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MDPCloudSimulation.py
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MDPCloudSimulation.py
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from typing import Union, Tuple, Callable, Any
import numpy as np
import random
from multiprocessing_decorator import multiprocessing_decorator
# We have a state space (m,n) in [0, b] x [1, k]. We represent them as s = m*k + n - 1
# We have an action space alpha(j) where j is in [1, k] and corresponds to maintain only j servers
# We have a probability distribution of packets arrival. We have maximum of l packets that can arrive
class MDPCloud:
def __init__(self, queue_capacity: int, max_servers_num: int, max_arrivals: int,
server_flow: int, probability_distribution: Union[str, np.array],
cost_vm_run: int, cost_vm_activation: int, cost_vm_deactivation: int, cost_client: int):
p = None
if probability_distribution is str:
if probability_distribution != "uniform":
print("This distribution is not supported")
raise "Distribution is not supported exception"
p = np.array([1 / (max_arrivals + 1) for i in range(max_arrivals + 1)])
else:
p = probability_distribution
self.queue_capacity = queue_capacity
self.max_servers_num = max_servers_num
self.max_arrivals = max_arrivals
self.server_flow = server_flow
self.probability_distribution = p
self.cost_vm_run = cost_vm_run
self.cost_vm_activation = cost_vm_activation
self.cost_vm_deactivation = cost_vm_deactivation
self.cost_client = cost_client
self.set_params()
self.transition_matrix, self.cost_matrix = MDPCloud. \
define_transition_and_cost_matrix(MDPCloud, queue_capacity, max_servers_num, max_arrivals,
server_flow, p, cost_vm_run, cost_vm_activation,
cost_vm_deactivation, cost_client)
def set_params(self, episodes: int = -1, max_game_steps: int = -1,
discount: float = -1.0, eps: float = -1.0, alpha: float = -1.0):
self.episodes = episodes
self.max_game_steps = max_game_steps
self.discount = discount
self.eps = eps
self.alpha = alpha
# indicator function
@staticmethod
def ind(a: int, b: int):
if a > b:
return 1
return 0
@staticmethod
def calc_cost(cls, j: int, n: int, m: int, cf: int, ca: int, cd: int, ch: int) -> int:
return j * cf + (j - n) * cls.ind(j, n) * ca + (n - j) * cls.ind(n, j) * cd + m * ch
@staticmethod
def define_transition_and_cost_matrix(cls, b: int, k: int, l: int, d: int, p: np.array,
cf: int, ca: int, cd: int, ch: int) -> Tuple[
np.ndarray, np.ndarray]:
t = np.zeros([(b + 1) * k, (k + 1), (b + 1) * k])
r = np.zeros([(b + 1) * k, (k + 1)])
for m in range(b + 1):
for n in range(1, k + 1):
s = m * k + n - 1
for i in range(1, k + 1):
for j in range(l + 1):
npr = i
mp = min(b, max(0, m + j - npr * d))
sp = mp * k + npr - 1
t[s][npr][sp] = t[s][npr][sp] + p[j]
r[s][npr] = cls.calc_cost(MDPCloud, npr, n, m, cf, ca, cd, ch)
return t, r
@staticmethod
def get_random(distribution: np.array) -> int:
x = random.random()
s = 0.0
for i in range(len(distribution)):
if s <= x <= s + distribution[i]:
return i
s += distribution[i]
return len(distribution) - 1
@staticmethod
def get_best_action(q: np.ndarray, s: int) -> Any:
return 1 + np.argmin(np.array([q[s][a] for a in range(1, q.shape[1])]))
@staticmethod
def get_best_policy(cls, q: np.ndarray) -> np.array:
return np.array([cls.get_best_action(q, s) for s in range(q.shape[0])])
def show_best_policy(self, pi: np.array, filename=None) -> None:
f = None
if filename is not None:
f = open(filename, 'w')
for i in range(self.queue_capacity + 1):
for j in range(1, self.max_servers_num + 1):
print(f'In state ({i}, {j}) do: {pi[i * self.max_servers_num + j - 1]}')
if f is not None:
f.write(f'In state ({i}, {j}) do: {pi[i * self.max_servers_num + j - 1]}')
f.write("\n")
if f is not None:
f.close()
def value_iteration(self, callback: Callable[[Any, int, int, int, np.array, Any], None],
graph: Any, frequency: int, filename: Any) -> Tuple[np.ndarray, np.ndarray]:
if self.episodes == -1 or self.discount == -1:
raise "Can't execute. Minimum requirements are discount and episodes number. " \
"Set them via set_params function"
v = np.zeros(shape=[self.transition_matrix.shape[0]])
vp = np.zeros(shape=[self.transition_matrix.shape[0]])
pi = np.zeros(shape=[self.transition_matrix.shape[0]])
for i in range(self.episodes):
for j in range(self.transition_matrix.shape[0]):
v[j] = min(map(lambda x: sum(list([self.transition_matrix[j][x][sp] *
(self.cost_matrix[j][x] + self.discount * vp[sp])
for sp in range(self.transition_matrix.shape[0])])),
list(range(1, self.transition_matrix.shape[1]))))
vp = v[:]
callback(graph, i, frequency, self.episodes, v, filename)
for s in range(self.transition_matrix.shape[0]):
a = list(map(lambda x: sum(
list([self.transition_matrix[s][x][sp] * (self.cost_matrix[s][x] + self.discount * v[sp])
for sp in range(self.transition_matrix.shape[0])])),
list(range(1, self.transition_matrix.shape[1]))))
pi[s] = 1 + np.argmin(np.array(a))
return pi, v
def q_learning(self, max_reward: int, callback: Callable[[Any, int, int, int, np.array, Any], None], graph: Any,
frequency: int, filename: Any) -> np.ndarray:
if self.episodes == -1 or self.eps == -1.0 or self.discount == -1.0 or self.alpha == -1 or self.max_game_steps == -1:
raise "All parameters are required. Please set them via set_params function"
q = max_reward * np.random.rand(self.cost_matrix.shape[0], self.cost_matrix.shape[1])
for i in range(1, self.cost_matrix.shape[1]):
q[self.cost_matrix.shape[0] - 1][i] = 0
for i in range(self.episodes):
s = 0
j = 0
while j < self.max_game_steps:
action = 1 + MDPCloud.get_random(np.array([(1 / (self.cost_matrix.shape[1] - 1))
for _ in range(self.cost_matrix.shape[1] - 1)]))
if random.uniform(0, 1) >= self.eps:
action = MDPCloud.get_best_action(q, s)
arrivals = MDPCloud.get_random(self.probability_distribution)
m = int(s // (self.cost_matrix.shape[1] - 1))
mp = min((self.cost_matrix.shape[0] // (self.cost_matrix.shape[1] - 1) - 1),
max(0, m + arrivals - action * self.server_flow))
sp = mp * (self.cost_matrix.shape[1] - 1) + action - 1
q[s][action] = q[s][action] + self.alpha * (self.cost_matrix[s][action] - q[s][action] + self.discount *
min([q[sp][a] for a in
range(1, self.cost_matrix.shape[1])]))
s = sp
j += 1
callback(graph, i, frequency, self.episodes, q, filename)
return q
def sarsa(self, max_reward: int, callback: Callable[[Any, int, int, int, np.array, Any], None], graph: Any,
frequency: int, filename: Any) -> np.ndarray:
if self.episodes == -1 or self.eps == -1.0 or self.discount == -1.0 or self.alpha == -1 or self.max_game_steps == -1:
raise "All parameters are required. Please set them via set_params function"
q = max_reward * np.random.rand(self.cost_matrix.shape[0], self.cost_matrix.shape[1])
for i in range(1, self.cost_matrix.shape[1]):
q[self.cost_matrix.shape[0] - 1][i] = 0
for i in range(self.episodes):
s = 0
j = 0
while j < self.max_game_steps and s != (self.cost_matrix.shape[0] - 1):
action = 1 + MDPCloud.get_random(np.array([(1 / (self.cost_matrix.shape[1] - 1))
for _ in range(self.cost_matrix.shape[1] - 1)]))
if random.uniform(0, 1) >= self.eps:
action = MDPCloud.get_best_action(q, s)
arrivals = MDPCloud.get_random(self.probability_distribution)
m = int(s // (self.cost_matrix.shape[1] - 1))
mp = min((self.cost_matrix.shape[0] // (self.cost_matrix.shape[1] - 1) - 1),
max(0, m + arrivals - action * self.server_flow))
sp = mp * (self.cost_matrix.shape[1] - 1) + action - 1
action_p = 1 + MDPCloud.get_random(np.array([(1 / (self.cost_matrix.shape[1] - 1))
for _ in range(self.cost_matrix.shape[1] - 1)]))
if random.uniform(0, 1) >= self.eps:
action_p = MDPCloud.get_best_action(q, sp)
q[s][action] = q[s][action] + self.alpha * (self.cost_matrix[s][action] - q[s][action] +
self.discount * q[sp][action_p])
s = sp
j += 1
if s == (self.cost_matrix.shape[0] - 1):
print("Lost, in the game")
callback(graph, i, frequency, self.episodes, q, filename)
return q