def greedy(wrkld, spd, pwrusg, idle, idleusg, pwrcap, plcy):
"""Greedly schedules tasks according to a certain policy (no transitions while executing a task)
Arguments:
wrkld: list of workloads of each task
spd: list of speeds of configurations states
- for every task i, every machine j, and every configuration k,
- spd[i][j][k] is the speed of task i in machine j while in configuration k
pwrusg: list of power usages of configuration states
- for every task i, every machine j, and every configuration k,
- pwrusg[i][j][k] is the power usage of task i in machine j while in configuration k
idle: list of idle configuration states
- for every machine j
- idle[j] is the idle configuration of machine j (i.e., the state with less power usage)
idleusg: list of power usages of idle configuration states
- for every machine j
- idleusg[j] is the power usage of the idle configuration of machine j when no task is running
pwrcap: power limit of the system
plcy: function that receives wrkld, spd, pwrusg and two triples (i1,j1,k1) and (i2,j2,k2) and returns True
if and only if (i1,j1,k1) < (i2,j2,k2) in the policy used to greedly allocate the task
(i.e., triple (i1,j1,k1) is preferred over (i2,j2,k2))
--> plcy may assume that it will receive triples that don't yield zero speed
Returns: A triple (order, trn, run)
order: list of orderings of tasks on machines
- for every machine j,
- order[j] is a list [i1, ..., ik] that describes the tasks that will be run on machine j and their order
trn: list of state transitions
- for every t in range(len(trn)),
- trn[t].time is the time of transition t
- trn[t].config is a list of machine configurations
-- for every machine j,
-- trn[t].config[j] is the configuration to which machine j has transitioned
run: list of completion times of tasks
- for every machine j, and every t in len(order[j])
- task order[j] runs on machine j from time run[j][t] to time run[j][t+1]
Exceptions raised:
- no_solution if pwrcap cannot be satisfied
Assumptions:
Compatibility of sizes
Non-negative values
Non-zero tasks, machines and configurations
Idle state usages are less than when tasks are being run
Every task i on idle state idle[j] has same usage pwrusg[i][j][idle[j]] as idleusg[j]
Every task on an idle state has speed zero
"""
tasks = len(spd)
machines = len(spd[0])
configs = len(spd[0][0])
order = [None] * machines
trn = []
run = [None] * machines
for j in range(machines):
order[j] = []
run[j] = [0]
possib = [(i,j,k)
for i in range(tasks)
for j in range(machines)
for k in range(configs)
if pwrusg[i][j][k] <= pwrcap and spd[i][j][k] > 0 #exclude violating configs and zero speeds
]
possib.sort(key=less2key(lambda t1,t2: plcy(wrkld,spd,pwrusg,t1,t2), tuple))
taskcompleted = [False] * tasks
events = [(0, #time
0)]#machine that became free (first value is irrelevant)
currentconfigs = [idle[j] for j in range(machines)]
currentpwrusgs = [idleusg[j] for j in range(machines)]
currenttotalpwrusg = sum(currentpwrusgs)
currentfree = [True] * machines
numberoffree = machines
while True: #Equivalent to while len(events) != 0 here
(time, becamefree) = heapq.heappop(events)
# currentfree update block
if time != 0: #to exclude first iteration
while True:
currentfree[becamefree] = True
numberoffree += 1
currenttotalpwrusg += idleusg[becamefree] - currentpwrusgs[becamefree]
currentpwrusgs[becamefree] = idleusg[becamefree]
currentconfigs[becamefree] = idle[becamefree]
if len(events) == 0 or events[0][0] != time:
break
#next event has the same time (i.e., more machines may have become free at time)
becamefree = heapq.heappop(events)[1]
# End currentfree update block
psbind = 0 #since deletion in list possib is involved, we must do it like this
while numberoffree:
while psbind < len(possib):
i,j,k = possib[psbind]
if taskcompleted[i]: # task is completed: can be removed from possibilities
del possib[psbind]
continue # avoid incrementing index psbind
if currentfree[j] and currenttotalpwrusg - currentpwrusgs[j] + pwrusg[i][j][k] <= pwrcap:
break # found best valid triple!
psbind += 1
else: # (while's else) cannot run any more tasks at this time
if numberoffree < machines:
#at least one occupied machine, wait for it to finish
#(that is leave the while loop skipping the "Run task block")
break
#no occupied machine: either we are done or there is no solution
if False in taskcompleted: #some task is left: no solution
raise no_solution
for j in range(machines):# Fix run for machines that never ran any task
if len(order[j]) == 0:
run[j] = []
trn.append(stateTran(time,currentconfigs))#add final transition to idle states at the end
return (order,trn,run) #RETURN IS HERE!!
# Run i on j with config k block
taskcompleted[i] = True
del possib[psbind]
order[j].append(i)
currenttotalpwrusg += pwrusg[i][j][k] - currentpwrusgs[j]
currentconfigs[j] = k
currentpwrusgs[j] = pwrusg[i][j][k]
#transition left to be updated after all tasks of this time are processed
completiontime = time + float(wrkld[i]) / spd[i][j][k] #speed guaranteed to be non-zero
run[j].append(completiontime)
heapq.heappush(events,(completiontime,j)) #machine j will become free at time completiontime
currentfree[j] = False
numberoffree -= 1
# End of run i on j with config k block
#update transition of this time
trn.append(stateTran(time,currentconfigs[:])) #the slicing is to generate a copy
def getRealTransitionsFromPseudo(trn, run, finaltrnconfig=None):
"""Computes the transitions into real system states from transitions into pseudo system states and
assignment/completion times (does not check for correctness of the solution)
Arguments:
trn: list of state transitions
- for every t in range(len(trn)),
- trn[t].time is the time of transition t
- trn[t].configcoeff is an numpy.array of machine configurations
-- for every system configuration (k1,...,km), where m is the number of machines,
-- trn[t].configcoeff[k1,...,km] is the coefficient of real system configuration (k1,...,km) in the
pseudo system configuration to which machine j has transitioned
run: describes when each task runs on each machine (see getAssignmentCompletionRealTransitionsFromPseudo)
-- for every machine j, and every t in len(order[j])
-- task order[j][t] runs on machine j from time run[j][t] to time run[j][t+1]
finaltrnconfig: list of machine configurations to be put at the end
(or None (default), which is equivalent to [0]*machines)
--- for every machine j,
--- finaltrnconfig[j] is the configuration to which machine j has transitioned
(this is typically the list of idle configurations)
Returns: a list of real state transitions realtrn, where
- realtrn: is the list of real state transitions
-- for every t in range(len(realtrn)),
-- realtrn[t].time is the time of transition t
-- realtrn[t].config is a list of machine configurations
--- for every machine j,
--- realtrn[t].config[j] is the configuration to which machine j has transitioned
"""
events = []
realtrn = []
machines = len(run)
nconfigs = len(trn[0].configcoeff) # number of configurations
if finaltrnconfig == None:
finaltrnconfig = [0]*machines
for j in range(machines):
if run[j]:
for t in range(1,len(run[j])):
events.append((run[j][t],j,t))
for t in range(1,len(trn)):
events.append((trn[t].time,machines,t)) # we put the transitions with a dummy marker on second coordinate
events.sort()
lasttime = trn[0].time
psdnow = [(trn[0].configcoeff[sysconf], list(sysconf))
for sysconf in itertools.product(range(nconfigs), repeat=machines)# iterator for system configs
if trn[0].configcoeff[sysconf] != 0] # first pseudo system state
for (time,j,t) in events:
if lasttime < time:
difftime = time - lasttime
splittime = lasttime
for (p,sysconf) in psdnow:
realtrn.append(stateTran(splittime,sysconf))
splittime += p * difftime
lasttime = time
if j == machines: # it is a pseudo system state transition
psdnow = [(trn[t].configcoeff[sysconf], list(sysconf))
for sysconf in itertools.product(range(nconfigs), repeat=machines)# iter for system configs
if trn[t].configcoeff[sysconf] != 0]
#The part below normalizes the solution by putting a final state transition at the end
realtrn.append(stateTran(lasttime,finaltrnconfig))
return realtrn
def halfHeartedGreedy(wrkld, spd, pwrusg, idle, idleusg, pwrcap, plcies, makecopy=True, reorder=True):
"""Greedly schedules tasks according to a certain policy (allows transitions while executing a task)
Arguments:
wrkld: list of workloads of each task
spd: list of speeds of configurations states
- for every task i, every machine j, and every configuration k,
- spd[i][j][k] is the speed of task i in machine j while in configuration k
pwrusg: list of power usages of configuration states
- for every task i, every machine j, and every configuration k,
- pwrusg[i][j][k] is the power usage of task i in machine j while in configuration k
idle: list of idle configuration states
- for every machine j
- idle[j] is the idle configuration of machine j (i.e., the state with less power usage)
idleusg: list of power usages of idle configuration states
- for every machine j
- idleusg[j] is the power usage of the idle configuration of machine j when no task is running
pwrcap: power limit of the system
plcies: list of functions that receive wrkld, spd, pwrusg and two triples (i1,j1,k1) and (i2,j2,k2) and return
True if and only if (i1,j1,k1) < (i2,j2,k2) in the policy used to greedly allocate the task
(i.e., triple (i1,j1,k1) is preferred over (i2,j2,k2))
--> plcy may assume that it will receive triples that don't yield zero speed
makecopy: boolean, if True, algorithm does not change any of its parameters (see Data races)
reorder: reorder triples (task, machine, configuration) after each task completion (needed if policy is to
use workload left instead of initial workload of tasks)
Returns: A triple (order, trn, run)
order: list of orderings of tasks on machines
- for every machine j,
- order[j] is a list [i1, ..., ik] that describes the tasks that will be run on machine j and their order
trn: list of state transitions
- for every t in range(len(trn)),
- trn[t].time is the time of transition t
- trn[t].config is a list of machine configurations
-- for every machine j,
-- trn[t].config[j] is the configuration to which machine j has transitioned
run: list of completion times of tasks
- for every machine j, and every t in len(order[j])
- task order[j] runs on machine j from time run[j][t] to time run[j][t+1]
Exceptions raised:
- no_solution if pwrcap cannot be satisfied
Assumptions:
Compatibility of sizes
Non-negative values
Non-zero tasks, machines and configurations
Idle state usages are less than when tasks are being run
Every task i on idle state idle[j] has same usage pwrusg[i][j][idle[j]] as idleusg[j]
Every task on an idle state has speed zero
plcies non-empty
Data races:
If makecopy = False, then
- wrkld is modified
"""
if makecopy:
wrkld = wrkld[:]
tasks = len(spd)
machines = len(spd[0])
configs = len(spd[0][0])
order = [None] * machines
trn = []
run = [None] * machines
for j in range(machines):
order[j] = []
run[j] = [0]
nplcies = len(plcies)
possibs = [None] * nplcies
possibs[0] = [(i,j,k)
for i in range(tasks)
for j in range(machines)
for k in range(configs)
if pwrusg[i][j][k] <= pwrcap and spd[i][j][k] > 0 #exclude violating configs and zero speeds
]
keys = [None] * nplcies
for p in range(1,nplcies):
possibs[p] = possibs[0][:] #make copy
keys[p]=less2key(lambda t1,t2: plcies[p](wrkld,spd,pwrusg,t1,t2), tuple)
possibs[p].sort(key=keys[p])
taskstatus = [0] * tasks #0: waiting, 1: running, 2: completed
events = [(0, #time
0)]#machine that became free (first value is irrelevant)
idletotalpwrusg = sum(idleusg)
currentrunning = [None] * machines
time = 0
#The below will be true in the first iteration, but do not need to be initialized here:
#currentconfigs = [idle[j] for j in range(machines)]
#currentpwrusgs = [idleusg[j] for j in range(machines)]
#currentfree = [True] * machines
#numberoffree = machines
#currenttotalpwrusg = idletotalpwrusg
while True: #Equivalent to while len(events) != 0 here
prevtime = time
time = events[0][0]
# taskstatus update block
if prevtime != time: #to exclude first iteration
# determine the minimum completion time
for (t,mc) in events:
if t < time:
time = t
# consider tasks that finish at time time completed
for (t,machinecompleted) in events:
if t == time:
taskstatus[currentrunning[machinecompleted]] = 2 #completed
run[machinecompleted].append(time)
currentrunning[machinecompleted] = None
# End taskstatus update block
# wrkld update block
deltat = time - prevtime
for j in range(machines):
if currentrunning[j] != None:
wrkld[currentrunning[j]] -= spd[currentrunning[j]][j][currentconfigs[j]] * deltat
# End wrkld update block
# Falsely transition every occupied machine to idle state (so that the algorithm can choose new configs)
currentconfigs = [idle[j] for j in range(machines)]
currentpwrusgs = [idleusg[j] for j in range(machines)]
currenttotalpwrusg = idletotalpwrusg
currentcompletiontimes = [None] * machines
someOccupied = False
for p in range(nplcies):
# Since wrklds might have been updated, we may need to sort the triples again
if (reorder):
possibs[p].sort(key=keys[p])
psbind = 0 #since deletion in list possibs[p] is involved, we must do it like this
numberofnotconsidered = machines
currentnotconsidered = [True] * machines
while numberofnotconsidered:
while psbind < len(possibs[p]):
i,j,k = possibs[p][psbind]
if taskstatus[i] == 2: # task is completed: can be removed from possibilities
del possibs[p][psbind]
continue # avoid incrementing index psbind
if (currentnotconsidered[j] and
((currentrunning[j] == None and taskstatus[i] == 0) or currentrunning[j] == i) and
currenttotalpwrusg - currentpwrusgs[j] + pwrusg[i][j][k] <= pwrcap):
break # found best valid triple!
psbind += 1
else: # (while's else) cannot run any more tasks at this time
if p+1 < nplcies or someOccupied:
#we are not finished deciding or there is at least one occupied machine
#(that is leave the while loop skipping the "Run task block")
break
#no occupied machine: either we are done or there is no solution
if 0 in taskstatus: #some task is left: no solution
raise no_solution
for j in range(machines):# Fix run for machines that never ran any task
if len(order[j]) == 0:
run[j] = []
trn.append(stateTran(time,currentconfigs))#add final transition to idle states at the end
return (order,trn,run) #RETURN IS HERE!!
# Consider running i on j with config k block
taskstatus[i] = 1 #running
if currentrunning[j] == None:
order[j].append(i)
currentrunning[j] = i
currenttotalpwrusg += pwrusg[i][j][k] - currentpwrusgs[j]
currentconfigs[j] = k
currentpwrusgs[j] = pwrusg[i][j][k]
#transition left to be updated after all tasks of this time are processed
completiontime = time + float(wrkld[i]) / spd[i][j][k] #speed guaranteed to be non-zero
#if we don't change our mind, machine j will become free at time completiontime:
currentcompletiontimes[j] = completiontime
someOccupied = True
currentnotconsidered[j] = False
numberofnotconsidered -= 1
# End of consider running i on j with config k block
#out of for: commit to decision and update transition of this time
events = [(currentcompletiontimes[j],j) for j in range(machines) if currentcompletiontimes[j] != None]
trn.append(stateTran(time,currentconfigs[:])) #the slicing is to generate a copy
#!/usr/bin/python
#-*- coding: utf-8 -*-
from commonclasses import stateTran, pseudoStateTran
from numpy import array
workload = [10] * 6
speed = [[[1, 2, 3]] * 3] * 6
order = [[0,1],
[2,3],
[4,5]]
realtransitions = [stateTran(0,[0,0,0]),
stateTran(2,[1,2,0]),
stateTran(5,[2,0,1]),
stateTran(7,[2,2,2]),
stateTran(10,[1,1,1])]
pseudotransitions = [
pseudoStateTran(0,array([
[[1,0,0],[0,0,0],[0,0,0]],
[[0,0,0],[0,0,0],[0,0,0]],
[[0,0,0],[0,0,0],[0,0,0]]])),
pseudoStateTran(2,array([
[[1.0/2,0,1.0/2],[0,0,0],[0,0,0]],
[[0,0,0],[0,0,0],[0,0,0]],
[[0,0,0],[0,0,0],[0,0,0]]])),
pseudoStateTran(5,array([
[[1.0/4,0,1.0/4],[0,0,0],[1.0/4,0,1.0/4]],
[[0,0,0],[0,0,0],[0,0,0]],
[[0,0,0],[0,0,0],[0,0,0]]])),
