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 = 239 Testing Large Numbers of Scenarios
Acknowledgements
This solution is based on the work of Anna Laws 
and Mike Allen from the PenCHORD team at the University of Exeter.
When working out the best possible configuration for a service, you may wish to try out a large number of scenarios.
Let’s return to our branching model (with the reproducibility set via sim-tools as described in chapter Chapter 13).
39.1 Scenarios
We have a number of parameters available to us in this model:
We can first create a python dictionary of the possible parameter values.
Warning
Be careful - the total number of possible permutations starts to grow very rapidly when you have lots of parameters with multiple options for each!
scenarios = {
'patient_inter': [4, 8, 12],
'mean_reception_time': [2, 3],
'mean_n_consult_time': [6, 10, 14],
'mean_d_consult_time': [10, 20],
'number_of_receptionists': [1, 2],
'number_of_nurses': [1, 2, 3],
'number_of_doctors': [2, 3, 4],
'prob_seeing_doctor': [0.6, 0.8]
}
Tip
Make sure to use exactly the same naming for the dictionary keys as is used in your g class.
This is because we will reset the values of the g class for each Trial programmatically.
Tip
For a small number of possibilities, setting the variables by hand will be fine.
For a larger number, you may want to use the range function.
e.g. to get 6, 10, 14 you would do
[i for i in range(6, 15, 4)][6, 10, 14]Next we use the itertools package to create every possible permutation of the scenarios.
import itertools
# Generate all scenarios:
all_scenarios_tuples = [
x for x in itertools.product(*scenarios.values())]
# Convert list of tuples back to list of dictionaries:
all_scenarios_dicts = [
dict(zip(scenarios.keys(), p)) for p in all_scenarios_tuples]Let’s take a look at the first 3 scenario dictionaries.
all_scenarios_dicts[0:3][{'patient_inter': 4,
'mean_reception_time': 2,
'mean_n_consult_time': 6,
'mean_d_consult_time': 10,
'number_of_receptionists': 1,
'number_of_nurses': 1,
'number_of_doctors': 2,
'prob_seeing_doctor': 0.6},
{'patient_inter': 4,
'mean_reception_time': 2,
'mean_n_consult_time': 6,
'mean_d_consult_time': 10,
'number_of_receptionists': 1,
'number_of_nurses': 1,
'number_of_doctors': 2,
'prob_seeing_doctor': 0.8},
{'patient_inter': 4,
'mean_reception_time': 2,
'mean_n_consult_time': 6,
'mean_d_consult_time': 10,
'number_of_receptionists': 1,
'number_of_nurses': 1,
'number_of_doctors': 3,
'prob_seeing_doctor': 0.6}]We can see that all that has changed is the probability of seeing a doctor (the last key-value pair in each dictionary).
How many scenarios have we created?
len(all_scenarios_dicts)1296Now let’s update our model code.
39.2 Coding the model
Tip
Throughout the code, anything new that’s been added will be followed by the comment ##NEW - so look out for that in the following code chunks.
39.2.1 g class
We’ll just add in a space to for the scenario name.
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 = 2
scenario_name = 0 ##NEW39.2.2 Patient and model classes
These remained unchanged.
39.2.3 Trial class
39.2.3.1 The init method
The scenario is add to the results dataframe, along with some other results metrics.
def __init__(self):
self.df_trial_results = pd.DataFrame()
self.df_trial_results["Run Number"] = [0]
self.df_trial_results["scenario"] = [0] ##NEW
self.df_trial_results["average_inter_arrival"] = [0.0] ##NEW
self.df_trial_results["num_recep"] = [0] ##NEW
self.df_trial_results["num_nurses"] = [0] ##NEW
self.df_trial_results["num_doctors"] = [0] ##NEW
self.df_trial_results["average_reception_time"] = [0.0] ##NEW
self.df_trial_results["average_nurse_time"] = [0.0] ##NEW
self.df_trial_results["average_doctor_time"] = [0.0] ##NEW
self.df_trial_results["prob_need_doctor"] = [0.0] ##NEW
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)39.2.4 The print_trial_results method
This remains unchanged.
39.2.5 The run_trial method
This is updated to include the scenario name and other new metrics.
def run_trial(self):
for run in range(g.number_of_runs):
random.seed(run)
my_model = Model(run)
patient_level_results = my_model.run()
##NEW
self.df_trial_results.loc[run] = [
g.scenario_name,
g.patient_inter,
g.number_of_receptionists,
g.number_of_nurses,
g.number_of_doctors,
g.mean_reception_time,
g.mean_n_consult_time,
g.mean_d_consult_time,
g.prob_seeing_doctor,
len(patient_level_results),
my_model.mean_q_time_recep,
my_model.mean_q_time_nurse,
my_model.mean_q_time_doctor
]
return self.df_trial_results39.3 The full code
The full updated code for the model is given below.
Click here to view the code
import simpy
import random
import pandas as pd
from sim_tools.distributions import Exponential
# 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 = 2
scenario_name = 0 ##NEW
# 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() ##NEW
# 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() ##NEW
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() ##NEW
# 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["scenario"] = [0] ##NEW
self.df_trial_results["average_inter_arrival"] = [0.0] ##NEW
self.df_trial_results["num_recep"] = [0] ##NEW
self.df_trial_results["num_nurses"] = [0] ##NEW
self.df_trial_results["num_doctors"] = [0] ##NEW
self.df_trial_results["average_reception_time"] = [0.0] ##NEW
self.df_trial_results["average_nurse_time"] = [0.0] ##NEW
self.df_trial_results["average_doctor_time"] = [0.0] ##NEW
self.df_trial_results["prob_need_doctor"] = [0.0] ##NEW
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):
# 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()
##NEW
self.df_trial_results.loc[run] = [
g.scenario_name,
g.patient_inter,
g.number_of_receptionists,
g.number_of_nurses,
g.number_of_doctors,
g.mean_reception_time,
g.mean_n_consult_time,
g.mean_d_consult_time,
g.prob_seeing_doctor,
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, return the final results
return self.df_trial_results39.4 Running the scenarios
Let’s now create all of the scenario objects.
results = []
for index, scenario_to_run in enumerate(all_scenarios_dicts):
g.scenario_name = index
# Overwrite defaults from the passed dictionary
for key in scenario_to_run:
setattr(g, key, scenario_to_run[key])
my_trial = Trial()
# Call the run_trial method of our Trial object
results.append(my_trial.run_trial())
pd.concat(results).groupby("scenario").mean().head(20)| average_inter_arrival | num_recep | num_nurses | num_doctors | average_reception_time | average_nurse_time | average_doctor_time | prob_need_doctor | Arrivals | Mean Q Time Recep | Mean Q Time Nurse | Mean Q Time Doctor | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| scenario | ||||||||||||
| 0.0 | 4.0 | 1.0 | 1.0 | 2.0 | 2.0 | 6.0 | 10.0 | 0.6 | 144.0 | 1.099929 | 133.505891 | 0.676479 |
| 1.0 | 4.0 | 1.0 | 1.0 | 2.0 | 2.0 | 6.0 | 10.0 | 0.8 | 144.0 | 1.099929 | 105.505442 | 1.263302 |
| 2.0 | 4.0 | 1.0 | 1.0 | 3.0 | 2.0 | 6.0 | 10.0 | 0.6 | 144.0 | 1.099929 | 129.216818 | 0.014072 |
| 3.0 | 4.0 | 1.0 | 1.0 | 3.0 | 2.0 | 6.0 | 10.0 | 0.8 | 144.0 | 1.099929 | 107.602443 | 0.147246 |
| 4.0 | 4.0 | 1.0 | 1.0 | 4.0 | 2.0 | 6.0 | 10.0 | 0.6 | 144.0 | 1.099929 | 129.216818 | 0.000000 |
| 5.0 | 4.0 | 1.0 | 1.0 | 4.0 | 2.0 | 6.0 | 10.0 | 0.8 | 144.0 | 1.099929 | 95.026033 | 0.032971 |
| 6.0 | 4.0 | 1.0 | 2.0 | 2.0 | 2.0 | 6.0 | 10.0 | 0.6 | 144.0 | 1.099929 | 5.215946 | 2.477255 |
| 7.0 | 4.0 | 1.0 | 2.0 | 2.0 | 2.0 | 6.0 | 10.0 | 0.8 | 144.0 | 1.099929 | 7.497472 | 1.842969 |
| 8.0 | 4.0 | 1.0 | 2.0 | 3.0 | 2.0 | 6.0 | 10.0 | 0.6 | 144.0 | 1.099929 | 4.266968 | 0.592513 |
| 9.0 | 4.0 | 1.0 | 2.0 | 3.0 | 2.0 | 6.0 | 10.0 | 0.8 | 144.0 | 1.099929 | 9.260408 | 0.089449 |
| 10.0 | 4.0 | 1.0 | 2.0 | 4.0 | 2.0 | 6.0 | 10.0 | 0.6 | 144.0 | 1.099929 | 5.405535 | 0.063385 |
| 11.0 | 4.0 | 1.0 | 2.0 | 4.0 | 2.0 | 6.0 | 10.0 | 0.8 | 144.0 | 1.099929 | 8.370422 | 0.015803 |
| 12.0 | 4.0 | 1.0 | 3.0 | 2.0 | 2.0 | 6.0 | 10.0 | 0.6 | 144.0 | 1.099929 | 0.833707 | 1.786491 |
| 13.0 | 4.0 | 1.0 | 3.0 | 2.0 | 2.0 | 6.0 | 10.0 | 0.8 | 144.0 | 1.099929 | 0.871273 | 2.689420 |
| 14.0 | 4.0 | 1.0 | 3.0 | 3.0 | 2.0 | 6.0 | 10.0 | 0.6 | 144.0 | 1.099929 | 1.155603 | 0.142991 |
| 15.0 | 4.0 | 1.0 | 3.0 | 3.0 | 2.0 | 6.0 | 10.0 | 0.8 | 144.0 | 1.099929 | 0.697876 | 0.615490 |
| 16.0 | 4.0 | 1.0 | 3.0 | 4.0 | 2.0 | 6.0 | 10.0 | 0.6 | 144.0 | 1.099929 | 0.925463 | 0.009072 |
| 17.0 | 4.0 | 1.0 | 3.0 | 4.0 | 2.0 | 6.0 | 10.0 | 0.8 | 144.0 | 1.099929 | 0.540083 | 0.186033 |
| 18.0 | 4.0 | 2.0 | 1.0 | 2.0 | 2.0 | 6.0 | 10.0 | 0.6 | 144.0 | 0.091630 | 134.540431 | 0.676479 |
| 19.0 | 4.0 | 2.0 | 1.0 | 2.0 | 2.0 | 6.0 | 10.0 | 0.8 | 144.0 | 0.091630 | 106.515917 | 1.263302 |
Finally the following will give you a nice dictionary of all of your scenarios.
pd.DataFrame.from_dict(all_scenarios_dicts).head()| patient_inter | mean_reception_time | mean_n_consult_time | mean_d_consult_time | number_of_receptionists | number_of_nurses | number_of_doctors | prob_seeing_doctor | |
|---|---|---|---|---|---|---|---|---|
| 0 | 4 | 2 | 6 | 10 | 1 | 1 | 2 | 0.6 |
| 1 | 4 | 2 | 6 | 10 | 1 | 1 | 2 | 0.8 |
| 2 | 4 | 2 | 6 | 10 | 1 | 1 | 3 | 0.6 |
| 3 | 4 | 2 | 6 | 10 | 1 | 1 | 3 | 0.8 |
| 4 | 4 | 2 | 6 | 10 | 1 | 1 | 4 | 0.6 |
pd.DataFrame.from_dict(all_scenarios_dicts).tail()| patient_inter | mean_reception_time | mean_n_consult_time | mean_d_consult_time | number_of_receptionists | number_of_nurses | number_of_doctors | prob_seeing_doctor | |
|---|---|---|---|---|---|---|---|---|
| 1291 | 12 | 3 | 14 | 20 | 2 | 3 | 2 | 0.8 |
| 1292 | 12 | 3 | 14 | 20 | 2 | 3 | 3 | 0.6 |
| 1293 | 12 | 3 | 14 | 20 | 2 | 3 | 3 | 0.8 |
| 1294 | 12 | 3 | 14 | 20 | 2 | 3 | 4 | 0.6 |
| 1295 | 12 | 3 | 14 | 20 | 2 | 3 | 4 | 0.8 |