running_parallel_cpus.qmd

---
title: Parallelisation
execute:
  eval: false
jupyter: python3
---

> "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](https://en.wikipedia.org/wiki/Parallel_computing)

:::{.callout-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

:::{.callout-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.
:::

## 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.

```{python}
#| eval: true

squared_numbers = []
for i in range(1, 11, 1):
  squared_numbers.append(i * i)

print(squared_numbers)
```

We can simplify the code above into a list comprehension.

```{python}
#| eval: true

[i*i for i in range(1, 11, 1)]

```

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.

```{python}
#| eval: true

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))

```

## A code example

::: {.callout-note}
Thanks go to [Michael Allen](https://orcid.org/0000-0002-8746-9957) for providing an example of how this can be achieved in SimPy. His repository can be found [here](https://github.com/MichaelAllen1966/2004_simple_simpy_parallel).
:::

We will make use of the [Joblib](https://joblib.readthedocs.io/en/latest/parallel.html) package to easily split our SimPy code to run across multiple processor cores.

We will take the model created in the Reproducibility chapter (@sec-reproducibility) and add parallelisation to it.

### 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.

```{python}
from joblib import Parallel, delayed
```

### The g, Patient and Model classes

Our g, patient and model classes are unchanged.

### 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.

:::{.callout-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.
:::

#### The __init__ method

Let's start by adjusting our `__init__` method for our new way of carrying out the results collection.

```{python}
def  __init__(self):
    self.df_trial_results = []
```

#### 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.

```{python}
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)
```

#### the print_trial_results method

Because we went to the effort of setting the index in the step above, this method can remain unchanged.

#### the run_single method

First, let's look back at how our `run_trial` function was written before.

```{python}
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.

```{python}
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 results
```

#### 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`.

:::{.callout-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.

```{python}
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()`.

```{python}
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.

## Evaluating the code outputs

First, let's run this the original way and time how long it takes.

```{python}
#| eval: true
#| echo: false

import simpy
import random
import pandas as pd
from sim_tools.distributions import Exponential
from joblib import Parallel, delayed ##NEW

# Class to store global parameter values.  We don't create an instance of this
# class - we just refer to the class blueprint itself to access the numbers
# inside.
class g:
    patient_inter = 5
    mean_reception_time = 2
    mean_n_consult_time = 6
    mean_d_consult_time = 20
    number_of_receptionists = 1
    number_of_nurses = 1
    number_of_doctors = 2
    prob_seeing_doctor = 0.6
    sim_duration = 600
    number_of_runs = 1000

# Class representing patients coming in to the clinic.
class Patient:
    def __init__(self, p_id):
        self.id = p_id
        self.q_time_recep = 0
        self.q_time_nurse = 0
        self.q_time_doctor = 0

# Class representing our model of the clinic.
class Model:
    # Constructor to set up the model for a run.  We pass in a run number when
    # we create a new model.
    def __init__(self, run_number):
        # Create a SimPy environment in which everything will live
        self.env = simpy.Environment()

        # Create a patient counter (which we'll use as a patient ID)
        self.patient_counter = 0

        # Create our resources
        self.receptionist = simpy.Resource(
            self.env, capacity=g.number_of_receptionists
        )
        self.nurse = simpy.Resource(self.env, capacity=g.number_of_nurses)
        self.doctor = simpy.Resource(
            self.env, capacity=g.number_of_doctors)

        # Store the passed in run number
        self.run_number = run_number

        # Create a new Pandas DataFrame that will store some results against
        # the patient ID (which we'll use as the index).
        self.results_df = pd.DataFrame()
        self.results_df["Patient ID"] = [1]
        self.results_df["Q Time Recep"] = [0.0]
        self.results_df["Time with Recep"] = [0.0]
        self.results_df["Q Time Nurse"] = [0.0]
        self.results_df["Time with Nurse"] = [0.0]
        self.results_df["Q Time Doctor"] = [0.0]
        self.results_df["Time with Doctor"] = [0.0]
        self.results_df.set_index("Patient ID", inplace=True)

        # Create an attribute to store the mean queuing times across this run of
        # the model
        self.mean_q_time_recep = 0
        self.mean_q_time_nurse = 0
        self.mean_q_time_doctor = 0

        self.patient_inter_arrival_dist = Exponential(mean = g.patient_inter, random_seed = self.run_number*2)
        self.patient_reception_time_dist = Exponential(mean = g.mean_reception_time, random_seed = self.run_number*3)
        self.nurse_consult_time_dist = Exponential(mean = g.mean_n_consult_time, random_seed = self.run_number*4)
        self.doctor_consult_time_dist = Exponential(mean = g.mean_d_consult_time, random_seed = self.run_number*5)

    # A generator function that represents the DES generator for patient
    # arrivals
    def generator_patient_arrivals(self):
        # We use an infinite loop here to keep doing this indefinitely whilst
        # the simulation runs
        while True:
            # Increment the patient counter by 1 (this means our first patient
            # will have an ID of 1)
            self.patient_counter += 1

            # Create a new patient - an instance of the Patient Class we
            # defined above.  Remember, we pass in the ID when creating a
            # patient - so here we pass the patient counter to use as the ID.
            p = Patient(self.patient_counter)

            # Tell SimPy to start up the attend_clinic generator function with
            # this patient (the generator function that will model the
            # patient's journey through the system)
            self.env.process(self.attend_clinic(p))

            # Randomly sample the time to the next patient arriving.  Here, we
            # sample from an exponential distribution (common for inter-arrival
            # times), and pass in a lambda value of 1 / mean.  The mean
            # inter-arrival time is stored in the g class.
            sampled_inter = self.patient_inter_arrival_dist.sample()

            # Freeze this instance of this function in place until the
            # inter-arrival time we sampled above has elapsed.  Note - time in
            # SimPy progresses in "Time Units", which can represent anything
            # you like (just make sure you're consistent within the model)
            yield self.env.timeout(sampled_inter)

    # A generator function that represents the pathway for a patient going
    # through the clinic.
    # The patient object is passed in to the generator function so we can
    # extract information from / record information to it
    def attend_clinic(self, patient):
        start_q_recep = self.env.now

        with self.receptionist.request() as req:
            yield req

            end_q_recep = self.env.now

            patient.q_time_recep = end_q_recep - start_q_recep

            sampled_recep_act_time = self.patient_reception_time_dist.sample()

            self.results_df.at[patient.id, "Q Time Recep"] = (
                 patient.q_time_recep
            )
            self.results_df.at[patient.id, "Time with Recep"] = (
                 sampled_recep_act_time
            )

            yield self.env.timeout(sampled_recep_act_time)

        # Here's where the patient finishes with the receptionist, and starts
        # queuing for the nurse

        # Record the time the patient started queuing for a nurse
        start_q_nurse = self.env.now

        # This code says request a nurse resource, and do all of the following
        # block of code with that nurse resource held in place (and therefore
        # not usable by another patient)
        with self.nurse.request() as req:
            # Freeze the function until the request for a nurse can be met.
            # The patient is currently queuing.
            yield req

            # When we get to this bit of code, control has been passed back to
            # the generator function, and therefore the request for a nurse has
            # been met.  We now have the nurse, and have stopped queuing, so we
            # can record the current time as the time we finished queuing.
            end_q_nurse = self.env.now

            # Calculate the time this patient was queuing for the nurse, and
            # record it in the patient's attribute for this.
            patient.q_time_nurse = end_q_nurse - start_q_nurse

            # Now we'll randomly sample the time this patient with the nurse.
            # Here, we use an Exponential distribution for simplicity, but you
            # would typically use a Log Normal distribution for a real model
            # (we'll come back to that).  As with sampling the inter-arrival
            # times, we grab the mean from the g class, and pass in 1 / mean
            # as the lambda value.
            sampled_nurse_act_time = self.nurse_consult_time_dist.sample()

            # Here we'll store the queuing time for the nurse and the sampled
            # time to spend with the nurse in the results DataFrame against the
            # ID for this patient.  In real world models, you may not want to
            # bother storing the sampled activity times - but as this is a
            # simple model, we'll do it here.
            # We use a handy property of pandas called .at, which works a bit
            # like .loc.  .at allows us to access (and therefore change) a
            # particular cell in our DataFrame by providing the row and column.
            # Here, we specify the row as the patient ID (the index), and the
            # column for the value we want to update for that patient.
            self.results_df.at[patient.id, "Q Time Nurse"] = (
                patient.q_time_nurse)
            self.results_df.at[patient.id, "Time with Nurse"] = (
                sampled_nurse_act_time)

            # Freeze this function in place for the activity time we sampled
            # above.  This is the patient spending time with the nurse.
            yield self.env.timeout(sampled_nurse_act_time)

            # When the time above elapses, the generator function will return
            # here.  As there's nothing more that we've written, the function
            # will simply end.  This is a sink.  We could choose to add
            # something here if we wanted to record something - e.g. a counter
            # for number of patients that left, recording something about the
            # patients that left at a particular sink etc.

        # Conditional logic to see if patient goes on to see doctor
        # We sample from the uniform distribution between 0 and 1.  If the value
        # is less than the probability of seeing a doctor (stored in g Class)
        # then we say the patient sees a doctor.
        # If not, this block of code won't be run and the patient will just
        # leave the system (we could add in an else if we wanted a branching
        # path to another activity instead)
        if random.uniform(0,1) < g.prob_seeing_doctor:
            start_q_doctor = self.env.now

            with self.doctor.request() as req:
                yield req

                end_q_doctor = self.env.now

                patient.q_time_doctor = end_q_doctor - start_q_doctor

                sampled_doctor_act_time = self.nurse_consult_time_dist.sample()

                self.results_df.at[patient.id, "Q Time Doctor"] = (
                    patient.q_time_doctor
                )
                self.results_df.at[patient.id, "Time with Doctor"] = (
                    sampled_doctor_act_time
                )

                yield self.env.timeout(sampled_doctor_act_time)

    # This method calculates results over a single run.  Here we just calculate
    # a mean, but in real world models you'd probably want to calculate more.
    def calculate_run_results(self):
        # Take the mean of the queuing times across patients in this run of the
        # model.
        self.mean_q_time_recep = self.results_df["Q Time Recep"].mean()
        self.mean_q_time_nurse = self.results_df["Q Time Nurse"].mean()
        self.mean_q_time_doctor = self.results_df["Q Time Doctor"].mean()

    # The run method starts up the DES entity generators, runs the simulation,
    # and in turns calls anything we need to generate results for the run
    def run(self):
        # Start up our DES entity generators that create new patients.  We've
        # only got one in this model, but we'd need to do this for each one if
        # we had multiple generators.
        self.env.process(self.generator_patient_arrivals())

        # Run the model for the duration specified in g class
        self.env.run(until=g.sim_duration)

        # Now the simulation run has finished, call the method that calculates
        # run results
        self.calculate_run_results()

        # Print the run number with the patient-level results from this run of
        # the model
        return (self.results_df)

# Class representing a Trial for our simulation - a batch of simulation runs.
class Trial:
    # The constructor sets up a pandas dataframe that will store the key
    # results from each run against run number, with run number as the index.
    def  __init__(self):
        self.df_trial_results = pd.DataFrame()
        self.df_trial_results["Run Number"] = [0]
        self.df_trial_results["Arrivals"] = [0]
        self.df_trial_results["Mean Q Time Recep"] = [0.0]
        self.df_trial_results["Mean Q Time Nurse"] = [0.0]
        self.df_trial_results["Mean Q Time Doctor"] = [0.0]
        self.df_trial_results.set_index("Run Number", inplace=True)

    # Method to print out the results from the trial.  In real world models,
    # you'd likely save them as well as (or instead of) printing them
    def print_trial_results(self):
        print ("Trial Results")
        print (self.df_trial_results.round(2))
        print(self.df_trial_results.mean().round(2))

    # Method to run a trial
    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()

```

```{python}
#| eval: true
#| echo: false

import time

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()

print("")
print(f"It took {(time.time() - start_time):.4f} seconds to do 10 runs without parallelisation")
```

Now let's run it again with parallisation.


:::{.callout-note collapse="true"}

### Click here to view the full code

```{python}
#| eval: true
#| echo: false

import simpy
import random
import pandas as pd
from sim_tools.distributions import Exponential
from joblib import Parallel, delayed ##NEW

# Class to store global parameter values.  We don't create an instance of this
# class - we just refer to the class blueprint itself to access the numbers
# inside.
class g:
    patient_inter = 5
    mean_reception_time = 2
    mean_n_consult_time = 6
    mean_d_consult_time = 20
    number_of_receptionists = 1
    number_of_nurses = 1
    number_of_doctors = 2
    prob_seeing_doctor = 0.6
    sim_duration = 600
    number_of_runs = 1000

# Class representing patients coming in to the clinic.
class Patient:
    def __init__(self, p_id):
        self.id = p_id
        self.q_time_recep = 0
        self.q_time_nurse = 0
        self.q_time_doctor = 0

# Class representing our model of the clinic.
class Model:
    # Constructor to set up the model for a run.  We pass in a run number when
    # we create a new model.
    def __init__(self, run_number):
        # Create a SimPy environment in which everything will live
        self.env = simpy.Environment()

        # Create a patient counter (which we'll use as a patient ID)
        self.patient_counter = 0

        # Create our resources
        self.receptionist = simpy.Resource(
            self.env, capacity=g.number_of_receptionists
        )
        self.nurse = simpy.Resource(self.env, capacity=g.number_of_nurses)
        self.doctor = simpy.Resource(
            self.env, capacity=g.number_of_doctors)

        # Store the passed in run number
        self.run_number = run_number

        # Create a new Pandas DataFrame that will store some results against
        # the patient ID (which we'll use as the index).
        self.results_df = pd.DataFrame()
        self.results_df["Patient ID"] = [1]
        self.results_df["Q Time Recep"] = [0.0]
        self.results_df["Time with Recep"] = [0.0]
        self.results_df["Q Time Nurse"] = [0.0]
        self.results_df["Time with Nurse"] = [0.0]
        self.results_df["Q Time Doctor"] = [0.0]
        self.results_df["Time with Doctor"] = [0.0]
        self.results_df.set_index("Patient ID", inplace=True)

        # Create an attribute to store the mean queuing times across this run of
        # the model
        self.mean_q_time_recep = 0
        self.mean_q_time_nurse = 0
        self.mean_q_time_doctor = 0

        self.patient_inter_arrival_dist = Exponential(mean = g.patient_inter, random_seed = self.run_number*2)
        self.patient_reception_time_dist = Exponential(mean = g.mean_reception_time, random_seed = self.run_number*3)
        self.nurse_consult_time_dist = Exponential(mean = g.mean_n_consult_time, random_seed = self.run_number*4)
        self.doctor_consult_time_dist = Exponential(mean = g.mean_d_consult_time, random_seed = self.run_number*5)

    # A generator function that represents the DES generator for patient
    # arrivals
    def generator_patient_arrivals(self):
        # We use an infinite loop here to keep doing this indefinitely whilst
        # the simulation runs
        while True:
            # Increment the patient counter by 1 (this means our first patient
            # will have an ID of 1)
            self.patient_counter += 1

            # Create a new patient - an instance of the Patient Class we
            # defined above.  Remember, we pass in the ID when creating a
            # patient - so here we pass the patient counter to use as the ID.
            p = Patient(self.patient_counter)

            # Tell SimPy to start up the attend_clinic generator function with
            # this patient (the generator function that will model the
            # patient's journey through the system)
            self.env.process(self.attend_clinic(p))

            # Randomly sample the time to the next patient arriving.  Here, we
            # sample from an exponential distribution (common for inter-arrival
            # times), and pass in a lambda value of 1 / mean.  The mean
            # inter-arrival time is stored in the g class.
            sampled_inter = self.patient_inter_arrival_dist.sample()

            # Freeze this instance of this function in place until the
            # inter-arrival time we sampled above has elapsed.  Note - time in
            # SimPy progresses in "Time Units", which can represent anything
            # you like (just make sure you're consistent within the model)
            yield self.env.timeout(sampled_inter)

    # A generator function that represents the pathway for a patient going
    # through the clinic.
    # The patient object is passed in to the generator function so we can
    # extract information from / record information to it
    def attend_clinic(self, patient):
        start_q_recep = self.env.now

        with self.receptionist.request() as req:
            yield req

            end_q_recep = self.env.now

            patient.q_time_recep = end_q_recep - start_q_recep

            sampled_recep_act_time = self.patient_reception_time_dist.sample()

            self.results_df.at[patient.id, "Q Time Recep"] = (
                 patient.q_time_recep
            )
            self.results_df.at[patient.id, "Time with Recep"] = (
                 sampled_recep_act_time
            )

            yield self.env.timeout(sampled_recep_act_time)

        # Here's where the patient finishes with the receptionist, and starts
        # queuing for the nurse

        # Record the time the patient started queuing for a nurse
        start_q_nurse = self.env.now

        # This code says request a nurse resource, and do all of the following
        # block of code with that nurse resource held in place (and therefore
        # not usable by another patient)
        with self.nurse.request() as req:
            # Freeze the function until the request for a nurse can be met.
            # The patient is currently queuing.
            yield req

            # When we get to this bit of code, control has been passed back to
            # the generator function, and therefore the request for a nurse has
            # been met.  We now have the nurse, and have stopped queuing, so we
            # can record the current time as the time we finished queuing.
            end_q_nurse = self.env.now

            # Calculate the time this patient was queuing for the nurse, and
            # record it in the patient's attribute for this.
            patient.q_time_nurse = end_q_nurse - start_q_nurse

            # Now we'll randomly sample the time this patient with the nurse.
            # Here, we use an Exponential distribution for simplicity, but you
            # would typically use a Log Normal distribution for a real model
            # (we'll come back to that).  As with sampling the inter-arrival
            # times, we grab the mean from the g class, and pass in 1 / mean
            # as the lambda value.
            sampled_nurse_act_time = self.nurse_consult_time_dist.sample()

            # Here we'll store the queuing time for the nurse and the sampled
            # time to spend with the nurse in the results DataFrame against the
            # ID for this patient.  In real world models, you may not want to
            # bother storing the sampled activity times - but as this is a
            # simple model, we'll do it here.
            # We use a handy property of pandas called .at, which works a bit
            # like .loc.  .at allows us to access (and therefore change) a
            # particular cell in our DataFrame by providing the row and column.
            # Here, we specify the row as the patient ID (the index), and the
            # column for the value we want to update for that patient.
            self.results_df.at[patient.id, "Q Time Nurse"] = (
                patient.q_time_nurse)
            self.results_df.at[patient.id, "Time with Nurse"] = (
                sampled_nurse_act_time)

            # Freeze this function in place for the activity time we sampled
            # above.  This is the patient spending time with the nurse.
            yield self.env.timeout(sampled_nurse_act_time)

            # When the time above elapses, the generator function will return
            # here.  As there's nothing more that we've written, the function
            # will simply end.  This is a sink.  We could choose to add
            # something here if we wanted to record something - e.g. a counter
            # for number of patients that left, recording something about the
            # patients that left at a particular sink etc.

        # Conditional logic to see if patient goes on to see doctor
        # We sample from the uniform distribution between 0 and 1.  If the value
        # is less than the probability of seeing a doctor (stored in g Class)
        # then we say the patient sees a doctor.
        # If not, this block of code won't be run and the patient will just
        # leave the system (we could add in an else if we wanted a branching
        # path to another activity instead)
        if random.uniform(0,1) < g.prob_seeing_doctor:
            start_q_doctor = self.env.now

            with self.doctor.request() as req:
                yield req

                end_q_doctor = self.env.now

                patient.q_time_doctor = end_q_doctor - start_q_doctor

                sampled_doctor_act_time = self.nurse_consult_time_dist.sample()

                self.results_df.at[patient.id, "Q Time Doctor"] = (
                    patient.q_time_doctor
                )
                self.results_df.at[patient.id, "Time with Doctor"] = (
                    sampled_doctor_act_time
                )

                yield self.env.timeout(sampled_doctor_act_time)

    # This method calculates results over a single run.  Here we just calculate
    # a mean, but in real world models you'd probably want to calculate more.
    def calculate_run_results(self):
        # Take the mean of the queuing times across patients in this run of the
        # model.
        self.mean_q_time_recep = self.results_df["Q Time Recep"].mean()
        self.mean_q_time_nurse = self.results_df["Q Time Nurse"].mean()
        self.mean_q_time_doctor = self.results_df["Q Time Doctor"].mean()

    # The run method starts up the DES entity generators, runs the simulation,
    # and in turns calls anything we need to generate results for the run
    def run(self):
        # Start up our DES entity generators that create new patients.  We've
        # only got one in this model, but we'd need to do this for each one if
        # we had multiple generators.
        self.env.process(self.generator_patient_arrivals())

        # Run the model for the duration specified in g class
        self.env.run(until=g.sim_duration)

        # Now the simulation run has finished, call the method that calculates
        # run results
        self.calculate_run_results()

        # Print the run number with the patient-level results from this run of
        # the model
        return (self.results_df)

# Class representing a Trial for our simulation - a batch of simulation runs.
class Trial:
    # The constructor sets up an empty list, which we will place dictionaries
    # into. Each dictionary will be the results from a single run.
    def  __init__(self):
        self.df_trial_results = [] ## NEW

    ## NEW
    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)

    # Method to print out the results from the trial.  In real world models,
    # you'd likely save them as well as (or instead of) printing them
    def print_trial_results(self):
        print("Trial Results")
        print(self.df_trial_results.round(2))
        print(self.df_trial_results.mean().round(2))

    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 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()

```

:::

```{python}
#| eval: true
#| echo: false

import time

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()

print("")
print(f"It took {(time.time() - start_time):.4f} seconds to do 10 runs **with** parallelisation")
```

## 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.

```{python}
#| eval: true
#| echo: false
#|
class Trial:
    # The constructor sets up an empty list, which we will place dictionaries
    # into. Each dictionary will be the results from a single run.
    def  __init__(self):
        self.df_trial_results = [] ## NEW

    ## NEW
    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)

    # Method to print out the results from the trial.  In real world models,
    # you'd likely save them as well as (or instead of) printing them
    def print_trial_results(self):
        print("Trial Results")
        print(self.df_trial_results.round(2))
        print(self.df_trial_results.mean().round(2))

    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 results


    def run_trial(self, cores):
        # Run the simulation for the number of runs specified in g class.

        self.df_trial_results = Parallel(n_jobs=cores)(delayed(self.run_single)(run) for run in range(g.number_of_runs))
```

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.

```{python}
#| eval: true

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)
```

```{python}
#| eval: true
#| echo: false

import plotly.express as px

fig = px.line(timing_results, x="Cores", y="Run Time (seconds)")

fig.show()
```


Let'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.

```{python}
#| eval: true
#| echo: false

speed = []

g.number_of_runs = 1000

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)
```

```{python}
#| eval: true
#| echo: false

import plotly.express as px

fig = px.line(timing_results, x="Cores", y="Run Time (seconds)")

fig.show()
```