diff --git a/README.md b/README.md
index effaa96d7f9800b46166a9848101ec03ea3fbaca..7efb6f46857ab12275f1074090fea03c460be350 100644
--- a/README.md
+++ b/README.md
@@ -21,6 +21,13 @@ summarized in a table.
| Taskset | taskset.py | Code representation of a taskset. Includes functions to compute utilization, optimal number of schedules, and hyperperiod. |
| Schedule | schedule.py | Code representation of a schedule. Includes function to check for validity. |
+* The Benchmark tests used to produce the results in the paper can be run using
+ the Makefile presented in the Code directory. It generates tasksets, stores
+ them as well as their solution in a separate directory (named "data"). The
+ class __FileSystemManager__ can then be used to access the solution.
+* The format of which the result pdf (see __Results__) needs the data is
+ generated through the __generate\_result\_file.py__ script.
+
### Results
In the __Results__ directory, the results generated by our benchmark can be
found. Each page in the pdf-file contains the results from the experiments
diff --git a/code/Makefile b/code/Makefile
new file mode 100644
index 0000000000000000000000000000000000000000..582c8652fbdc4421fee2e1ae227f8fc69812cef1
--- /dev/null
+++ b/code/Makefile
@@ -0,0 +1,9 @@
+all:
+ # max_hyperiod nbr_tests max_nbr_tasks max_timeout
+ sh tests/run_benchmark.sh 100 1000 3 1
+ make -s clean
+clean:
+ find . -name '__pycache__' -exec rm -rf exec {} \;
+deepclean:
+ rm -rf ../data/
+ make -s clean
diff --git a/code/benchmark.py b/code/benchmark.py
new file mode 100644
index 0000000000000000000000000000000000000000..e97017936302e84484276b3459d1ab6927f01d4d
--- /dev/null
+++ b/code/benchmark.py
@@ -0,0 +1,92 @@
+from os import getpid
+import multiprocessing as mp
+import time
+import sys
+
+from lib.fixedpriority import FixedPriority
+from lib.task import Task
+from lib.taskset import Taskset
+from lib.schedule import Schedule
+from lib.scheduleset import ScheduleSet
+from lib.solver import Solver
+from lib.filesystemmanager import FileSystemManager
+from lib.filesystemgenerator import FileSystemGenerator
+
+# ------------------------------------------------
+# Essential variables declaration
+
+hyperperiod = int(sys.argv[1])
+volume = int(sys.argv[2])
+nbr_tasks = int(sys.argv[3])
+max_tout = int(sys.argv[4])
+nbr_cpus = mp.cpu_count() - 1
+
+# ------------------------------------------------
+# Multiprocessed functions
+
+def solve(ts, finished_q, max_timeout, max_hyperperiod, nbr_tasks):
+ # Generate the schedules for this taskset
+ solver = Solver(max_hyperperiod, nbr_tasks)
+ solved = solver.solve(ts, max_timeout)
+ finished_q.put(getpid())
+
+ # If schedules empty we passed timeout time.
+ if not solved:
+ print('Timeout for process', getpid())
+ else:
+ print('Schedules found for process', getpid())
+ return solved
+
+# NOTE: Script starts here -------------------------------------
+# Generating the tasksets
+# Read synthetic tasksets from file in case there is a file, otherwise generate them
+#NOTE READ AND CREATE TASKSETS
+timed_tasksets = FileSystemGenerator(hyperperiod, nbr_tasks).generate_unsolved_tasksets(volume, max_tout)
+tasksets = [ts for ts, _ in timed_tasksets]
+
+if len(tasksets) > volume:
+ print('Too many tasksets')
+ sys.exit(0)
+
+# Check whether all tasksets are valid or not.
+for ts in tasksets:
+ if not FixedPriority(ts).schedulable:
+ print('NOT VALID!')
+ print(ts)
+ sys.exit(0)
+
+print('Success! {} schedules loaded'.format(len(tasksets)))
+# --------------------------------------------------------------
+#Calculates the optimal schedule set and writes it to file
+# --------------------------------------------------------------
+t_tot_start = time.time()
+
+# Create a process queue which will contain the results
+finished_q = mp.Queue()
+
+taskset_nbr = 0
+# Parallelice the tasksets
+processes = dict()
+finished = dict()
+running = 0
+# While we still have tasksets to compute
+while len(finished) < len(tasksets) or taskset_nbr < len(tasksets):
+ # Wait for the processes to join
+ while running < nbr_cpus and taskset_nbr < len(tasksets):
+ ts = tasksets[taskset_nbr]
+ # Create a process for current taskset
+ process = mp.Process(target=solve, args=(ts, finished_q, max_tout, hyperperiod, nbr_tasks, ))
+ process.start()
+ processes[process.pid] = process
+ taskset_nbr += 1
+ running += 1
+
+ while not finished_q.empty():
+ running -= 1
+ process_id = finished_q.get()
+ finished[process_id] = True
+
+# Finished the benchmark test
+t_tot_end_solve = time.time()
+print('Finished')
+print('Total elapsed time:', t_tot_end_solve - t_tot_start, 's')
diff --git a/code/generate_result_file.py b/code/generate_result_file.py
new file mode 100644
index 0000000000000000000000000000000000000000..78ad197561a28d4a9c3d18058359a0fbc236db9f
--- /dev/null
+++ b/code/generate_result_file.py
@@ -0,0 +1,39 @@
+from lib.filesystemfinder import FileSystemFinder
+from lib.resultenum import ResultEnum
+from lib.countenum import CountEnum
+
+from pathlib import Path
+import sys
+
+class ResultFileGenerator:
+
+ def __init__(self, max_hyperperiod, nbr_tasks, path_to_dir=''):
+ self.base_path = path_to_dir
+ self.hp = max_hyperperiod
+ self.n = nbr_tasks
+ self.finder = FileSystemFinder(max_hyperperiod, nbr_tasks)
+
+ # Overwrites current file with new data
+ def create_solved_file(self):
+ with open('{}solved{}-{}.csv'.format(self.base_path, self.hp, self.n), 'w') as f:
+ # Write header
+ f.write('{},{},{},{}\n'.format( \
+ ResultEnum.UTILIZATION.name, \
+ ResultEnum.ENTROPY.name, \
+ ResultEnum.TIME.name, \
+ ResultEnum.HYPERPERIOD.name))
+ results = self.finder.get_all_results()
+ for scheduleset, time in results:
+ f.write('{},{},{},{}\n'.format( \
+ sum(scheduleset.taskset.utilisation()[1:]), \
+ scheduleset.upper_approximated_entropy, \
+ time, \
+ scheduleset.taskset.hyperperiod()))
+
+
+if __name__ == '__main__':
+ for hp in range(100, 501, 100):
+ print('Writing to data{} file in results folder'.format(hp))
+ for nbr_tasks in range(2, 11):
+ rfg = ResultFileGenerator(hp, nbr_tasks, '../../results/data/data{}/'.format(hp))
+ rfg.create_solved_file()
diff --git a/code/lib/constraintBuilder.py b/code/lib/constraintBuilder.py
new file mode 100644
index 0000000000000000000000000000000000000000..dcbce404a1f6a41b0a6d425259e30113fe43ebed
--- /dev/null
+++ b/code/lib/constraintBuilder.py
@@ -0,0 +1,98 @@
+from ortools.constraint_solver import pywrapcp
+from lib.taskset import Taskset
+
+class ConstraintBuilder:
+
+ # taskset = Taskset object
+ # timeout_ = Time before constraint builder should terminate (given in seconds)
+ def __init__(self, taskset, timeout_):
+ self.ts = taskset
+ self.timeout = timeout_
+
+ def generate_schedules(self):
+ # Create the solver.
+ solver = pywrapcp.Solver('ScheduleGenerator')
+
+ # Initialize useful variables.
+ row_len = self.ts.hyperperiod()
+ col_len = self.ts.k_opt()
+ n_opt = self.ts.n_opt()
+ slots = list(range(row_len))
+ schedules = list(range(col_len))
+ min_task = n_opt.index(min(n_opt))
+ tasks = list(range(len(n_opt)))
+
+ # Find the grid points corresponding to the lowest utilized task
+ slot = 0
+ i = 0
+ grid_points = {}
+ while slot < row_len:
+ for added in range(n_opt[min_task]):
+ grid_points[(i, slot)] = min_task
+ i += 1
+ if i >= col_len: i = 0
+ slot += 1
+
+ # Assign Variable domain to each grid point.
+ grid = {}
+ for j in slots:
+ for i in schedules:
+ grid[(i, j)] = solver.IntVar(min(tasks), max(tasks), 'grid %i %i' % (i, j))
+
+ # For each schedule
+ for i in schedules:
+ schedule = [grid[(i, j)] for j in slots]
+ # For each task
+ for t in tasks:
+ exectime, period = self.ts.attributes(t)
+ # Add the fundamental period constraints to the solver:
+ # A task has to execute exectime nbr of times in each period
+ for p in range(round(row_len/period)):
+ solver.Add(solver.Count(schedule[p*period:(p+1)*period], t, exectime))
+
+ # For each slot
+ for j in slots:
+ slot = [grid[(i, j)] for i in schedules]
+ # Add the constraint that we want the optimal nbr of each task in each slot
+ for t in tasks:
+ solver.Add(solver.Count(slot, t, n_opt[t]))
+
+ # Constraint the lowest utilized task
+ for p in grid_points:
+ solver.Add(grid[p] == min_task)
+
+ # Regroup all variables into a list
+ all_vars = [grid[(i, j)] for i in schedules for j in slots]
+
+ # Create search phases
+ # Pick variables (grid points) simple: First element first
+ # Pick values for the variables simple: First element first
+ vars_phase = solver.Phase(all_vars,
+ solver.INT_VAR_SIMPLE,
+ solver.ASSIGN_RANDOM_VALUE)
+
+ solution = solver.Assignment()
+ solution.Add(all_vars)
+ # Stop once we find 1 solution
+ collector = solver.FirstSolutionCollector(solution)
+ # Or if we reach the timelimit
+ timelimit = solver.TimeLimit(self.timeout*1000)
+
+ # And solve.
+ solver.Solve(vars_phase, [collector, timelimit])
+
+ if timelimit.Crossed():
+ return []
+
+ elif collector.SolutionCount() == 1:
+ result = list()
+ for i in schedules:
+ result.append([int(collector.Value(0, grid[(i, j)])) for j in slots])
+
+ return result
+
+ else:
+ print('Something failed!')
+ print('Task\tExec\tPeriod\tHP\tu')
+ for t in self.ts.taskset: print(t.priority, '\t', t.exectime, '\t', t.period, '\t', \
+ self.ts.hyperperiod(), '\t', sum([x.exectime/x.period for x in self.ts.taskset]))
diff --git a/code/lib/filesystemfinder.py b/code/lib/filesystemfinder.py
new file mode 100644
index 0000000000000000000000000000000000000000..1ac9a975888c41db6420acbcaa87e10c2ed937df
--- /dev/null
+++ b/code/lib/filesystemfinder.py
@@ -0,0 +1,189 @@
+from pathlib import Path
+import os
+from lib.scheduleset import ScheduleSet
+from lib.headerenum import HeaderEnum
+from lib.taskenum import TaskEnum
+from lib.taskset import Taskset
+from lib.task import Task
+
+class FileSystemFinder:
+
+ def __init__(self, max_hyperperiod, nbr_tasks):
+ self.base_path = '../data/tasksets/hyperperiod{}-nbrtasks{}/'.format(max_hyperperiod, nbr_tasks)
+ self.max_hyperperiod = max_hyperperiod
+ self.nbr_tasks = nbr_tasks
+
+ # collects all hashcodes in taskset_dictionary
+ # Return: List(folder_names)
+ def get_all_hash_codes(self):
+ path = self.base_path
+ directory = os.listdir(path)
+ return list(map(lambda x: int(x), directory))
+
+ # Collect and return all tasksets with hash_codes
+ # Return: List(Taskset)
+ def get_all_tasksets(self, hash_codes=None):
+ if hash_codes is None:
+ # Find all hash_codes
+ hash_codes = self.get_all_hash_codes()
+ assert hash_codes, 'No tasksets exist'
+
+ path = self.base_path
+ tasksets = list()
+ for hash_code in hash_codes:
+ ts = self.get_taskset(hash_code)
+ if ts is not None:
+ tasksets.append(ts)
+
+ return tasksets
+
+ # Get taskset with hash_code
+ # Return: Taskset
+ def get_taskset(self, hash_code):
+ path = self.base_path + str(hash_code) + '/taskset.csv'
+ try:
+ with open(path, 'r') as f:
+ next(f) # Skip header
+ tasks = []
+ for line in f:
+ t = line.split(',')
+ tasks.append(Task(int(t[TaskEnum.PRIORITY.value]), int(t[TaskEnum.EXECTIME.value]), int(t[TaskEnum.PERIOD.value]), int(t[TaskEnum.DEADLINE.value])))
+
+ return Taskset(tasks)
+ except:
+ print('Taskset with hash_code {} could not be found'.format(hash_code))
+
+ # Return list of schedule sets with the results of the given taskset as well as the corresponding solution time
+ # return: ScheduleSet, Time
+ def get_all_results(self, tasksets=None):
+ if tasksets is None: tasksets = self.get_all_solved()
+
+ if type(tasksets) is list:
+ schedule_sets = list()
+ for ts in tasksets: schedule_sets.append(self.get_result(ts))
+ return schedule_sets
+ else:
+ return self.get_result(tasksets)
+
+ # Return schedule set with the results of the given taskset
+ # return: ScheduleSet, Time
+ def get_result(self, taskset):
+ path = self.base_path + str(taskset.to_hash()) + '/result.csv'
+ lines = open(path, 'r').readlines()
+ # Make sure we have a solution
+ assert len(lines) != 0, 'Taskset does not have a solution'
+
+ schedules = list()
+ for line in lines:
+ l = line.split(',')
+ schedules.append(list(map(lambda x: int(x), l)))
+
+ return (ScheduleSet(taskset, schedules), self.get_time(taskset))
+
+ # returns the maximum time this taskset has been run for.
+ # Return: Time
+ def get_time(self, ts):
+ path = self.base_path + str(ts.to_hash()) + '/header.csv'
+ lines = open(path, 'r').readlines()
+ line = lines[1][:-1].split(',')
+ return int(line[HeaderEnum.SOLVEDTIME.value])
+
+ # Collect all tasksets which HAVE NOT been solved (failed tasksets)
+ # Return: List(Taskset)
+ def get_all_not_solved(self):
+ return self._get_flag(str(False), HeaderEnum.SOLVED)
+
+ # Collect all tasksets which HAVE NOT been solved (failed tasksets)
+ # Return: List(Taskset)
+ def get_all_not_yet_solved(self):
+ return self._get_flag(str(None), HeaderEnum.SOLVED)
+
+ # Collect all tasksets which HAVE been solved (Successful tasksets)
+ # Return: List(Taskset)
+ def get_all_solved(self):
+ return self._get_flag(str(True), HeaderEnum.SOLVED)
+
+ # Collect all tasksets which HAVE not yet been solved in time less than TIME
+ # Return tasksets and corresponding max-time
+ # Return: List((Taskset, Time))
+ def get_all_max_time_not_solved(self, max_time):
+ return self._get_all_time(False, max_time)
+
+ # Collect all tasksets which HAVE been solved
+ # Return tasksets and corresponding solution-time
+ # Return: List((Taskset, Time))
+ def get_all_max_time_solved(self, max_time):
+ return self._get_all_time(True, max_time)
+
+ # Help function to get all tasksets and times of a certain type.
+ def _get_all_time(self, solved, max_time):
+ hash_codes = self.get_all_hash_codes()
+ result = list()
+ for code in hash_codes:
+ path = self.base_path + str(code) + '/header.csv'
+ try:
+ t = open(path, 'r').readlines()
+ t = t[1][:-1].split(',')
+
+ # NOTE: This is not a good function structure. Although, it is better than duplicating almost all of the code
+ if solved and t[HeaderEnum.SOLVED.value] == str(True) and int(t[HeaderEnum.SOLVEDTIME.value]) <= max_time:
+ result.append((self.get_taskset(code), int(t[HeaderEnum.SOLVEDTIME.value])))
+
+ elif not solved and (t[HeaderEnum.SOLVED.value] == str(False) or t[HeaderEnum.SOLVED.value] == str(None)) and int(t[HeaderEnum.SOLVEDTIME.value]) < max_time:
+ result.append((self.get_taskset(code), int(t[HeaderEnum.SOLVEDTIME.value])))
+ except:
+ print('{} could not be found'.format(path))
+ return result
+
+
+
+ # Help function to get all of a certain flag with ceratin string
+ def _get_flag(self, condition_string, flag):
+ hash_codes = self.get_all_hash_codes()
+ result = list()
+ for code in hash_codes:
+ path = self.base_path + str(code) + '/header.csv'
+ try:
+ t = open(path, 'r').readlines()[1][:-1].split(',')
+ if t[flag.value] == condition_string:
+ result.append(self.get_taskset(code))
+ except:
+ print('{} could not be found'.format(path))
+ return result
+
+
+ # Return status of SOLVED on the taskset as well as the currently longest test-time
+ # Return: Boolean
+ def is_solved(self, ts):
+ solved_string = self.get_flag_string(ts, HeaderEnum.SOLVED)
+ time_string = self.get_flag_string(ts, HeaderEnum.SOLVEDTIME)
+ solved = True if solved_string == str(True) else False
+ time = int(time_string)
+ return solved, time
+
+ # Counts the number of tasksets in the given folder and returns the answer as an int
+ # Return: Nbr_Tasksets
+ def get_nbr_tasksets(self):
+ return sum(os.path.isdir(self.base_path + i) for i in os.listdir(self.base_path))
+
+ # Counts the number of unsolved tasksets in the given folder and returns the answer as an int
+ # Return: Nbr_Tasksets
+ def get_nbr_unsolved_tasksets(self):
+ return self.get_count(HeaderEnum.SOLVED)
+
+ # Help function for counting: uncounted and unsolved methods
+ def get_count(self, flag):
+ hash_codes = self.get_all_hash_codes()
+ nbr = 0
+ for code in hash_codes:
+ path = self.base_path + str(code) + '/header.csv'
+ t = open(path, 'r').readlines()[1][:-1].split(',')
+ if t[flag.value] == str(False) or t[flag.value] == str(None): nbr += 1
+ return nbr
+
+ # Get the string in the dictionary for the given hash_code and flag
+ def get_flag_string(self, ts, flag):
+ path = self.base_path + ts.to_hash() + '/header.csv'
+ t = open(path, 'r').readlines()[1][:-1].split(',')
+ return t[flag.value]
+
diff --git a/code/lib/filesystemgenerator.py b/code/lib/filesystemgenerator.py
new file mode 100644
index 0000000000000000000000000000000000000000..4f795d76af92c54ff66d2efbccb73328bd2ebbf8
--- /dev/null
+++ b/code/lib/filesystemgenerator.py
@@ -0,0 +1,33 @@
+from lib.filesystemmanager import FileSystemManager
+from lib.tasksetgenerator import TasksetGenerator
+
+class FileSystemGenerator:
+
+ def __init__(self, max_hyperperiod, nbr_tasks):
+ self.manager = FileSystemManager(max_hyperperiod, nbr_tasks)
+ self.max_hyperperiod = max_hyperperiod
+ self.nbr_tasks = nbr_tasks
+
+ # Generate and collect unsolved tasksets in the given category
+ def generate_unsolved_tasksets(self, volume, max_timeout):
+ # Get the ones we have that we haven't been able to solve in max_timeout minutes
+ tasksets = self.manager.get_all_not_solved_time(max_timeout)
+ # If this is less than the number we want:
+ # Create some more and save them
+ if tasksets is None or len(tasksets) < volume:
+ created_tasksets = self.create_tasksets(volume)
+ self.manager.save_tasksets(created_tasksets)
+
+ # If we created some new ones: update the ones we can run on.
+ if tasksets is None or len(tasksets) != self.manager.get_nbr_unsolved_tasksets():
+ tasksets = self.manager.get_all_not_solved_time(max_timeout)
+
+ return tasksets
+
+ # NOTE: TAKE A NEW LOOK AT THIS ONE
+ def load_tasksets(self, volume):
+ if self.manager.get_nbr_tasksets(self.max_hyperperiod, self.nbr_tasks) < volume:
+ pass
+
+ def create_tasksets(self, volume):
+ return TasksetGenerator(self.max_hyperperiod, self.nbr_tasks).generate_tasksets(volume)
diff --git a/code/lib/filesystemmanager.py b/code/lib/filesystemmanager.py
new file mode 100644
index 0000000000000000000000000000000000000000..7a9cc0c55dc5ac1e6dbcc23e261112f690f9bc08
--- /dev/null
+++ b/code/lib/filesystemmanager.py
@@ -0,0 +1,70 @@
+from pathlib import Path
+from lib.filesystemfinder import FileSystemFinder
+from lib.filesystemupdater import FileSystemUpdater
+
+class FileSystemManager:
+
+ def __init__(self, max_hyperperiod, nbr_tasks):
+ # Create base structure
+ base_path = '../data/'
+ Path(base_path).mkdir(parents=True, exist_ok=True)
+ base_path += 'tasksets/'
+ Path(base_path).mkdir(parents=True, exist_ok=True)
+ base_path += 'hyperperiod{}-nbrtasks{}/'.format(max_hyperperiod, nbr_tasks)
+ Path(base_path).mkdir(parents=True, exist_ok=True)
+ self.finder = FileSystemFinder(max_hyperperiod, nbr_tasks)
+ self.updater = FileSystemUpdater(max_hyperperiod, nbr_tasks)
+
+ # Loads all the tasksets with the given hash_codes and returns them as a list
+ # if hash_codes has been emitted: Return all tasksets
+ def load_tasksets(self, hash_codes=None):
+ return self.finder.get_all_tasksets(hash_codes)
+
+ # Saves the tasksets in the given folder structure
+ # Tasksets argument could be one or more tasksets
+ def save_tasksets(self, tasksets):
+ # If list is empty, stop
+ assert tasksets, "No tasksets to save"
+ self.updater.save_tasksets(tasksets)
+
+ # Collect all tasksets which HAVE NOT BEEN solved (failed tasksets)
+ def get_all_not_solved(self):
+ return self.finder.get_all_not_solved()
+
+ # Collect all tasksets which HAVE NOT BEEN solved (failed tasksets)
+ def get_all_not_yet_solved(self):
+ return self.finder.get_all_not_yet_solved()
+
+ # Collect all tasksets which HAVE BEEN solved (Successful tasksets)
+ def get_all_solved(self):
+ return self.finder.get_all_solved()
+
+ # Collect all tasksets which HAVE been solved within the given time
+ def get_all_solved_time(self, max_time):
+ return self.finder.get_all_max_time_solved(max_time)
+
+ # Collect all tasksets which HAVE NOT been solved within the given time
+ def get_all_not_solved_time(self, max_time):
+ return self.finder.get_all_max_time_not_solved(max_time)
+
+ # Return the upper-approximated entropy for each of the tasksets in tasksets
+ # Tasksets argument could be one or more tasksets
+ def get_all_results(self, tasksets=None):
+ return self.finder.get_all_results(tasksets)
+
+ # Return the number of tasksets existing of the given type
+ def get_nbr_tasksets(self):
+ return self.finder.get_nbr_tasksets()
+
+ # Return the number of tasksets existing of the given type
+ def get_nbr_unsolved_tasksets(self):
+ return self.finder.get_nbr_unsolved_tasksets()
+
+ # Save all the results acquired from the constraint optimization algorithm.
+ # tasksets and solutions arguments could be single arguments or multiple
+ def save_timing_results(self, tasksets, time, solutions):
+ self.updater.save_timing_results(tasksets, time, solutions)
+
+ # Returns whether this taskset has a solution or not,
+ def is_solved(self, ts):
+ return self.finder.is_solved(ts)
diff --git a/code/lib/filesystemupdater.py b/code/lib/filesystemupdater.py
new file mode 100644
index 0000000000000000000000000000000000000000..9086232a125a6b0908b242531f107c9d0a88c904
--- /dev/null
+++ b/code/lib/filesystemupdater.py
@@ -0,0 +1,95 @@
+from pathlib import Path
+from lib.timeenum import TimeEnum
+from lib.taskenum import TaskEnum
+from lib.headerenum import HeaderEnum
+
+class FileSystemUpdater:
+
+ def __init__(self, max_hyperperiod, nbr_tasks):
+ self.base_path = '../data/tasksets/hyperperiod{}-nbrtasks{}/'.format(max_hyperperiod, nbr_tasks)
+ self.max_hyperperiod = max_hyperperiod
+ self.nbr_tasks = nbr_tasks
+
+ # Save all tasksets in list tasksets
+ def save_tasksets(self, tasksets):
+ # If tasksets is not list: assume it is taskset
+ if type(tasksets) is list:
+ # For each taskset: Save it in a folder, given that the folder does not exist.
+ for ts in tasksets:
+ self.save_taskset(ts)
+ else:
+ self.save_taskset(tasksets)
+
+ # Save all the results acquired from the constraint optimization algorithm.
+ def save_timing_results(self, tasksets, time, solutions):
+ # If tasksets and solutions are not lists: assume they are taskset and matrix
+ if type(tasksets) is list and type(solutions) is list:
+ for i in range(len(tasksets)):
+ self.save_timing_result(tasksets[i], time, solutions[i])
+ else:
+ self.save_timing_result(tasksets, time, solutions)
+
+ # Save taskset unless it already exist
+ def save_taskset(self, ts):
+ path = self.base_path
+ ts_exists = self.taskset_exists(ts)
+ if not ts_exists:
+ taskset_path = path + ts.to_hash() + '/'
+ p = Path(taskset_path).mkdir(parents=True)
+ self.create_file(taskset_path + 'taskset.csv', text=self.parse(ts))
+ self.create_file(taskset_path + 'nbr_valid_schedules.txt')
+ self.create_file(taskset_path + 'timing_results.csv', text='{},{}\n'.format(TimeEnum.TIME.name, TimeEnum.RESULT.name))
+ self.create_file(taskset_path + 'result.csv')
+ self.create_file(taskset_path + 'header.csv', text='{},{},{}\n{},{},{}\n'.format(HeaderEnum.SOLVED.name, HeaderEnum.COUNTED.name, HeaderEnum.SOLVEDTIME.name, str(None), str(None), 0))
+
+ # Save the result acquired from the constraint optimization algorithm running.
+ def save_timing_result(self, ts, time, solution):
+ successful = True if solution else False
+ path = self.base_path + ts.to_hash() + '/'
+ self.change_header(path + 'header.csv', HeaderEnum.SOLVED, str(successful))
+ self.change_header(path + 'header.csv', HeaderEnum.SOLVEDTIME, str(time))
+
+ # If we have results: Add matrix to result file
+ if successful:
+ s = ''
+ for schedule in range(len(solution)):
+ for slot in range(len(solution[0])):
+ s += str(solution[schedule][slot]) + ','
+ s = s[:-1] # Remove last comma in line
+ s += '\n' # add new line delim
+ open(path + 'result.csv', 'w').write(s)
+
+ open(path + 'timing_results.csv', 'a').write('{},{}\n'.format(time, str(successful)))
+
+ # Change this tasksets header file with flag to string
+ def change_header(self, path, flag, new_string):
+ text = open(path, 'r').read()
+ idx = text.find('\n')
+ for i in range(flag.value):
+ idx = text.find(',', idx + 1)
+ idx1 = text.find(',', idx + 1)
+ idx2 = text.find('\n', idx + 1)
+
+ idx_end = idx1 if idx1 < idx2 else idx2
+
+ new_text = text[:idx + 1] + new_string + text[idx_end:]
+ open(path, 'w').write(new_text)
+
+
+ # Return whether taskset has been saved or not.
+ def taskset_exists(self, ts):
+ path = self.base_path + ts.to_hash() +'/'
+ return Path(path).exists()
+
+ # Create file with path containing text
+ def create_file(self, path_name, text=''):
+ p = Path(path_name)
+ p.touch(exist_ok=True)
+ p.write_text(text)
+
+ # Parse taskset to a .csv friendly format.
+ def parse(self, ts):
+ string_representation = '{},{},{},{}\n'.format(TaskEnum.PRIORITY.name, TaskEnum.EXECTIME.name, TaskEnum.PERIOD.name, TaskEnum.DEADLINE.name)
+ for task in ts.taskset:
+ string_representation += str(task.priority) + ',' + str(task.exectime) + ',' + str(task.period) + ',' + str(task.deadline) + '\n'
+ return string_representation
diff --git a/code/lib/fixedpriority.py b/code/lib/fixedpriority.py
new file mode 100644
index 0000000000000000000000000000000000000000..5b90d8655c1b6b5dad3b10492dff7169a097010c
--- /dev/null
+++ b/code/lib/fixedpriority.py
@@ -0,0 +1,34 @@
+from lib.taskset import Taskset
+from lib.schedule import Schedule
+
+class FixedPriority:
+
+ def __init__(self, taskset):
+ self.taskset = taskset
+ self.schedulable = True
+ self.schedule = self.generate_schedule()
+
+ def generate_schedule(self):
+ hyperperiod = self.taskset.hyperperiod()
+ schedule = [0] * hyperperiod
+
+ for x in self.taskset.taskset:
+ num_activations = int(hyperperiod / x.period)
+ activations = [a * x.period for a in range(num_activations)]
+
+ for i in activations:
+ exectime = x.exectime
+ deadline = i + x.deadline
+ t = i # let's start with activation time
+
+ while exectime > 0:
+ if schedule[t] == 0: # if I don't have a task
+ schedule[t] = x.priority # assign me
+ exectime = exectime - 1 # reduce execution time
+ t = t + 1 # and advance time
+ if t == deadline and not exectime == 0:
+ self.schedulable = False
+ return Schedule(self.taskset, list())
+
+ return Schedule(self.taskset, schedule)
+
diff --git a/code/lib/headerenum.py b/code/lib/headerenum.py
new file mode 100644
index 0000000000000000000000000000000000000000..fee9de031235e4322d3b07c806ee0ba9174bf50e
--- /dev/null
+++ b/code/lib/headerenum.py
@@ -0,0 +1,7 @@
+from enum import Enum
+
+class HeaderEnum(Enum):
+
+ SOLVED = 0
+ COUNTED = 1
+ SOLVEDTIME = 2
diff --git a/code/lib/periodrandomizer.py b/code/lib/periodrandomizer.py
new file mode 100644
index 0000000000000000000000000000000000000000..fb0db3bc6380fda82427ddf463d0ad46178b67e7
--- /dev/null
+++ b/code/lib/periodrandomizer.py
@@ -0,0 +1,61 @@
+import lib.util
+import math
+
+from random import Random
+
+class PeriodRandomizer:
+
+ def __init__(self, max_hyperperiod_, nbr_tasks_):
+ self.rng = Random(max_hyperperiod_ - nbr_tasks_)
+ self.max_hyperperiod = max_hyperperiod_
+ self.nbr_tasks = nbr_tasks_
+
+ # The function which generates volume amount of period sets with lcm(periods) <= self.max_hyperperiod
+ def generate_periods(self, volume, divisor=2):
+ l = list()
+ counter = 0
+ prev_len = len(l)
+ while len(l) < volume:
+ periods = self.generate_valid_period_set(divisor)
+ periods.sort()
+ if periods not in l: l.append(periods)
+
+ # Safety mechanism to promise we don't run forever
+ if prev_len == len(l):
+ counter += 1
+ if counter >= 10000:
+ return l
+ else:
+ counter = 0
+ prev_len = len(l)
+
+ return l
+
+ def generate_valid_period_set(self, divisor=2):
+ periods = [10000000]*self.nbr_tasks
+ while lib.util.lcm(periods) > self.max_hyperperiod:
+ # Initialize possible periods
+ possible_periods = [i for i in range(self.nbr_tasks, math.floor(self.max_hyperperiod/divisor) + 1)]
+
+ # For each task:
+ # Randomize a positive integer number, to represent its period,
+ # Within n <= period <= max_hyperperiod (feasibility reasons)
+ for i in range(self.nbr_tasks):
+ #if possible_periods is empty: Break
+ if not possible_periods: break
+
+ periods[i] = self.rng.choice(possible_periods)
+ # Remove periods that would force the hyperperiod to pass the max_hyperperiod
+ self.prune_possible_periods(possible_periods, periods[:(i+1)])
+
+ return periods
+
+ def prune_possible_periods(self, possible_periods, periods):
+ temp_pos_periods = list(possible_periods)
+
+ for i in temp_pos_periods:
+ periods.append(i)
+ if lib.util.lcm(periods) > self.max_hyperperiod:
+ possible_periods.remove(i)
+
+ periods = periods[:-1]
diff --git a/code/lib/resultenum.py b/code/lib/resultenum.py
new file mode 100644
index 0000000000000000000000000000000000000000..14e36d7192fa7726ec96cf5ecf382f996ae4c84b
--- /dev/null
+++ b/code/lib/resultenum.py
@@ -0,0 +1,9 @@
+from enum import Enum
+
+class ResultEnum(Enum):
+
+ UTILIZATION = 0
+ ENTROPY = 1
+ TIME = 2
+ HYPERPERIOD = 3
+ COUNT = 4
diff --git a/code/lib/schedule.py b/code/lib/schedule.py
new file mode 100644
index 0000000000000000000000000000000000000000..1bb0dd282ccf4f2902f2f92990273e52e44578e7
--- /dev/null
+++ b/code/lib/schedule.py
@@ -0,0 +1,48 @@
+from lib.taskset import Taskset
+
+class Schedule:
+
+ def __init__(self, taskset, schedule):
+ self.taskset = taskset
+ self.schedule = schedule
+
+ # this function works well only if deadline <= period
+ # in case of relaxed deadlines, the check is not correct
+ # since it should verify that for each activation-deadline
+ # there are a certain number of computation units and
+ # keep track of that in analyzing the schedule
+ def isValid(self):
+ # Initialize hyperperiod
+ hyperperiod = self.taskset.hyperperiod()
+
+ if not len(self.schedule) == hyperperiod:
+ return False
+
+ # For each task
+ for x in self.taskset.taskset:
+ # For each period check whether task x exists exectime nbr of times before each deadline.
+ for p in range(0, hyperperiod, x.period):
+ executed = 0
+ for slot in range(p, p + x.deadline):
+ executed = executed + (1 if self.schedule[slot] == x.priority else 0)
+
+ if executed != x.exectime: return False
+
+ return True
+
+ def count_context_switches(self):
+ count = 0
+ for i in range(len(self.schedule)-1):
+ if self.schedule[i] != self.schedule[i+1] and self.schedule[i+1] != 0:
+ count += 1
+ return count
+
+ def __str__(self):
+ res = "Taskset (hyperperiod " + str(self.taskset.hyperperiod()) + "):\n"
+ for i in self.taskset.taskset:
+ res += " - prio=" + str(i.priority) + ", exec=" + \
+ str(i.exectime) + ", period=" + str(i.period) + \
+ ", deadline=" + str(i.deadline) + "\n"
+ res += "Schedule:\n " + str(self.schedule)
+
+ return res
diff --git a/code/lib/scheduleset.py b/code/lib/scheduleset.py
new file mode 100644
index 0000000000000000000000000000000000000000..4127360d87d1804e5ac40ac679c91d5d66747996
--- /dev/null
+++ b/code/lib/scheduleset.py
@@ -0,0 +1,65 @@
+from lib.schedule import Schedule
+from functools import reduce
+import math
+
+class ScheduleSet:
+
+ def __init__(self, taskset, schedule_set):
+ self.taskset = taskset
+ self.schedule_set = schedule_set
+ self.schedule_set_size = len(schedule_set)
+ if self.schedule_set_size > 0:
+ self.pro_sets = self.compute_probabilities()
+ self.slot_entropy = self.compute_slot_entropy()
+ self.upper_approximated_entropy = self.upper_approx_entropy()
+ else:
+ self.upper_approximated_entropy = 0
+
+ """
+ This function computes the probability that a task i is active at every time t, 0 <= t <= hyperperiod
+ """
+ def compute_probabilities(self):
+ # potential values are 1..n and 0 for idle
+ alternatives = self.taskset.numtasks
+ hyperperiod = int(self.taskset.hyperperiod())
+
+ # create a probability set for the idle task
+ idle_pro_set = [0] * hyperperiod
+ for i in range(hyperperiod):
+ total_idles = sum([1 for x in self.schedule_set if x[i] == 0])
+ idle_pro_set[i] = float(total_idles) / float(self.schedule_set_size)
+
+ # create probability sets for the other values
+ pro_sets = list()
+ for val in range(1, alternatives + 1):
+ val_pro_set = [0] * hyperperiod
+ for i in range(hyperperiod):
+ total_vals = sum([1 for x in self.schedule_set if x[i] == val])
+ val_pro_set[i] = float(total_vals) / float(self.schedule_set_size)
+
+ pro_sets.append(val_pro_set)
+
+ # Add idle probability set to probability sets
+ pro_sets.append(idle_pro_set)
+
+ # order is 1..n and idle
+ return pro_sets
+
+ """
+ This function computes the slot entropy H_Gamma at time each time t as the sum of all the task probabilities
+ """
+ def compute_slot_entropy(self):
+ hyperperiod = int(self.taskset.hyperperiod())
+ slot_entropy = [0] * hyperperiod
+ for i in range(hyperperiod):
+ for j in self.pro_sets:
+ cur_set = j
+ if cur_set[i] == 0.0:
+ slot_entropy[i] -= 0.0
+ else:
+ slot_entropy[i] -= cur_set[i] * math.log(cur_set[i], 2)
+
+ return slot_entropy
+
+ def upper_approx_entropy(self):
+ return reduce(lambda x, y: x+y, self.slot_entropy)
diff --git a/code/lib/solver.py b/code/lib/solver.py
new file mode 100644
index 0000000000000000000000000000000000000000..055f6a6678f3117638b32ead0c6e47fe283dc766
--- /dev/null
+++ b/code/lib/solver.py
@@ -0,0 +1,31 @@
+import time
+from lib.filesystemmanager import FileSystemManager
+from lib.constraintBuilder import ConstraintBuilder
+
+class Solver:
+
+ def __init__(self, max_hyperperiod, nbr_tasks):
+ self.max_hyperperiod = max_hyperperiod
+ self.nbr_tasks = nbr_tasks
+ self.manager = FileSystemManager(max_hyperperiod, nbr_tasks)
+
+ # Tries to find schedules for a given taskset in less than or equal to the number of minutes given (max_time)
+ # If it has already been solved or times up to max_time has been tried: Nothing is done
+ # Return True if solved and false if not
+ def solve(self, ts, max_time):
+ solved, solved_time = self.manager.is_solved(ts)
+ if not solved and solved_time < max_time:
+ # Start time
+ t_start = time.time()
+ # Compute schedule set for current time. Convert time to seconds
+ schedules = ConstraintBuilder(ts, max_time*60).generate_schedules()
+ # resulting time
+ t_res = int((time.time() - t_start)/60) + 1
+
+ # Save result to filesystem structure
+ if schedules:
+ self.manager.save_timing_results(ts, t_res, schedules)
+ return True
+ else:
+ self.manager.save_timing_results(ts, max_time, schedules)
+ return False
diff --git a/code/lib/task.py b/code/lib/task.py
new file mode 100644
index 0000000000000000000000000000000000000000..7c1188ac03a68e220fa52b3f5af9e57ab51fc5be
--- /dev/null
+++ b/code/lib/task.py
@@ -0,0 +1,15 @@
+class Task:
+
+ # priority: lower number means higher priority
+ def __init__(self, priority, exectime, period, deadline = None):
+ if deadline is None: deadline = period
+ self.priority = int(priority)
+ self.exectime = int(exectime)
+ self.period = int(period)
+ self.deadline = int(deadline)
+
+ def __eq__(self, other):
+ return self.priority == other.priority \
+ and self.exectime == other.exectime \
+ and self.period == other.period \
+ and self.deadline == other.deadline
diff --git a/code/lib/taskenum.py b/code/lib/taskenum.py
new file mode 100644
index 0000000000000000000000000000000000000000..61066031e3dfe2bbae8fa6e2bfb93cac7248500b
--- /dev/null
+++ b/code/lib/taskenum.py
@@ -0,0 +1,8 @@
+from enum import Enum
+
+class TaskEnum(Enum):
+
+ PRIORITY = 0
+ EXECTIME = 1
+ PERIOD = 2
+ DEADLINE = 3
diff --git a/code/lib/taskset.py b/code/lib/taskset.py
new file mode 100644
index 0000000000000000000000000000000000000000..b25306e3d6e42c6cd9b86e90af686f84f010e560
--- /dev/null
+++ b/code/lib/taskset.py
@@ -0,0 +1,96 @@
+from lib.task import Task
+import numpy as np
+from math import log
+import lib.util
+
+class Taskset:
+
+ def __init__(self, taskset):
+ self.numtasks = len(taskset)
+ priority_uniques = np.unique([x.priority for x in taskset])
+ assert priority_uniques.size == len(taskset), "Priorities not unique"
+ # ensure tasks are ordered by priority
+ self.taskset = sorted(taskset, key = lambda x: x.priority)
+
+ # Returns the hyperperiod of this taskset
+ def hyperperiod(self):
+ periods = [x.period for x in self.taskset]
+ return round(lib.util.lcm(periods))
+
+ # Returns the upper bound on the entropy
+ def upper_bound_entropy(self):
+ utilisation = self.utilisation()
+ upper_bound = 0
+
+ for p in utilisation:
+ if p != 0: upper_bound += p*log(p, 2)
+
+ return -self.hyperperiod()*upper_bound
+
+ # Gives a vector with the relationship C_i/T_i in it
+ def utilisation(self):
+ u = list()
+
+ # Add idle task to the relationship list
+ l = self.hyperperiod()
+ idle_exec_t = l - sum([x.exectime*l / x.period for x in self.taskset])
+ u.append(idle_exec_t/l)
+
+ # Add all other tasks to relationship list
+ for task in self.taskset:
+ u.append(task.exectime/task.period)
+
+ return u
+
+ # returns the value k_opt
+ def k_opt(self):
+ l = self.hyperperiod()
+ u = self.utilisation()
+ denominator = round(u[0]*l)
+ for i in range(self.numtasks + 1):
+ denominator = lib.util.gcd(denominator, round(u[i]*l))
+
+ return round(l / denominator)
+
+ # Return exectime and period for task
+ def attributes(self, task):
+ period = 0
+ exectime = 0
+ if task == 0:
+ period = self.hyperperiod()
+ exectime = round(self.utilisation()[0]*period)
+ else:
+ period = self.taskset[task - 1].period
+ exectime = self.taskset[task - 1].exectime
+
+ return exectime, period
+
+ # Return optimal number of each task for each slot (or if you'd like C_{i, j, K*})
+ def n_opt(self):
+ u = self.utilisation()
+ k = self.k_opt()
+ return [round(u[x]*k) for x in range(len(u))]
+
+ # To string representation of this taskset
+ def __str__(self):
+ s = ''
+ for task in self.taskset:
+ s += str(task.priority) + '\t' + str(task.exectime) + '\t' + str(task.period) + '\t' + str(task.deadline) + '\n'
+ s = s[:-1]
+ return s
+
+ # Equal operation for this taskset
+ def __eq__(self, other):
+ if len(self.taskset) != len(other.taskset): return False
+ for task_nbr in range(len(self.taskset)):
+ if not self.taskset[task_nbr] == other.taskset[task_nbr]:
+ return False
+
+ return True
+
+ def to_hash(self):
+ string = ''
+ for task in self.taskset:
+ string += '{}{}{}{}'.format(task.priority, task.exectime, task.period, task.deadline)
+
+ return string
diff --git a/code/lib/tasksetfilegenerator.py b/code/lib/tasksetfilegenerator.py
new file mode 100644
index 0000000000000000000000000000000000000000..793c0863967911a054652727be1ef9ab370fa8b9
--- /dev/null
+++ b/code/lib/tasksetfilegenerator.py
@@ -0,0 +1,51 @@
+from lib.task import Task
+from lib.taskset import Taskset
+from lib.tasksetgenerator import TasksetGenerator
+from lib.fixedpriority import FixedPriority
+
+class TasksetFileGenerator:
+
+ # nbr_tasks = number of tasks in each taskset (not including idle task
+ # hyperperiod = maximum hyperperiod allowed
+ # nbr_exp = How many tasksets should exist in each utilisation group (10 groups)
+ def __init__(self, nbr_tasks_, hyperperiod_, volume_):
+ self.file_name = '../data/taskset' + str(nbr_tasks_) + '-' + str(hyperperiod_) + '.csv'
+ self.nbr_tasks = nbr_tasks_
+ self.hyperperiod = hyperperiod_
+ self.volume = volume_
+ self.seed = hyperperiod_ - nbr_tasks_
+
+ # Generates and returns a set of tasksets
+ # If a file exists containing already generated tasksets:
+ # Return those tasksets
+ def generate_tasksets(self, divisor=2):
+ tasksets = list()
+
+ # Try to open file where there should be tasksets located.
+ try:
+ with open(self.file_name, 'r') as f:
+ lines = f.readlines()
+ parse = lambda x: int(float(x))
+ for ts in range(0, len(lines), self.nbr_tasks):
+ tasks = []
+ for task in range(ts, ts+self.nbr_tasks):
+ t = lines[task].split(",")
+ tasks.append(Task(parse(t[0]), parse(t[1]), parse(t[2]), parse(t[3])))
+ tasksets.append(Taskset(tasks))
+
+ print('Loaded {} tasksets from {}'.format(len(tasksets), self.file_name))
+
+ # If such a file didn't exist, create a new file with such tasksets.
+ except:
+ print('Could not find file with tasksets of {} tasks and hyperperiod {}'.format(self.nbr_tasks, self.hyperperiod))
+ tg = TasksetGenerator(self.hyperperiod, self.nbr_tasks)
+ tasksets = tg.generate_tasksets(self.volume, divisor)
+
+ # Write generated tasksets to file.
+ with open(self.file_name, 'w') as f:
+ for ts in tasksets:
+ for task in ts.taskset:
+ f.write(str(task.priority) + "," + str(task.exectime) + "," + str(task.period) + "," + str(task.deadline) + "\n")
+
+ # Return generated or retrieved tasksets.
+ return tasksets
diff --git a/code/lib/tasksetgenerator.py b/code/lib/tasksetgenerator.py
new file mode 100644
index 0000000000000000000000000000000000000000..d810b0d36bcc06e8cda486234675d89a7fec53a2
--- /dev/null
+++ b/code/lib/tasksetgenerator.py
@@ -0,0 +1,71 @@
+from lib.periodrandomizer import PeriodRandomizer
+from lib.fixedpriority import FixedPriority
+from lib.taskset import Taskset
+from lib.task import Task
+
+from random import Random
+import math
+
+class TasksetGenerator:
+
+ def __init__(self, max_hyperperiod, nbr_tasks):
+ self.max_hyperperiod = max_hyperperiod
+ self.nbr_tasks = nbr_tasks
+ self.rng = Random(max_hyperperiod - nbr_tasks)
+
+ # volume = The number of tasksets needed
+ # divisor = The maximum period length in comparison to the hyperperiod (max_period = max_hyperperiod/divisor)
+ def generate_tasksets(self, volume, divisor=2):
+ tasksets = list()
+
+ # Generate as many period sets as possible but no more than volume
+ period_sets = PeriodRandomizer(self.max_hyperperiod, self.nbr_tasks).generate_periods(volume, divisor)
+ period_sets.sort(reverse=True)
+
+ for i in range(10):
+ #utilization list
+ u_list = list()
+
+ # Find the exectime based on the randomized periods and the randomized task_utilizations
+ for periods in period_sets:
+ # UUniFast algorithm for utilization
+ u = self.rng.uniform(i*0.1, (i+1)*0.1)
+ task_utilizations = self.task_u(u)
+
+ exectimes = list(map(lambda x:
+ max(math.floor(task_utilizations[x] * periods[x]), 1),
+ list(range(self.nbr_tasks)))) # The task numbers to iterate
+
+ # pseudo_u = the taskset utilization we will achieve with these exectimes and periods
+ pseudo_u = sum([exectimes[x]/periods[x] for x in range(self.nbr_tasks)])
+
+ if pseudo_u > i*0.1 and pseudo_u < (i+1)*0.1:
+ tasks = []
+ for j in range(self.nbr_tasks):
+ # j+1 since tasks start enumerating from 1 and not 0
+ t = Task(j+1, exectimes[j], periods[j])
+ tasks.append(t)
+ ts = Taskset(tasks)
+
+ if ts not in tasksets and FixedPriority(ts).schedulable:
+ tasksets.append(ts)
+
+ print('Taking {} random tasksets from {} available tasksets'.format(volume if volume < len(tasksets) else len(tasksets), len(tasksets)))
+ return self.rng.sample(tasksets, volume if volume < len(tasksets) else len(tasksets))
+
+ # Generate individual task utilizations
+ def task_u(self, utilization):
+ validGeneration = False
+ while not validGeneration:
+ utilizations = list()
+ sum_utilization = utilization
+ for i in range(1, self.nbr_tasks):
+ next_sum_utilization = sum_utilization * self.rng.random() ** (1.0 / (self.nbr_tasks - i))
+ utilizations.append(sum_utilization - next_sum_utilization)
+ sum_utilization = next_sum_utilization
+
+ utilizations.append(next_sum_utilization)
+ if len(list(filter(lambda x: x > 1.0, utilizations))) == 0:
+ validGeneration = True
+
+ return utilizations
diff --git a/code/lib/timeenum.py b/code/lib/timeenum.py
new file mode 100644
index 0000000000000000000000000000000000000000..0c75e1952845357b7d470ba13f4fd8bcff7697a2
--- /dev/null
+++ b/code/lib/timeenum.py
@@ -0,0 +1,6 @@
+from enum import Enum
+
+class TimeEnum(Enum):
+
+ TIME = 0
+ RESULT = 1
diff --git a/code/lib/util.py b/code/lib/util.py
new file mode 100644
index 0000000000000000000000000000000000000000..4b9c24c218252b44351e1431f8290bc07338ac54
--- /dev/null
+++ b/code/lib/util.py
@@ -0,0 +1,16 @@
+from functools import reduce
+
+# Compute the greatest common divisor of a and b
+def gcd(a, b):
+ while b > 0:
+ a, b = b, a % b
+ return a
+
+# Compute the lowest common multiple of a and b
+def lcm_two(a, b):
+ return a * b / gcd(a, b)
+
+# Compute the lowest common multiple of the elements of a list
+def lcm(l):
+ return reduce(lambda x, y: lcm_two(x, y), l)
+
diff --git a/code/tests/run_benchmark.sh b/code/tests/run_benchmark.sh
new file mode 100755
index 0000000000000000000000000000000000000000..74fc1fed84c1a891e455431fa98b9f1a61440281
--- /dev/null
+++ b/code/tests/run_benchmark.sh
@@ -0,0 +1,26 @@
+#!/bin/bash
+
+echo "\nInitializing Benchmark Script..."
+
+# Maximum hyperperiod
+hyperperiod=$1
+
+# The number of tasksets in each utilization group
+volume=$2
+
+# The maximum number of tasks to run the benchmark script for
+# The benchmark script runs 2 -> MAX_NBR_TASKS times
+max_nbr_tasks=$3
+
+# How long each taskset is allowed to execute at maximum (in minutes)
+max_timeout=$4
+
+task=2
+while [ "$task" -le "$max_nbr_tasks" ]
+do
+ echo "Executing Benchmark for $task Tasks..."
+ python3 benchmark.py $hyperperiod $volume $task $max_timeout
+ task=$(($task+1))
+done
+
+echo "Benchmark script completed!"
diff --git a/results/Makefile b/results/Makefile
new file mode 100644
index 0000000000000000000000000000000000000000..65309039c6d7b8e7ceb8c3ea3212f3e5d692f4d9
--- /dev/null
+++ b/results/Makefile
@@ -0,0 +1,11 @@
+all:
+ mkdir -p img
+ pdflatex --shell-escape results.tex
+ pdflatex --shell-escape results.tex
+ make -s clean
+
+clean:
+ rm -f results.bbl results.aux results.blg results.log results.vtc results.out results.auxlock
+
+distclean:
+ rm -rf img
diff --git a/results/data/data100/solved100-10.csv b/results/data/data100/solved100-10.csv
new file mode 100644
index 0000000000000000000000000000000000000000..21726fba746fd54af10f882765838227115329df
--- /dev/null
+++ b/results/data/data100/solved100-10.csv
@@ -0,0 +1,881 @@
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diff --git a/results/data/data100/solved100-2.csv b/results/data/data100/solved100-2.csv
new file mode 100644
index 0000000000000000000000000000000000000000..67905d545a643ada1694fb818c7e2e3312bb539f
--- /dev/null
+++ b/results/data/data100/solved100-2.csv
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diff --git a/results/data/data100/solved100-3.csv b/results/data/data100/solved100-3.csv
new file mode 100644
index 0000000000000000000000000000000000000000..7c3d7987cb207d2a4c30d78fb8e58a58bb9d6f9e
--- /dev/null
+++ b/results/data/data100/solved100-3.csv
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diff --git a/results/data/data100/solved100-4.csv b/results/data/data100/solved100-4.csv
new file mode 100644
index 0000000000000000000000000000000000000000..effafd2f9ab44cc0eab4951730145a714e2a0a72
--- /dev/null
+++ b/results/data/data100/solved100-4.csv
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diff --git a/results/data/data100/solved100-5.csv b/results/data/data100/solved100-5.csv
new file mode 100644
index 0000000000000000000000000000000000000000..618cf6deda3addfe45e274381cd13ffc1808fa56
--- /dev/null
+++ b/results/data/data100/solved100-5.csv
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diff --git a/results/data/data100/solved100-6.csv b/results/data/data100/solved100-6.csv
new file mode 100644
index 0000000000000000000000000000000000000000..fee8272fe2d3f0535988b23a7a6e87e4907e4dfe
--- /dev/null
+++ b/results/data/data100/solved100-6.csv
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diff --git a/results/data/data100/solved100-7.csv b/results/data/data100/solved100-7.csv
new file mode 100644
index 0000000000000000000000000000000000000000..0c7a18a41f71fef58a20458203a1aa8a9130d36b
--- /dev/null
+++ b/results/data/data100/solved100-7.csv
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diff --git a/results/data/data100/solved100-8.csv b/results/data/data100/solved100-8.csv
new file mode 100644
index 0000000000000000000000000000000000000000..1120d4e0b46b38697190c4ecc8c3fa5ee636c110
--- /dev/null
+++ b/results/data/data100/solved100-8.csv
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diff --git a/results/data/data100/solved100-9.csv b/results/data/data100/solved100-9.csv
new file mode 100644
index 0000000000000000000000000000000000000000..cb84343c293aca7b675f760db5e5c8ddc3c57472
--- /dev/null
+++ b/results/data/data100/solved100-9.csv
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diff --git a/results/data/data200/solved200-10.csv b/results/data/data200/solved200-10.csv
new file mode 100644
index 0000000000000000000000000000000000000000..52d1b3178eafb6cab05ce490130051499ac2c43b
--- /dev/null
+++ b/results/data/data200/solved200-10.csv
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diff --git a/results/data/data200/solved200-2.csv b/results/data/data200/solved200-2.csv
new file mode 100644
index 0000000000000000000000000000000000000000..4738afc1042c8eb16002151bc8bff37c782fea88
--- /dev/null
+++ b/results/data/data200/solved200-2.csv
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diff --git a/results/data/data200/solved200-3.csv b/results/data/data200/solved200-3.csv
new file mode 100644
index 0000000000000000000000000000000000000000..57a499ac760b277c6c1949daac3045714da63d6c
--- /dev/null
+++ b/results/data/data200/solved200-3.csv
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diff --git a/results/data/data200/solved200-4.csv b/results/data/data200/solved200-4.csv
new file mode 100644
index 0000000000000000000000000000000000000000..4ada8e65d70e5f3fd94ff0ce275aa44a68f687eb
--- /dev/null
+++ b/results/data/data200/solved200-4.csv
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diff --git a/results/data/data200/solved200-5.csv b/results/data/data200/solved200-5.csv
new file mode 100644
index 0000000000000000000000000000000000000000..4d9ea7a505c444236cd4862ca3c6189462827815
--- /dev/null
+++ b/results/data/data200/solved200-5.csv
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diff --git a/results/data/data200/solved200-6.csv b/results/data/data200/solved200-6.csv
new file mode 100644
index 0000000000000000000000000000000000000000..ddc186cdea15bf58cdecf0e5530c13a73e2d3f23
--- /dev/null
+++ b/results/data/data200/solved200-6.csv
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diff --git a/results/data/data200/solved200-7.csv b/results/data/data200/solved200-7.csv
new file mode 100644
index 0000000000000000000000000000000000000000..59830233889c2ac5a3e75c781e8244da7a51bd09
--- /dev/null
+++ b/results/data/data200/solved200-7.csv
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diff --git a/results/data/data200/solved200-8.csv b/results/data/data200/solved200-8.csv
new file mode 100644
index 0000000000000000000000000000000000000000..49db660cb17779efc737a3098ab97281b3e95d15
--- /dev/null
+++ b/results/data/data200/solved200-8.csv
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diff --git a/results/data/data200/solved200-9.csv b/results/data/data200/solved200-9.csv
new file mode 100644
index 0000000000000000000000000000000000000000..1d8c280f2234b01c61bf66d517530f8d838bb8e5
--- /dev/null
+++ b/results/data/data200/solved200-9.csv
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diff --git a/results/data/data300/solved300-10.csv b/results/data/data300/solved300-10.csv
new file mode 100644
index 0000000000000000000000000000000000000000..affbf9af5de8b29449738f1c5f51fb08f04831cd
--- /dev/null
+++ b/results/data/data300/solved300-10.csv
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diff --git a/results/data/data300/solved300-2.csv b/results/data/data300/solved300-2.csv
new file mode 100644
index 0000000000000000000000000000000000000000..23b88e00cc350716dc45aec3b6fcfa8835dda83e
--- /dev/null
+++ b/results/data/data300/solved300-2.csv
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diff --git a/results/data/data300/solved300-3.csv b/results/data/data300/solved300-3.csv
new file mode 100644
index 0000000000000000000000000000000000000000..336e93ae9010881299ab5a8a8ff29897ea84a55c
--- /dev/null
+++ b/results/data/data300/solved300-3.csv
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diff --git a/results/data/data300/solved300-4.csv b/results/data/data300/solved300-4.csv
new file mode 100644
index 0000000000000000000000000000000000000000..2b57dd02763275dc0462c9ce4f552e506f2b3a80
--- /dev/null
+++ b/results/data/data300/solved300-4.csv
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diff --git a/results/data/data300/solved300-5.csv b/results/data/data300/solved300-5.csv
new file mode 100644
index 0000000000000000000000000000000000000000..d8ec741d2f68fadd72ebd25e585342882a79363c
--- /dev/null
+++ b/results/data/data300/solved300-5.csv
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diff --git a/results/data/data300/solved300-6.csv b/results/data/data300/solved300-6.csv
new file mode 100644
index 0000000000000000000000000000000000000000..aca35ace5c13a2e57b3b054285939d9c53737c8e
--- /dev/null
+++ b/results/data/data300/solved300-6.csv
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diff --git a/results/data/data300/solved300-7.csv b/results/data/data300/solved300-7.csv
new file mode 100644
index 0000000000000000000000000000000000000000..9fa9bfcee600b1b1d629cfc91ea3c6b7a7c3ac62
--- /dev/null
+++ b/results/data/data300/solved300-7.csv
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diff --git a/results/data/data300/solved300-8.csv b/results/data/data300/solved300-8.csv
new file mode 100644
index 0000000000000000000000000000000000000000..f6171f28d99260f7fce79a9127c9d0422fd3fc7d
--- /dev/null
+++ b/results/data/data300/solved300-8.csv
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diff --git a/results/data/data300/solved300-9.csv b/results/data/data300/solved300-9.csv
new file mode 100644
index 0000000000000000000000000000000000000000..d941cf811b1891185371b1e7388b38fdf86a9e8a
--- /dev/null
+++ b/results/data/data300/solved300-9.csv
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diff --git a/results/data/data400/solved400-10.csv b/results/data/data400/solved400-10.csv
new file mode 100644
index 0000000000000000000000000000000000000000..b8b9054d39f589d916f5b597bb33ce8dd340d8b2
--- /dev/null
+++ b/results/data/data400/solved400-10.csv
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diff --git a/results/data/data400/solved400-2.csv b/results/data/data400/solved400-2.csv
new file mode 100644
index 0000000000000000000000000000000000000000..b5ae0d7bc40aa613d336c0c173c3475e9aea2131
--- /dev/null
+++ b/results/data/data400/solved400-2.csv
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diff --git a/results/data/data400/solved400-3.csv b/results/data/data400/solved400-3.csv
new file mode 100644
index 0000000000000000000000000000000000000000..41e2ce7ec3a3336ebeb7a1944b875e53c8de359e
--- /dev/null
+++ b/results/data/data400/solved400-3.csv
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diff --git a/results/data/data400/solved400-4.csv b/results/data/data400/solved400-4.csv
new file mode 100644
index 0000000000000000000000000000000000000000..e047b80e9a9ee5b503cab12ce8a13e6c1c41063b
--- /dev/null
+++ b/results/data/data400/solved400-4.csv
@@ -0,0 +1,709 @@
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diff --git a/results/data/data400/solved400-5.csv b/results/data/data400/solved400-5.csv
new file mode 100644
index 0000000000000000000000000000000000000000..0462626fe740ec2e813959abb622eafb0cdea7b7
--- /dev/null
+++ b/results/data/data400/solved400-5.csv
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diff --git a/results/data/data400/solved400-6.csv b/results/data/data400/solved400-6.csv
new file mode 100644
index 0000000000000000000000000000000000000000..69b2ed1f0f0928095d8ef557532f2940f07c2487
--- /dev/null
+++ b/results/data/data400/solved400-6.csv
@@ -0,0 +1,527 @@
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diff --git a/results/data/data400/solved400-7.csv b/results/data/data400/solved400-7.csv
new file mode 100644
index 0000000000000000000000000000000000000000..965e2fb02934324571fc40fc053c775b09a633b8
--- /dev/null
+++ b/results/data/data400/solved400-7.csv
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diff --git a/results/data/data400/solved400-8.csv b/results/data/data400/solved400-8.csv
new file mode 100644
index 0000000000000000000000000000000000000000..b4b198344e388948481437399411794f96230f4d
--- /dev/null
+++ b/results/data/data400/solved400-8.csv
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diff --git a/results/data/data400/solved400-9.csv b/results/data/data400/solved400-9.csv
new file mode 100644
index 0000000000000000000000000000000000000000..7103db1c660048aece0cf7e5790cbf00637128b4
--- /dev/null
+++ b/results/data/data400/solved400-9.csv
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new file mode 100644
index 0000000000000000000000000000000000000000..40f79bc2ebbea9cc6c89508d1e872eb38196d57c
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diff --git a/results/data/data500/solved500-3.csv b/results/data/data500/solved500-3.csv
new file mode 100644
index 0000000000000000000000000000000000000000..5a20fa3a40dff30fb297f15dc6cc57a19d5f0388
--- /dev/null
+++ b/results/data/data500/solved500-3.csv
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diff --git a/results/data/data500/solved500-4.csv b/results/data/data500/solved500-4.csv
new file mode 100644
index 0000000000000000000000000000000000000000..04bf303517370287119ac8a1b6436cc18f717593
--- /dev/null
+++ b/results/data/data500/solved500-4.csv
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diff --git a/results/data/data500/solved500-5.csv b/results/data/data500/solved500-5.csv
new file mode 100644
index 0000000000000000000000000000000000000000..69d0208645d0f22d89511707b859a0bf098b120b
--- /dev/null
+++ b/results/data/data500/solved500-5.csv
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diff --git a/results/data/data500/solved500-6.csv b/results/data/data500/solved500-6.csv
new file mode 100644
index 0000000000000000000000000000000000000000..00e5ee493b9520b19c4c25bac1c11c0561519be0
--- /dev/null
+++ b/results/data/data500/solved500-6.csv
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diff --git a/results/data/data500/solved500-7.csv b/results/data/data500/solved500-7.csv
new file mode 100644
index 0000000000000000000000000000000000000000..3d424fed5fe5163cfe70f082f5b826fedd7f311c
--- /dev/null
+++ b/results/data/data500/solved500-7.csv
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diff --git a/results/data/data500/solved500-8.csv b/results/data/data500/solved500-8.csv
new file mode 100644
index 0000000000000000000000000000000000000000..570af7bc5b7af85fbc76affe83bf4b4a1070d97e
--- /dev/null
+++ b/results/data/data500/solved500-8.csv
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diff --git a/results/data/data500/solved500-9.csv b/results/data/data500/solved500-9.csv
new file mode 100644
index 0000000000000000000000000000000000000000..08cb5936d42d80981ce6d440779e10717daa9716
--- /dev/null
+++ b/results/data/data500/solved500-9.csv
@@ -0,0 +1,288 @@
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diff --git a/results/img/results-figure9.md5 b/results/img/results-figure9.md5
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index 0000000000000000000000000000000000000000..67e7f4ce8511304fff952b7867540112b2254fbc
--- /dev/null
+++ b/results/img/results-figure9.md5
@@ -0,0 +1 @@
+\def \tikzexternallastkey {A585B5C14C80FA8DAA096067440B9739}%
diff --git a/results/img/results-figure9.pdf b/results/img/results-figure9.pdf
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diff --git a/results/results.pdf b/results/results.pdf
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diff --git a/results/results.tex b/results/results.tex
new file mode 100644
index 0000000000000000000000000000000000000000..8cc8de813ce3f219abd082d1cad30104c6c62c6b
--- /dev/null
+++ b/results/results.tex
@@ -0,0 +1,36 @@
+\documentclass{article}
+
+\usepackage[landscape, margin=2cm]{geometry}
+
+\usepackage{amsmath, amssymb, amsthm}
+\usepackage{xfrac}
+\usepackage{datatool}
+\usepackage{caption}
+\usepackage{tikz,pgfplots}
+\usetikzlibrary{shapes, fit}
+
+\usepgfplotslibrary{external}
+\tikzexternalize[prefix=./img/]
+
+\begin{document}
+
+\section*{Maximum Hyperperiod: 100}
+\input{sec/figures100.tex}
+\clearpage
+%
+\section*{Maximum Hyperperiod: 200}
+\input{sec/figures200.tex}
+\clearpage
+%
+\section*{Maximum Hyperperiod: 300}
+\input{sec/figures300.tex}
+\clearpage
+%
+\section*{Maximum Hyperperiod: 400}
+\input{sec/figures400.tex}
+\clearpage
+%
+\section*{Maximum Hyperperiod: 500}
+\input{sec/figures500.tex}
+
+\end{document}
diff --git a/results/sec/figures100.tex b/results/sec/figures100.tex
new file mode 100644
index 0000000000000000000000000000000000000000..83a4075c2a3a81a4a39f56799070837ab54ce91b
--- /dev/null
+++ b/results/sec/figures100.tex
@@ -0,0 +1,343 @@
+\hspace{0.02\textwidth} \begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{2} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-2tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data100/solved100-2.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ legend style = {draw = none, fill = none, font=\scriptsize,
+ at={(0.5,1.01)}, anchor=south},
+ legend cell align = {left},
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ \addlegendentry{$\tilde{h}^{ub}/\ell$}
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ \addlegendentry{$-log_2 \left( \sfrac{1}{(1+m)} \right)$}
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \addlegendentry{$-\{(1-u) \cdot log_2(1-u) + u \cdot log_2(\sfrac{u}{m})\}$}
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {100.0\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+\begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{3} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-3tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data100/solved100-3.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ legend pos = north west, % legend position
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {100.0\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+\begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{4} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-4tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data100/solved100-4.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ legend pos = south east, % legend position
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {99.7\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+
+\begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{5} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-5tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data100/solved100-5.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ legend pos = south east, % legend position
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {97.4\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+\begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{6} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-6tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data100/solved100-6.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ legend style = {draw = none, fill = none, font=\scriptsize,
+ at={(0.5,1.01)}, anchor=south},
+ legend cell align = {left},
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {95.2\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+\begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{7} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-7tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data100/solved100-7.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ legend pos = north west, % legend position
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {92.8\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+
+\begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{8} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-8tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data100/solved100-8.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ legend pos = south east, % legend position
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {89.5\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+\begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{9} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-9tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data100/solved100-9.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ legend pos = south east, % legend position
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {89.0\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+\begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{10} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-10tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data100/solved100-10.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ legend pos = south east, % legend position
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {88.0\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+
diff --git a/results/sec/figures200.tex b/results/sec/figures200.tex
new file mode 100644
index 0000000000000000000000000000000000000000..eb26bded5142ff747c4a7f697bd68047a7882c9c
--- /dev/null
+++ b/results/sec/figures200.tex
@@ -0,0 +1,343 @@
+\hspace{0.02\textwidth} \begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{2} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-2tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data200/solved200-2.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ legend style = {draw = none, fill = none, font=\scriptsize,
+ at={(0.5,1.01)}, anchor=south},
+ legend cell align = {left},
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ \addlegendentry{$\tilde{h}^{ub}/\ell$}
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ \addlegendentry{$-log_2 \left( \sfrac{1}{(1+m)} \right)$}
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \addlegendentry{$-\{(1-u) \cdot log_2(1-u) + u \cdot log_2(\sfrac{u}{m})\}$}
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {99.9\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+\begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{3} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-3tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data200/solved200-3.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ legend pos = north west, % legend position
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {96.9\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+\begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{4} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-4tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data200/solved200-4.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ legend pos = south east, % legend position
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {90.5\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+
+\begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{5} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-5tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data200/solved200-5.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ legend pos = south east, % legend position
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {81.0\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+\begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{6} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-6tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data200/solved200-6.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ legend style = {draw = none, fill = none, font=\scriptsize,
+ at={(0.5,1.01)}, anchor=south},
+ legend cell align = {left},
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {76.6\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+\begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{7} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-7tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data200/solved200-7.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ legend pos = north west, % legend position
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {70.9\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+
+\begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{8} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-8tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data200/solved200-8.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ legend pos = south east, % legend position
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {67.3\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+\begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{9} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-9tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data200/solved200-9.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ legend pos = south east, % legend position
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {62.5\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+\begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{10} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-10tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data200/solved200-10.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ legend pos = south east, % legend position
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {59.4\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+
diff --git a/results/sec/figures300.tex b/results/sec/figures300.tex
new file mode 100644
index 0000000000000000000000000000000000000000..b8853e5ef67dc40b6f53b66972909ccb0a18ff75
--- /dev/null
+++ b/results/sec/figures300.tex
@@ -0,0 +1,343 @@
+\hspace{0.02\textwidth} \begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{2} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-2tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data300/solved300-2.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ legend style = {draw = none, fill = none, font=\scriptsize,
+ at={(0.5,1.01)}, anchor=south},
+ legend cell align = {left},
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ \addlegendentry{$\tilde{h}^{ub}/\ell$}
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ \addlegendentry{$-log_2 \left( \sfrac{1}{(1+m)} \right)$}
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \addlegendentry{$-\{(1-u) \cdot log_2(1-u) + u \cdot log_2(\sfrac{u}{m})\}$}
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {100.0\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+\begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{3} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-3tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data300/solved300-3.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ legend pos = north west, % legend position
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {92.1\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+\begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{4} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-4tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data300/solved300-4.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ legend pos = south east, % legend position
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {80.3\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+
+\begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{5} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-5tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data300/solved300-5.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ legend pos = south east, % legend position
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {69.7\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+\begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{6} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-6tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data300/solved300-6.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ legend style = {draw = none, fill = none, font=\scriptsize,
+ at={(0.5,1.01)}, anchor=south},
+ legend cell align = {left},
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {58.4\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+\begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{7} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-7tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data300/solved300-7.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ legend pos = north west, % legend position
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {56.9\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+
+\begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{8} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-8tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data300/solved300-8.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ legend pos = south east, % legend position
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {47.2\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+\begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{9} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-9tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data300/solved300-9.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ legend pos = south east, % legend position
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {45.5\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+\begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{10} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-10tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data300/solved300-10.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ legend pos = south east, % legend position
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {38.7\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+
diff --git a/results/sec/figures400.tex b/results/sec/figures400.tex
new file mode 100644
index 0000000000000000000000000000000000000000..d5718de5cb749cd596f30f25bf52812e08c7d5d5
--- /dev/null
+++ b/results/sec/figures400.tex
@@ -0,0 +1,343 @@
+\hspace{0.02\textwidth} \begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{2} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-2tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data400/solved400-2.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ legend style = {draw = none, fill = none, font=\scriptsize,
+ at={(0.5,1.01)}, anchor=south},
+ legend cell align = {left},
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ \addlegendentry{$\tilde{h}^{ub}/\ell$}
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ \addlegendentry{$-log_2 \left( \sfrac{1}{(1+m)} \right)$}
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \addlegendentry{$-\{(1-u) \cdot log_2(1-u) + u \cdot log_2(\sfrac{u}{m})\}$}
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {100.0\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+\begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{3} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-3tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data400/solved400-3.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ legend pos = north west, % legend position
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {85.9\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+\begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{4} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-4tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data400/solved400-4.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ legend pos = south east, % legend position
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {70.8\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+
+\begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{5} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-5tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data400/solved400-5.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ legend pos = south east, % legend position
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {61.7\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+\begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{6} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-6tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data400/solved400-6.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ legend style = {draw = none, fill = none, font=\scriptsize,
+ at={(0.5,1.01)}, anchor=south},
+ legend cell align = {left},
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {52.6\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+\begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{7} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-7tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data400/solved400-7.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ legend pos = north west, % legend position
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {45.2\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+
+\begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{8} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-8tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data400/solved400-8.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ legend pos = south east, % legend position
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {39.3\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+\begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{9} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-9tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data400/solved400-9.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ legend pos = south east, % legend position
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {37.1\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+\begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{10} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-10tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data400/solved400-10.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ legend pos = south east, % legend position
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {32.4\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+
diff --git a/results/sec/figures500.tex b/results/sec/figures500.tex
new file mode 100644
index 0000000000000000000000000000000000000000..b873a7ff2ae848d960a618ff7abb089e449653f6
--- /dev/null
+++ b/results/sec/figures500.tex
@@ -0,0 +1,343 @@
+\hspace{0.02\textwidth} \begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{2} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-2tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data500/solved500-2.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ legend style = {draw = none, fill = none, font=\scriptsize,
+ at={(0.5,1.01)}, anchor=south},
+ legend cell align = {left},
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ \addlegendentry{$\tilde{h}^{ub}/\ell$}
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ \addlegendentry{$-log_2 \left( \sfrac{1}{(1+m)} \right)$}
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \addlegendentry{$-\{(1-u) \cdot log_2(1-u) + u \cdot log_2(\sfrac{u}{m})\}$}
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {100.0\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+\begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{3} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-3tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data500/solved500-3.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ legend pos = north west, % legend position
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {82.4\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+\begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{4} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-4tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data500/solved500-4.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ legend pos = south east, % legend position
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {66.7\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+
+\begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{5} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-5tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data500/solved500-5.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ legend pos = south east, % legend position
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {52.5\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+\begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{6} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-6tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data500/solved500-6.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ legend style = {draw = none, fill = none, font=\scriptsize,
+ at={(0.5,1.01)}, anchor=south},
+ legend cell align = {left},
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {44.6\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+\begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{7} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-7tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data500/solved500-7.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ legend pos = north west, % legend position
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {38.4\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+
+\begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{8} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-8tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data500/solved500-8.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ legend pos = south east, % legend position
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {31.8\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+\begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{9} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-9tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data500/solved500-9.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ legend pos = south east, % legend position
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {28.7\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+\begin{minipage}[t]{0.3\textwidth}
+
+ \def\nmaxtask{10}
+ \def\slack{0.05}
+
+ \centering
+ \def\ntask{10} % parameter: number of tasks m (excluding idle)
+ \def\figlabel{fig:uae-10tasks}
+ \begin{tikzpicture}
+ \def\inputfile{data/data500/solved500-10.csv} % parameter: input file
+ \begin{axis}[
+ width = \textwidth, % figure width
+ height = 4.2cm, % figure height
+ xmin = -1*\slack, % coordinate xmin
+ xmax = 1 + 1*\slack, % coordinate xmax
+ ymin = 0.5 - 7*\slack, % coordinate ymin
+ ymax = -ln(1/(\nmaxtask+1))/ln(2) + 1*\slack, % coordinate ymax
+ legend pos = south east, % legend position
+ xlabel = {utilization}, % x label
+ ylabel = {average slot entropy}, % y label
+ ylabel near ticks,
+ ]
+ % adding the data from \inputfile
+ \addplot[black, only marks, mark=*, mark options={scale=0.75}]
+ table [x=UTILIZATION, y expr=\thisrow{ENTROPY}/\thisrow{HYPERPERIOD}, col sep=comma] {\inputfile};
+ % adding the unreachable upper bound -log2(1/(1+m))
+ \addplot[red, thick] {-ln(1/(\ntask+1))/ln(2)};
+ % adding the tight upper bound that takes into account the utilization
+ \addplot[blue, dashed, thick, domain={0.0000001:1}] {-(((1-x)*(ln(1-x)/ln(2))) + ((x)*(ln(x/\ntask)/ln(2))))};
+ \draw [red, thick, rounded corners, fill=red!10!white]
+ (axis cs:0.01,2.1) rectangle node {24.7\%} (axis cs:0.29,2.7);
+ \end{axis}
+ \end{tikzpicture}
+ \captionof{figure}{average slot entropy of random sets composed of \ntask\ tasks.}
+ \label{\figlabel}
+
+\end{minipage} \hspace{0.03\textwidth}
+