Progress on multiple objectives.

quorums/expr.py

@@ -1,4 +1,5 @@
 from typing import Dict, Iterator, Generic, List, Optional, Set, TypeVar
+import datetime
 import itertools
 import pulp
 
@@ -87,7 +88,8 @@ class Node(Expr[T]):
                  x: T,
                  capacity: Optional[float] = None,
                  read_capacity: Optional[float] = None,
-                 write_capacity: Optional[float] = None) -> None:
+                 write_capacity: Optional[float] = None,
+                 latency: datetime.timedelta = None) -> None:
         self.x = x
 
         # A user either specifies capacity or (read_capacity and
@@ -111,6 +113,12 @@ class Node(Expr[T]):
             raise ValueError('You must specify capacity or (read_capacity '
                              'and write_capacity)')
 
+        if latency is None:
+            self.latency = datetime.timedelta(seconds=1)
+        else:
+            self.latency = latency
+
+
     def __str__(self) -> str:
         return str(self.x)
 

quorums/quorum_system.py

@@ -5,8 +5,10 @@ from . import distribution
 from .distribution import Distribution
 from .expr import Expr, Node
 from .strategy import Strategy
-from typing import Dict, Iterator, Generic, List, Optional, Set, TypeVar
+from typing import (Callable, Dict, Iterator, Generic, List, Optional, Set,
+                    TypeVar)
 import collections
+import datetime
 import itertools
 import pulp
 
@@ -14,6 +16,14 @@ import pulp
 T = TypeVar('T')
 
 
+LOAD = 'load'
+NETWORK = 'network'
+LATENCY = 'latency'
+
+# TODO(mwhittaker): Add some other non-optimal strategies.
+# TODO(mwhittaker): Make it easy to make arbitrary strategies.
+
+
 class QuorumSystem(Generic[T]):
     def __init__(self, reads: Optional[Expr[T]] = None,
                        writes: Optional[Expr[T]] = None) -> None:
@@ -64,6 +74,10 @@ class QuorumSystem(Generic[T]):
         return self.writes.resilience()
 
     def strategy(self,
+                 optimize: str = LOAD,
+                 load_limit: Optional[float] = None,
+                 network_limit: Optional[float] = None,
+                 latency_limit: Optional[datetime.timedelta] = None,
                  read_fraction: Optional[Distribution] = None,
                  write_fraction: Optional[Distribution] = None,
                  f: int = 0) \
@@ -71,12 +85,28 @@ class QuorumSystem(Generic[T]):
         if f < 0:
             raise ValueError('f must be >= 0')
 
+        if optimize == LOAD and load_limit is not None:
+            raise ValueError(
+                'a load limit cannot be set when optimizing for load')
+
+        if optimize == NETWORK and network_limit is not None:
+            raise ValueError(
+                'a network limit cannot be set when optimizing for network')
+
+        if optimize == LATENCY and latency_limit is not None:
+            raise ValueError(
+                'a latency limit cannot be set when optimizing for latency')
+
         d = distribution.canonicalize_rw(read_fraction, write_fraction)
         if f == 0:
             return self._load_optimal_strategy(
                 list(self.read_quorums()),
                 list(self.write_quorums()),
-                d)
+                d,
+                optimize=optimize,
+                load_limit=load_limit,
+                network_limit=network_limit,
+                latency_limit=latency_limit)
         else:
             xs = [node.x for node in self.nodes()]
             read_quorums = list(self._f_resilient_quorums(f, xs, self.reads))
@@ -85,7 +115,14 @@ class QuorumSystem(Generic[T]):
                 raise ValueError(f'There are no {f}-resilient read quorums')
             if len(write_quorums) == 0:
                 raise ValueError(f'There are no {f}-resilient write quorums')
-            return self._load_optimal_strategy(read_quorums, write_quorums, d)
+            return self._load_optimal_strategy(
+                read_quorums,
+                write_quorums,
+                d,
+                optimize=optimize,
+                load_limit=load_limit,
+                network_limit=network_limit,
+                latency_limit=latency_limit)
 
     def dup_free(self) -> bool:
         return self.reads.dup_free() and self.writes.dup_free()
@@ -114,21 +151,46 @@ class QuorumSystem(Generic[T]):
              write_fraction: Optional[Distribution] = None,
              f: int = 0) \
              -> float:
-        sigma = self.strategy(read_fraction, write_fraction, f)
-        return sigma.load(read_fraction, write_fraction)
+        return 0
+        # TODO(mwhittaker): Remove.
+        # sigma = self.strategy(read_fraction, write_fraction, f)
+        # return sigma.load(read_fraction, write_fraction)
 
     def capacity(self,
                  read_fraction: Optional[Distribution] = None,
                  write_fraction: Optional[Distribution] = None,
                  f: int = 0) \
                  -> float:
-        return 1 / self.load(read_fraction, write_fraction, f)
+        return 0
+        # TODO(mwhittaker): Remove.
+        # return 1 / self.load(read_fraction, write_fraction, f)
 
-    def _load_optimal_strategy(self,
+    def _read_quorum_latency(self, quorum: Set[Node[T]]) -> datetime.timedelta:
+        return self._quorum_latency(quorum, self.is_read_quorum)
+
+    def _write_quorum_latency(self, quorum: Set[Node[T]]) -> datetime.timedelta:
+        return self._quorum_latency(quorum, self.is_write_quorum)
+
+    def _quorum_latency(self,
+                        quorum: Set[Node[T]],
+                        is_quorum: Callable[[Set[T]], bool]) \
+                        -> datetime.timedelta:
+        nodes = list(quorum)
+        nodes.sort(key=lambda node: node.latency)
+        for i in range(len(quorum)):
+            if is_quorum({node.x for node in nodes[:i+1]}):
+                return nodes[i].latency
+        raise ValueError('_quorum_latency called on a non-quorum')
+
+    def _load_optimal_strategy(
+            self,
             read_quorums: List[Set[T]],
             write_quorums: List[Set[T]],
-                               read_fraction: Dict[float, float]) \
-                               -> 'Strategy[T]':
+            read_fraction: Dict[float, float],
+            optimize: str = LOAD,
+            load_limit: Optional[float] = None,
+            network_limit: Optional[float] = None,
+            latency_limit: Optional[datetime.timedelta] = None) -> 'Strategy[T]':
         """
         Consider the following 2x2 grid quorum system.
 
@@ -184,7 +246,8 @@ class QuorumSystem(Generic[T]):
             0.5/rcap_c (r1) + 0.5/wcap_c (w0 + w2) <= L_0.5 # c's load
             0.5/rcap_d (r1) + 0.5/wcap_d (w1 + w3) <= L_0.5 # d's load
         """
-        nodes = self.reads.nodes() | self.writes.nodes()
+        nodes = self.nodes()
+        x_to_node = {node.x: node for node in nodes}
         read_capacity = {node.x: node.read_capacity for node in nodes}
         write_capacity = {node.x: node.write_capacity for node in nodes}
 
@@ -220,38 +283,92 @@ class QuorumSystem(Generic[T]):
             for x in write_quorum:
                 x_to_write_quorum_vars[x].append(v)
 
-        # Create a variable for every load.
-        load_vars = {fr: pulp.LpVariable(f'l_{fr}', 0, 1)
-                     for fr in read_fraction.keys()}
+        fr = sum(weight * f for (f, weight) in read_fraction.items())
+
+        def network() -> pulp.LpAffineExpression:
+            read_network = fr * sum(
+                v * len(rq)
+                for (rq, v) in zip(read_quorums, read_quorum_vars)
+            )
+            write_network = (1 - fr) * sum(
+                v * len(wq)
+                for (wq, v) in zip(write_quorums, write_quorum_vars)
+            )
+            return read_network + write_network
+
+        def latency() -> pulp.LpAffineExpression:
+            read_latency = fr * sum(
+                v * self._read_quorum_latency(quorum).total_seconds()
+                for (rq, v) in zip(read_quorums, read_quorum_vars)
+                for quorum in [{x_to_node[x] for x in rq}]
+            )
+            write_latency = (1 - fr) * sum(
+                v * self._write_quorum_latency(quorum).total_seconds()
+                for (wq, v) in zip(write_quorums, write_quorum_vars)
+                for quorum in [{x_to_node[x] for x in wq}]
+            )
+            return read_latency + write_latency
+
+        def fr_load(problem: pulp.LpProblem, fr: float) -> pulp.LpAffineExpression:
+            l = pulp.LpVariable(f'l_{fr}', 0, 1)
+
+            for node in 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) / read_capacity[x]
+
+                if x in x_to_write_quorum_vars:
+                    vs = x_to_write_quorum_vars[x]
+                    x_load += (1 - fr) * sum(vs) / write_capacity[x]
+
+                problem += (x_load <= l, f'{x}{fr}')
+
+            return l
+
+        def load(problem: pulp.LpProblem,
+                 read_fraction: Dict[float, float]) -> pulp.LpAffineExpression:
+            return sum(weight * fr_load(problem, fr)
+                       for (fr, weight) in read_fraction.items())
 
         # Form the linear program to find the load.
         problem = pulp.LpProblem("load", pulp.LpMinimize)
 
-        # First, we add our objective.
-        problem += sum(weight * load_vars[fr]
-                       for (fr, weight) in read_fraction.items())
-
-        # Next, we make sure that the probabilities we select form valid
-        # probabilty distributions.
+        # 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')
 
-        # Finally, we add constraints for every value of fr.
-        for fr, weight in read_fraction.items():
-            for node in nodes:
-                x = node.x
-                x_load: pulp.LpAffineExpression = 0
-                if x in x_to_read_quorum_vars:
-                    x_load += (fr * sum(x_to_read_quorum_vars[x]) /
-                               read_capacity[x])
-                if x in x_to_write_quorum_vars:
-                    x_load += ((1 - fr) * sum(x_to_write_quorum_vars[x]) /
-                                write_capacity[x])
-                problem += (x_load <= load_vars[fr], f'{x}{fr}')
+        # 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.
+        print(problem)
         problem.solve(pulp.apis.PULP_CBC_CMD(msg=False))
+        if problem.status != pulp.LpStatusOptimal:
+            raise ValueError('no strategy satisfies the given constraints')
 
+        # Prune out any quorums with 0 probability.
         non_zero_read_quorums = [
             (rq, v.varValue)
             for (rq, v) in zip(read_quorums, read_quorum_vars)

quorums/strategy.py

@@ -69,6 +69,34 @@ class Strategy(Generic[T]):
         return sum(weight * self._load(fr)
                    for (fr, weight) in d.items())
 
+    # TODO(mwhittaker): Rename throughput.
+    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(weight * f for (f, weight) in d.items())
+        read_network_load = fr * sum(
+            len(rq) * p
+            for (rq, p) in zip(self.reads, self.read_weights)
+        )
+        write_network_load = (1 - fr) * sum(
+            len(wq) * p
+            for (wq, p) in zip(self.writes, self.write_weights)
+        )
+        return read_network_load + write_network_load
+
+    def latency(self,
+                read_fraction: Optional[Distribution] = None,
+                write_fraction: Optional[Distribution] = None) -> float:
+        # TODO(mwhittaker): Implement.
+        return 0
+
     def node_load(self,
                   node: Node[T],
                   read_fraction: Optional[Distribution] = None,
@@ -78,11 +106,21 @@ class Strategy(Generic[T]):
         return sum(weight * self._node_load(node.x, fr)
                    for (fr, weight) in d.items())
 
-    def capacity(self,
+    def node_utilization(self,
+                         node: Node[T],
                          read_fraction: Optional[Distribution] = None,
                          write_fraction: Optional[Distribution] = None) \
                          -> float:
-        return 1 / self.load(read_fraction, write_fraction)
+        # TODO(mwhittaker): Implement.
+        return 0.0
+
+    def node_throghput(self,
+                       node: Node[T],
+                       read_fraction: Optional[Distribution] = None,
+                       write_fraction: Optional[Distribution] = None) \
+                       -> float:
+        # TODO(mwhittaker): Implement.
+        return 0.0
 
     def _node_load(self, x: T, fr: float) -> float:
         """