
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fr * r1 * rcap(d) + fw * (w1 + w3) * wcap(d) <= l
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To compute the load of a strategy with respect to a distribution of
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read_fractions, we compute the load for every value of fr and weight
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according to the distribution. For example, imagine fr is 0.9 80% of
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the time and 0.5 20% of the time. We have:
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min 0.8 * l0.9 + 0.2 * l0.5
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0.9 * r0 * rcap(a) + 0.1 * (w0 + w1) * wcap(a) <= l0.9
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0.9 * r0 * rcap(b) + 0.1 * (w2 + w3) * wcap(b) <= l0.9
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0.9 * r1 * rcap(c) + 0.1 * (w0 + w2) * wcap(c) <= l0.9
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0.9 * r1 * rcap(d) + 0.1 * (w1 + w3) * wcap(d) <= l0.9
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0.5 * r0 * rcap(a) + 0.5 * (w0 + w1) * wcap(a) <= l0.5
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0.5 * r0 * rcap(b) + 0.5 * (w2 + w3) * wcap(b) <= l0.5
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0.5 * r1 * rcap(c) + 0.5 * (w0 + w2) * wcap(c) <= l0.5
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0.5 * r1 * rcap(d) + 0.5 * (w1 + w3) * wcap(d) <= l0.5
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Let the expression for load be LOAD.
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Network
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=======
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The network load of a strategy is the expected size of a quorum. For a
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fixed fr, We can compute the network load as:
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fr * sum_i(size(read quorum i) * ri) +
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fw * sum_i(size(write quorum i) * ri)
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Using the example above:
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fr * (2*r0 + 2*r1) + fw * (2*w0 + 2*w1 + 2*w2 + 2*w3)
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For a distribution of read fractions, we compute the weighted average.
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Let the expression for network load be NETWORK.
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Latency
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=======
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The latency of a strategy is the expected latency of a quorum. We can
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compute the latency as:
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fr * sum_i(latency(read quorum i) * ri) +
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fw * sum_i(latency(write quorum i) * ri)
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Using the example above (assuming every node has a latency of 1):
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fr * (1*r0 + 1*r1) + fw * (1*w0 + 1*w1 + 1*w2 + 1*w3)
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For a distribution of read fractions, we compute the weighted average.
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Let the expression for latency be LATENCY.
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Linear Program
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==============
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To find an optimal strategy, we use a linear program. The objective
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specified by the user is minimized, and any provided constraints are
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added as constraints to the program. For example, imagine the user
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wants a load optimal strategy with network load <= 2 and latency <= 3.
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We form the program:
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min LOAD subject to
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sum_i(ri) = 1 # ensure we have a valid distribution on read quorums
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sum_i(wi) = 1 # ensure we have a valid distribution on write quorums
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NETWORK <= 2
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LATENCY <= 3
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Using the example above assuming a fixed fr, we have:
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min l subject to
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fr * r0 * rcap(a) + fw * (w0 + w1) * wcap(a) <= l
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fr * r0 * rcap(b) + fw * (w2 + w3) * wcap(b) <= l
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fr * r1 * rcap(c) + fw * (w0 + w2) * wcap(c) <= l
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fr * r1 * rcap(d) + fw * (w1 + w3) * wcap(d) <= l
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fr * (2*r0 + 2*r1) + fw * (2*w0 + 2*w1 + 2*w2 + 2*w3) <= 2
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fr * (1*r0 + 1*r1) + fw * (1*w0 + 1*w1 + 1*w2 + 1*w3) <= 3
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If we instead wanted to minimize network load with load <= 4 and
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latency <= 5, we would have the following program:
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min fr * (2*r0 + 2*r1) +
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fw * (2*w0 + 2*w1 + 2*w2 + 2*w3) subject to
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fr * r0 * rcap(a) + fw * (w0 + w1) * wcap(a) <= 4
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fr * r0 * rcap(b) + fw * (w2 + w3) * wcap(b) <= 4
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fr * r1 * rcap(c) + fw * (w0 + w2) * wcap(c) <= 4
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fr * r1 * rcap(d) + fw * (w1 + w3) * wcap(d) <= 4
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fr * (1*r0 + 1*r1) + fw * (1*w0 + 1*w1 + 1*w2 + 1*w3) <= 5
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"""
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# Create a variable for every read quorum and every write quorum. While
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# we do this, map each element x to the read and write quorums that
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# it's in. For example, image we have the following read and write
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# quorums:
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#
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# read_quorums = [{a}, {a, b}, {a, c}]
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# write_quorums = [{a, b}, {a, b, c}]
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#
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# Then, we'd have
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#
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# read_quorum_vars = [r0, r1, 2]
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# write_quorum_vars = [w0, w1]
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# x_to_read_quorum_vars = {a: [r1, r2, r3], b: [r1], c: [r2]}
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# x_to_write_quorum_vars = {a: [w1, w2], b: [w2, w2], c: [w2]}
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read_quorum_vars: List[pulp.LpVariable] = []
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x_to_read_quorum_vars: Dict[T, List[pulp.LpVariable]] = \
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collections.defaultdict(list)
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for (i, read_quorum) in enumerate(read_quorums):
|
|
v = pulp.LpVariable(f'r{i}', 0, 1)
|
|
read_quorum_vars.append(v)
|
|
for x in read_quorum:
|
|
x_to_read_quorum_vars[x].append(v)
|
|
|
|
write_quorum_vars: List[pulp.LpVariable] = []
|
|
x_to_write_quorum_vars: Dict[T, List[pulp.LpVariable]] = \
|
|
collections.defaultdict(list)
|
|
for (i, write_quorum) in enumerate(write_quorums):
|
|
v = pulp.LpVariable(f'w{i}', 0, 1)
|
|
write_quorum_vars.append(v)
|
|
for x in write_quorum:
|
|
x_to_write_quorum_vars[x].append(v)
|
|
|
|
fr = sum(p * fr for (fr, p) in read_fraction.items())
|
|
|
|
def network() -> pulp.LpAffineExpression:
|
|
reads = fr * sum(
|
|
v * len(rq)
|
|
for (rq, v) in zip(read_quorums, read_quorum_vars)
|
|
)
|
|
writes = (1 - fr) * sum(
|
|
v * len(wq)
|
|
for (wq, v) in zip(write_quorums, write_quorum_vars)
|
|
)
|
|
return reads + writes
|
|
|
|
def latency() -> pulp.LpAffineExpression:
|
|
reads = fr * sum(
|
|
v * self._read_quorum_latency(quorum).total_seconds()
|
|
for (rq, v) in zip(read_quorums, read_quorum_vars)
|
|
for quorum in [{self.node(x) for x in rq}]
|
|
)
|
|
writes = (1 - fr) * sum(
|
|
v * self._write_quorum_latency(quorum).total_seconds()
|
|
for (wq, v) in zip(write_quorums, write_quorum_vars)
|
|
for quorum in [{self.node(x) for x in wq}]
|
|
)
|
|
return reads + writes
|
|
|
|
def fr_load(problem: pulp.LpProblem, fr: float) -> pulp.LpAffineExpression:
|
|
l = pulp.LpVariable(f'l_{fr}', 0, 1)
|
|
|
|
for node in self.nodes():
|
|
x = node.x
|
|
x_load: pulp.LpAffineExpression = 0
|
|
|
|
if x in x_to_read_quorum_vars:
|
|
vs = x_to_read_quorum_vars[x]
|
|
x_load += fr * sum(vs) / self.node(x).read_capacity
|
|
|
|
if x in x_to_write_quorum_vars:
|
|
vs = x_to_write_quorum_vars[x]
|
|
x_load += (1 - fr) * sum(vs) / self.node(x).write_capacity
|
|
|
|
problem += (x_load <= l, f'{x}{fr}')
|
|
|
|
return l
|
|
|
|
def load(problem: pulp.LpProblem,
|
|
read_fraction: Dict[float, float]) -> pulp.LpAffineExpression:
|
|
return sum(p * fr_load(problem, fr)
|
|
for (fr, p) in read_fraction.items())
|
|
|
|
# Form the linear program.
|
|
problem = pulp.LpProblem("optimal_strategy", pulp.LpMinimize)
|
|
|
|
# We add these constraints to make sure that the probabilities we
|
|
# select form valid probabilty distributions.
|
|
problem += (sum(read_quorum_vars) == 1, 'valid read strategy')
|
|
problem += (sum(write_quorum_vars) == 1, 'valid write strategy')
|
|
|
|
# Add the objective.
|
|
if optimize == LOAD:
|
|
problem += load(problem, read_fraction)
|
|
elif optimize == NETWORK:
|
|
problem += network()
|
|
else:
|
|
assert optimize == LATENCY
|
|
problem += latency()
|
|
|
|
# Add any constraints.
|
|
if load_limit is not None:
|
|
problem += (load(problem, read_fraction) <= load_limit,
|
|
'load limit')
|
|
|
|
if network_limit is not None:
|
|
problem += (network() <= network_limit, 'network limit')
|
|
|
|
if latency_limit is not None:
|
|
problem += (latency() <= latency_limit.total_seconds(),
|
|
'latency limit')
|
|
|
|
# Solve the linear program.
|
|
problem.solve(pulp.apis.PULP_CBC_CMD(msg=False))
|
|
if problem.status != pulp.LpStatusOptimal:
|
|
raise NoStrategyFoundError(
|
|
'no strategy satisfies the given constraints')
|
|
|
|
# Prune out any quorums with 0 probability.
|
|
sigma_r = {
|
|
frozenset(rq): v.varValue
|
|
for (rq, v) in zip(read_quorums, read_quorum_vars)
|
|
if v.varValue != 0
|
|
}
|
|
sigma_w = {
|
|
frozenset(wq): v.varValue
|
|
for (wq, v) in zip(write_quorums, write_quorum_vars)
|
|
if v.varValue != 0
|
|
}
|
|
|
|
return Strategy(self, sigma_r, sigma_w)
|
|
|
|
|
|
class Strategy(Generic[T]):
|
|
def __init__(self,
|
|
qs: QuorumSystem[T],
|
|
sigma_r: Dict[FrozenSet[T], float],
|
|
sigma_w: Dict[FrozenSet[T], float]) -> None:
|
|
self.qs = qs
|
|
self.sigma_r = sigma_r
|
|
self.sigma_w = sigma_w
|
|
|
|
# The probability that x is chosen as part of a read quorum.
|
|
self.x_read_probability: Dict[T, float] = collections.defaultdict(float)
|
|
for (read_quorum, p) in self.sigma_r.items():
|
|
for x in read_quorum:
|
|
self.x_read_probability[x] += p
|
|
|
|
# The probability that x is chosen as part of a write quorum.
|
|
self.x_write_probability: Dict[T, float] = collections.defaultdict(float)
|
|
for (write_quorum, weight) in self.sigma_w.items():
|
|
for x in write_quorum:
|
|
self.x_write_probability[x] += weight
|
|
|
|
@no_type_check
|
|
def __str__(self) -> str:
|
|
# T may not comparable, so mypy complains about this sort.
|
|
reads = {tuple(sorted(rq)): p for (rq, p) in self.sigma_r.items()}
|
|
writes = {tuple(sorted(wq)): p for (wq, p) in self.sigma_w.items()}
|
|
return f'Strategy(reads={reads}, writes={writes})'
|
|
|
|
def quorum_system(self) -> QuorumSystem[T]:
|
|
return self.qs
|
|
|
|
def node(self, x: T) -> Node[T]:
|
|
return self.qs.node(x)
|
|
|
|
def nodes(self) -> Set[Node[T]]:
|
|
return self.qs.nodes()
|
|
|
|
def get_read_quorum(self) -> Set[T]:
|
|
return set(np.random.choice(list(self.sigma_r.keys()),
|
|
p=list(self.sigma_r.values())))
|
|
|
|
def get_write_quorum(self) -> Set[T]:
|
|
return set(np.random.choice(list(self.sigma_w.keys()),
|
|
p=list(self.sigma_w.values())))
|
|
|
|
def load(self,
|
|
read_fraction: Optional[Distribution] = None,
|
|
write_fraction: Optional[Distribution] = None) -> float:
|
|
d = distribution.canonicalize_rw(read_fraction, write_fraction)
|
|
return sum(p * self._load(fr) for (fr, p) in d.items())
|
|
|
|
def capacity(self,
|
|
read_fraction: Optional[Distribution] = None,
|
|
write_fraction: Optional[Distribution] = None) -> float:
|
|
return 1 / self.load(read_fraction, write_fraction)
|
|
|
|
def network_load(self,
|
|
read_fraction: Optional[Distribution] = None,
|
|
write_fraction: Optional[Distribution] = None) -> float:
|
|
d = distribution.canonicalize_rw(read_fraction, write_fraction)
|
|
fr = sum(p * fr for (fr, p) in d.items())
|
|
reads = fr * sum(p * len(rq) for (rq, p) in self.sigma_r.items())
|
|
writes = (1 - fr) * sum(p * len(wq) for (wq, p) in self.sigma_w.items())
|
|
return reads + writes
|
|
|
|
# mypy doesn't like calling sum with timedeltas.
|
|
@no_type_check
|
|
def latency(self,
|
|
read_fraction: Optional[Distribution] = None,
|
|
write_fraction: Optional[Distribution] = None) \
|
|
-> datetime.timedelta:
|
|
d = distribution.canonicalize_rw(read_fraction, write_fraction)
|
|
fr = sum(p * fr for (fr, p) in d.items())
|
|
|
|
reads = fr * sum((
|
|
p * self.qs._read_quorum_latency({self.node(x) for x in rq})
|
|
for (rq, p) in self.sigma_r.items()
|
|
), datetime.timedelta(seconds=0))
|
|
|
|
writes = (1 - fr) * sum((
|
|
p * self.qs._write_quorum_latency({self.node(x) for x in wq})
|
|
for (wq, p) in self.sigma_w.items()
|
|
), datetime.timedelta(seconds=0))
|
|
|
|
return reads + writes
|
|
|
|
def node_load(self,
|
|
node: Node[T],
|
|
read_fraction: Optional[Distribution] = None,
|
|
write_fraction: Optional[Distribution] = None) -> float:
|
|
d = distribution.canonicalize_rw(read_fraction, write_fraction)
|
|
return sum(p * self._node_load(node, fr) for (fr, p) in d.items())
|
|
|
|
def node_utilization(self,
|
|
node: Node[T],
|
|
read_fraction: Optional[Distribution] = None,
|
|
write_fraction: Optional[Distribution] = None) \
|
|
-> float:
|
|
d = distribution.canonicalize_rw(read_fraction, write_fraction)
|
|
return sum(p * self._node_utilization(node, fr)
|
|
for (fr, p) in d.items())
|
|
|
|
def node_throughput(self,
|
|
node: Node[T],
|
|
read_fraction: Optional[Distribution] = None,
|
|
write_fraction: Optional[Distribution] = None) -> float:
|
|
d = distribution.canonicalize_rw(read_fraction, write_fraction)
|
|
return sum(p * self._node_throughput(node, fr) for (fr, p) in d.items())
|
|
|
|
def _load(self, fr: float) -> float:
|
|
return max(self._node_load(node, fr) for node in self.nodes())
|
|
|
|
def _node_load(self, node: Node[T], fr: float) -> float:
|
|
fw = 1 - fr
|
|
return (fr * self.x_read_probability[node.x] / node.read_capacity +
|
|
fw * self.x_write_probability[node.x] / node.write_capacity)
|
|
|
|
def _node_utilization(self, node: Node[T], fr: float) -> float:
|
|
return self._node_load(node, fr) / self._load(fr)
|
|
|
|
def _node_throughput(self, node: Node[T], fr: float) -> float:
|
|
cap = 1 / self._load(fr)
|
|
fw = 1 - fr
|
|
return cap * (fr * self.x_read_probability[node.x] +
|
|
fw * self.x_write_probability[node.x])
|