def test_prob_poisson(self):
self.assertEqual(round(b.get_prob_poisson(1, 10, 0.01), 15),
0.090483741803596)
self.assertEqual(round(b.get_prob_poisson(4, 10, 0.0001), 27),
4.1625020826391e-14)
self.assertEqual(round(b.get_prob_poisson(4, 1, 0.001), 27),
4.1625020826391e-14)
def get_prob_schedulable(msgs, mi, boot_time, sync = True):
"""Returns the probability that message m is successfully transmitted even
in the presence of omission, commission, transmission faults. Here, although
m represents a single message, we compute the probability of successful
transmission collectively for all replicas of m, identified by a common
'tid' field. """
r = msgs.get_replication_factor(mi)
rprime = int(mpmath.floor(r / 2.0) + 1)
prob_msg_corrupted = 1 - br.get_prob_poisson(0, mi.deadline, msgs.po)
prob_msg_omitted = 1 - br.get_prob_poisson(0, boot_time, msgs.po)
# since pr(correct) is just a function of k <= r and pc,
# we compute it beforehand for all values (pc is commission fault prob.)
prob_correct = []
for k in range(0, r + 1):
if sync:
prob_correct.append(get_prob_correct_sync(k, prob_msg_corrupted))
else:
prob_correct.append(get_prob_correct_async(k, prob_msg_corrupted, rprime))
# need to iterate over all subsets of replica set of m
replica_ids = []
for mk in msgs:
if mk.tid == mi.tid:
replica_ids.append(mk.id)
assert r == len(replica_ids)
prob_success = 0
for omitted_ids in powerset(replica_ids):
for mk in msgs:
if mk.id in omitted_ids:
mk.omitted = True
else:
mk.omitted = False
s = r - len(omitted_ids)
prob_omitted = mpmath.power(prob_msg_omitted, r - s) * \
mpmath.power(1 - prob_msg_omitted, s)
prob_time_correct = 0
for k in range(1, s + 1):
prob_time_correct += get_prob_time_periodic(msgs, mi, k) * \
prob_correct[k]
prob_success += prob_omitted * prob_time_correct
return min(prob_success, 1)
def get_prob_time_periodic(msgs, mi, k):
""" Our timing analysis.
"""
faults = 0
prob = 0
while True:
timely_replicas = 0
for mk in msgs:
if mk.tid == mi.tid and mk.omitted == False:
if msgs.get_wctt(mk, faults) + mk.jitter <= mk.deadline:
timely_replicas += 1
if timely_replicas < k:
break
if timely_replicas == k:
prob += br.get_prob_poisson(faults, mi.deadline, msgs.mfr)
faults += 1
return prob
def test_prob_poisson(self):
self.assertEqual(round(b.get_prob_poisson(1, 10, 0.01), 15), 0.090483741803596)
self.assertEqual(round(b.get_prob_poisson(4, 10, 0.0001), 27), 4.1625020826391e-14)
self.assertEqual(round(b.get_prob_poisson(4, 1, 0.001), 27), 4.1625020826391e-14)
