squared_numbers = []
for i in range(1, 11, 1):
squared_numbers.append(i * i)
print(squared_numbers)[1, 4, 9, 16, 25, 36, 49, 64, 81, 100]27 Parallelisation
“Parallel computing is a type of computation in which many calculations or processes are carried out simultaneously. Large problems can often be divided into smaller ones, which can then be solved at the same time.” Wikipedia
Note
In the past, a computer processing unit (CPU) would have had a single core.
However, in more recent years, having multiple cores has become the norm. The benefit of this is that multiple tasks can be handled simultaneously.
By default, our Python code will not make use of multiple cores. Everything will be run sequentially on a single core.
However, for some kinds of code, running it across multiple cores at once can be a great way to speed things up.
Simpy is a good candidate for running code in parallel! By running our simpy code in parallel, we can potentially dramatically cut down the length of time
Warning
You may not be able to use parallelisation when deploying your code to the web - it will vary depending on your deployment/hosting choices.
27.1 A simple joblib example
First, it may be helpful to see a simpler example of joblib.
Let’s start by looking at a for loop to square the numbers 1 to 10.
We can simplify the code above into a list comprehension.
[i*i for i in range(1, 11, 1)][1, 4, 9, 16, 25, 36, 49, 64, 81, 100]Why is this important? Well, to use joblib, it’s easiest to write our loop as a list comprehension.
Instead of doing i * i to square our number, we have made a new function that does the same thing.
from joblib import Parallel, delayed
def multiply_by_self(input_number):
return input_number * input_number
Parallel(n_jobs=2)(delayed(multiply_by_self)(i) for i in range(1, 11, 1))[1, 4, 9, 16, 25, 36, 49, 64, 81, 100]27.2 A code example
Note
Thanks go to Michael Allen for providing an example of how this can be achieved in SimPy. His repository can be found here.
We will make use of the Joblib package to easily split our SimPy code to run across multiple processor cores.
We will take the model created in the Reproducibility chapter (Chapter 13) and add parallelisation to it.
27.2.1 Library imports
We will need to import Parallel and delayed from the joblib library.
You will need to run !pip install joblib if you have not previously made use of this library.
from joblib import Parallel, delayed27.2.2 The g, Patient and Model classes
Our g, patient and model classes are unchanged.
27.2.3 The trial class
In the trial class, we need to change a number of functions, tweak our attributes, and make use of the joblib library.
Warning
Because of the way joblib executes things, if we try to keep track of our results in the same way we have so far - setting up a dummy dataframe and then using the .loc accessor to write our results to the correct row of the dataframe for each run - we will end up with an empty results list.
Instead, we will create an empty list. Into this list we will place a dictionary of results from the run.
27.2.3.1 The init method
Let’s start by adjusting our __init__ method for our new way of carrying out the results collection.
def __init__(self):
self.df_trial_results = []27.2.3.2 The process_trial_results method
Next we want to create a new method that will turn our list of dictionaries into a Python dataframe.
All we need to do is call pd.DataFrame on that object. In this case, we overwrite the original df_trial_results object.
Next we set the index of the dataframe to the run number, which is how it was set up in the original code.
def process_trial_results(self):
self.df_trial_results = pd.DataFrame(self.df_trial_results)
self.df_trial_results.set_index("Run Number", inplace=True)27.2.3.3 the print_trial_results method
Because we went to the effort of setting the index in the step above, this method can remain unchanged.
27.2.3.4 the run_single method
First, let’s look back at how our run_trial function was written before.
def run_trial(self):
print(f"{g.number_of_receptionists} receptionists, {g.number_of_nurses} nurses, {g.number_of_doctors} doctors")
print("") # Print a blank line
# Run the simulation for the number of runs specified in g class.
# For each run, we create a new instance of the Model class and call its
# run method, which sets everything else in motion. Once the run has
# completed, we grab out the stored run results (just mean queuing time
# here) and store it against the run number in the trial results
# dataframe.
for run in range(g.number_of_runs):
random.seed(run)
my_model = Model(run)
patient_level_results = my_model.run()
self.df_trial_results.loc[run] = [
len(patient_level_results),
my_model.mean_q_time_recep,
my_model.mean_q_time_nurse,
my_model.mean_q_time_doctor
]
# Once the trial (ie all runs) has completed, print the final results
self.print_trial_results()To use parallelisation, we now split this out into two separate functions. The first is the run_single method.
Note that it’s very similar to the indented part of the for loop from the code above.
The main change is how the results are stored - they are now put into a dictionary. Remember, dictionaries use the format {“key”:value} - here we have made our column names the ‘keys’ and our results the ‘values’.
Finally, it’s important to return the results object from the function.
def run_single(self, run):
# For each run, we create a new instance of the Model class and call its
# run method, which sets everything else in motion. Once the run has
# completed, we grab out the stored run results (just mean queuing time
# here) and store it against the run number in the trial results
# dataframe.
random.seed(run)
my_model = Model(run)
patient_level_results = my_model.run()
results = {"Run Number":run,
"Arrivals": len(patient_level_results),
"Mean Q Time Recep": my_model.mean_q_time_recep,
"Mean Q Time Nurse": my_model.mean_q_time_nurse,
"Mean Q Time Doctor": my_model.mean_q_time_doctor
}
return results27.2.3.5 the run_trial method
Finally, we need to do a few things.
The key one is making our trial now use the Parallel class and delayed function.
We set up an instance of the Parallel class and set the number of jobs to -1.
Tip
-1 just means that the joblib library will use every available core to run the code.
You can instead specify a particular number of cores to use as a positive integer value.
We then pass in the self.run_single function to the delayed function.
Finally, we pass in the arguments that are required for the self.run_single function, which is just the run number.
The syntax can appear a little bit strange - just take a close look at the full line below and try and understand it.
self.df_trial_results = Parallel(n_jobs=-1)(delayed(self.run_single)(run) for run in range(g.number_of_runs))We assign all of this to the self.df_trial_results attribute of our class.
Now the only additional step is to run our new process_trial_results() function before we run print_trial_results().
def run_trial(self):
print(f"{g.number_of_receptionists} receptionists, {g.number_of_nurses} nurses, {g.number_of_doctors} doctors")
print("") # Print a blank line
# Run the simulation for the number of runs specified in g class.
self.df_trial_results = Parallel(n_jobs=-1)(delayed(self.run_single)(run) for run in range(g.number_of_runs))
# Once the trial (ie all runs) has completed, print the final results
self.process_trial_results()
self.print_trial_results()Voila! Our model is now set up to use parallelisation. Let’s take a look at how much faster this can make things.
27.3 Evaluating the code outputs
First, let’s run this the original way and time how long it takes.
1 receptionists, 1 nurses, 2 doctors
Trial Results
Arrivals Mean Q Time Recep Mean Q Time Nurse Mean Q Time Doctor
Run Number
0 102.0 0.00 57.19 1.15
1 125.0 1.84 144.69 0.02
2 112.0 0.85 15.30 1.13
3 120.0 1.08 82.67 0.04
4 132.0 1.94 107.47 0.51
... ... ... ... ...
995 97.0 0.59 36.91 0.00
996 111.0 1.10 68.32 0.18
997 129.0 0.99 122.27 0.06
998 140.0 1.73 92.57 0.30
999 109.0 0.67 45.83 0.39
[1000 rows x 4 columns]
Arrivals 120.98
Mean Q Time Recep 1.31
Mean Q Time Nurse 62.75
Mean Q Time Doctor 0.50
dtype: float64
It took 33.5614 seconds to do 10 runs without parallelisationNow let’s run it again with parallisation.
Click here to view the full code
1 receptionists, 1 nurses, 2 doctors
Trial Results
Arrivals Mean Q Time Recep Mean Q Time Nurse Mean Q Time Doctor
Run Number
0 102 0.00 57.19 1.15
1 125 1.84 144.69 0.02
2 112 0.85 15.30 1.13
3 120 1.08 82.67 0.04
4 132 1.94 107.47 0.51
... ... ... ... ...
995 97 0.59 36.91 0.00
996 111 1.10 68.32 0.18
997 129 0.99 122.27 0.06
998 140 1.73 92.57 0.30
999 109 0.67 45.83 0.39
[1000 rows x 4 columns]
Arrivals 120.98
Mean Q Time Recep 1.31
Mean Q Time Nurse 62.75
Mean Q Time Doctor 0.50
dtype: float64
It took 5.5744 seconds to do 10 runs **with** parallelisation27.4 Evaluating speed gains
Let’s run the model a few times, specifying a different number of cores to run it on each time.
This book is being compiled on a machine with a 14 core processor.
An argument has been added to the run_trial function to allow us to pass in the number of cores to use.
The results below all relate to 100 runs of the simulation.
speed = []
g.number_of_runs = 100
for i in range(1, 15, 1):
start_time = time.time()
# Create an instance of the Trial class
my_trial = Trial()
# Call the run_trial method of our Trial object
my_trial.run_trial(cores=i)
run_time = round((time.time() - start_time), 3)
speed.append({"Cores":i, "Run Time (seconds)": run_time})
timing_results = pd.DataFrame(speed)
print(timing_results) Cores Run Time (seconds)
0 1 3.437
1 2 2.234
2 3 1.580
3 4 1.372
4 5 1.215
5 6 1.092
6 7 1.118
7 8 0.709
8 9 0.678
9 10 0.691
10 11 1.055
11 12 0.620
12 13 0.602
13 14 0.593Let’s run it again and look at the speed gains when doing 1000 runs of the simulation.
Notice that doubling the number of cores doesn’t halve the time - there is fixed overhead that will take a certain amount of time. This can be even more noticeable with a smaller number of runs.
We make big gains at the beginning, but the fixed overheads mean that higher numbers of cores start to have less and less of an effect.
Cores Run Time (seconds)
0 1 34.700
1 2 18.816
2 3 14.274
3 4 10.761
4 5 9.242
5 6 7.829
6 7 7.329
7 8 6.765
8 9 6.443
9 10 6.294
10 11 6.426
11 12 5.954
12 13 5.790
13 14 5.519