simpy treatment centre model

`simpy` treatment centre model#

In this exercise you will learn how to set up and use an existing simulation model. The modelling framework has been setup with a Scenario class for parameterisation and a multiple_replications() wrapper function for running the model and returning results.

1. Problem description#

FirstTreatment: A health clinic based in the US. This example is based on exercise 13 from Nelson (2013) page 170.

Nelson. B.L. (2013). Foundations and methods of stochastic simulation. Springer.

Patients arrive to the health clinic between 6am and 12am following a non-stationary poisson process. After 12am arriving patients are diverted elsewhere and remaining WIP is completed. On arrival, all patients quickly sign-in and are triaged.

The health clinic expects two types of patient arrivals:

Trauma arrivals:

patients with severe illness and trauma that must first be stabilised in a trauma room.
these patients then undergo treatment in a cubicle before being discharged.

Non-trauma arrivals

patients with minor illness and no trauma go through registration and examination activities
a proportion of non-trauma patients require treatment in a cubicle before being discharged.

In this model treatment of trauma and non-trauma patients is modelled separately.

2. Imports#

The model has been setup as a python package and deployed to pypi: https://pypi.org/project/treat-sim/. It has been pip installed as part of the provided sim conda virtual environment.

The Scenario class and multiple_replications functions are contained in the treat_sim.model module.

An description of all model code is provided in an online Jupyter book: https://bit.ly/treat_sim

Let’s check the version of treat_sim we have installed

import treat_sim
treat_sim.__version__

'1.0.0'

from treat_sim.model import Scenario, multiple_replications

# we will also import pandas
import pandas as pd

3. Example: creating a default scenario#

default_scenario = Scenario()

# let's have a look at some of the default parameters
default_scenario.n_triage
default_scenario.n_exam

4. Example creating an alternative scenario#

There are many variables available to update in this model. Some examples are:

n_triage = number of triage bays
n_exam = number of examination rooms
n_cubicles_1 = number of non trauma treatment rooms
exam_mean = mean duration of an examination

From version 1.0.0 of treat_sim these are updated via the constructor as follows:

# by default there is 1 triage room
# set parameters through the consutuctor methods as follows
extra_triage = Scenario(n_triage=2)
extra_triage.n_triage

4. Running a scenario using the wrapper method#

by default the replications function runs the model 5 times. You can alter this using the n_reps parameter

results = multiple_replications(default_scenario, n_reps=10)

The variable results is a pandas.DataFrame containing key performance indicators (columns) and replications (rows)

results

	00_arrivals	01a_triage_wait	01b_triage_util	02a_registration_wait	02b_registration_util	03a_examination_wait	03b_examination_util	04a_treatment_wait(non_trauma)	04b_treatment_util(non_trauma)	05_total_time(non-trauma)	06a_trauma_wait	06b_trauma_util	07a_treatment_wait(trauma)	07b_treatment_util(trauma)	08_total_time(trauma)	09_throughput
rep
1	218.0	28.009290	0.542454	128.490438	0.854615	28.478642	0.847430	145.414321	0.853189	247.872229	8.595360	0.368908	214.198331	0.976808	399.200311	154.0
2	188.0	3.240469	0.475390	63.307540	0.749027	16.328179	0.795921	134.202786	0.846795	178.799154	65.146932	0.838521	231.603567	0.778634	392.064964	139.0
3	233.0	13.040936	0.528681	149.636381	0.839994	18.400280	0.847310	169.503295	0.827088	260.804457	78.130137	0.816547	251.835736	1.188287	369.276920	157.0
4	236.0	29.246780	0.623225	91.137899	0.876762	35.424440	0.881140	125.016255	0.858299	206.945928	225.471749	0.876984	95.601572	1.193115	385.752794	159.0
5	246.0	65.407658	0.647235	130.091608	0.827194	36.254401	0.824874	150.890149	0.840913	288.796547	168.014088	0.979189	13.244608	0.650671	339.817753	148.0
6	215.0	67.536960	0.617639	87.101852	0.807856	24.149025	0.810646	95.628440	0.841574	226.294148	82.263601	0.842665	207.090105	0.771464	418.710896	151.0
7	199.0	16.388866	0.479730	90.818931	0.764699	30.028974	0.812242	119.295530	0.785988	211.711285	70.318603	0.810452	295.851506	0.880920	462.818608	149.0
8	240.0	36.702969	0.676470	126.444397	0.860978	31.189935	0.866354	169.368888	0.858340	268.655456	152.750616	0.801632	171.917036	0.602400	433.502223	154.0
9	238.0	38.201228	0.595762	96.503846	0.878944	29.642379	0.887559	169.737929	0.898665	247.619831	68.075461	0.698513	307.067085	0.952312	477.145587	145.0
10	226.0	54.951247	0.652863	106.388692	0.845639	25.374935	0.846628	136.911866	0.900255	264.451897	85.030588	0.834798	210.969768	0.797586	503.115035	159.0

we can summarise results using the dataframe’s describe() method. The results are transposed to improve readability.

results.describe().T

	count	mean	std	min	25%	50%	75%	max
00_arrivals	10.0	223.900000	18.864723	188.000000	215.750000	229.500000	237.500000	246.000000
01a_triage_wait	10.0	35.272640	21.891014	3.240469	19.293972	32.974874	50.763742	67.536960
01b_triage_util	10.0	0.583945	0.072690	0.475390	0.532124	0.606701	0.641233	0.676470
02a_registration_wait	10.0	106.992158	26.076703	63.307540	90.898673	101.446269	127.978928	149.636381
02b_registration_util	10.0	0.830571	0.044482	0.749027	0.812690	0.842816	0.859387	0.878944
03a_examination_wait	10.0	27.527119	6.568842	16.328179	24.455503	29.060511	30.899695	36.254401
03b_examination_util	10.0	0.842010	0.030849	0.795921	0.815400	0.846969	0.861623	0.887559
04a_treatment_wait(non_trauma)	10.0	141.596946	24.505998	95.628440	127.312888	141.163093	164.749203	169.737929
04b_treatment_util(non_trauma)	10.0	0.851111	0.033026	0.785988	0.841078	0.849992	0.858330	0.900255
05_total_time(non-trauma)	10.0	240.195093	33.630061	178.799154	215.357001	247.746030	263.540037	288.796547
06a_trauma_wait	10.0	100.379713	62.925813	8.595360	68.636246	80.196869	135.820609	225.471749
06b_trauma_util	10.0	0.786821	0.162391	0.368908	0.803837	0.825673	0.841629	0.979189
07a_treatment_wait(trauma)	10.0	199.937931	88.990650	13.244608	180.710303	212.584049	246.777694	307.067085
07b_treatment_util(trauma)	10.0	0.879220	0.201709	0.602400	0.773256	0.839253	0.970684	1.193115
08_total_time(trauma)	10.0	418.140509	51.147329	339.817753	387.330837	408.955603	455.489512	503.115035
09_throughput	10.0	151.500000	6.433420	139.000000	148.250000	152.500000	156.250000	159.000000

5. Exercise#

Try running the following scenarios

extra triage capacity - increase triage bays to 2
extra examination capacity = increase examination rooms to 2
swap over 1 exam room for extra triage bay

Extra challenge:

Create a function called get_scenarios() that creates all of the function in one go and returns them to the calling code. Can you then loop through the scenarios and execute them in one after another?
One option is to setup the function so that it creates a python dictionary that has the name of the scenario as a key and the Scenario object as a value.
Can you combine the results into a single table?

# example answer that includes extra challenges.

def get_scenarios():
    '''
    Creates a dictionary object containing
    objects of type `Scenario` to run.
    
    Returns:
    --------
    dict
        Contains the scenarios for the model
    '''
    scenarios = {}
    scenarios['base'] = Scenario()
    
    # extra triage capacity
    scenarios['triage+1'] = Scenario(scenarios['base'].n_triage+1)
        
    # extra examination capacity
    scenarios['exam+1'] = Scenario(scenarios['base'].n_exam+1)
        
    # swap over 1 exam room for extra triage cubicle
    scenarios['swap_exam_triage'] = Scenario(scenarios['base'].n_triage+1,
                                             scenarios['base'].n_exam-1)
    return scenarios

def run_scenario_analysis(scenarios, n_reps):
    '''
    Run each of the scenarios for a specified results
    collection period and replications.
    
    Params:
    ------
    scenarios: dict
        dictionary of Scenario objects
        
    n_rep: int
        Number of replications
    
    '''
    print('Scenario Analysis')
    print(f'No. Scenario: {len(scenarios)}')
    print(f'Replications: {n_reps}')

    scenario_results = {}
    for sc_name, scenario in scenarios.items():
        
        print(f'Running {sc_name}', end=' => ')
        replications = multiple_replications(scenario, n_reps=n_reps)
        print('done.\n')
        
        #save the results
        scenario_results[sc_name] = replications
    
    print('Scenario analysis complete.')
    return scenario_results

def scenario_summary_frame(scenario_results):
    '''
    Mean results for each performance measure by scenario
    
    Parameters:
    ----------
    scenario_results: dict
        dictionary of replications.  
        Key identifies the performance measure
        
    Returns:
    -------
    pd.DataFrame
    '''
    columns = []
    summary = pd.DataFrame()
    for sc_name, replications in scenario_results.items():
        summary = pd.concat([summary, replications.mean()], axis=1)
        columns.append(sc_name)

    summary.columns = columns
    return summary

# run the analysis!

scenario_results = run_scenario_analysis(get_scenarios(), 10)
scenario_summary_frame(scenario_results)

Scenario Analysis
No. Scenario: 4
Replications: 10
Running base => 

done.

Running triage+1 => 

done.

Running exam+1 => 

done.

Running swap_exam_triage => 

done.

Scenario analysis complete.

	base	triage+1	exam+1	swap_exam_triage
00_arrivals	223.900000	223.900000	223.900000	223.900000
01a_triage_wait	35.272640	35.272640	35.272640	1.591082
01b_triage_util	0.583945	0.583945	0.583945	0.291972
02a_registration_wait	106.992158	106.992158	106.992158	136.547677
02b_registration_util	0.830571	0.830571	0.830571	0.837294
03a_examination_wait	27.527119	27.527119	27.527119	28.238646
03b_examination_util	0.842010	0.842010	0.842010	0.844921
04a_treatment_wait(non_trauma)	141.596946	141.596946	141.596946	145.386882
04b_treatment_util(non_trauma)	0.851111	0.851111	0.851111	0.852151
05_total_time(non-trauma)	240.195093	240.195093	240.195093	237.010351
06a_trauma_wait	100.379713	100.379713	100.379713	123.372108
06b_trauma_util	0.786821	0.786821	0.786821	0.786666
07a_treatment_wait(trauma)	199.937931	199.937931	199.937931	233.482451
07b_treatment_util(trauma)	0.879220	0.879220	0.879220	0.899172
08_total_time(trauma)	418.140509	418.140509	418.140509	430.158680
09_throughput	151.500000	151.500000	151.500000	151.400000