Ciw Call Centre Model

In this example, the model represents a simple urgent care call centre defined in Monks and Harper (2023).

Features of the model:

The JSON for this built-in example can be loaded using json2ciw.datasets.load_call_centre_model.

Call centre diagram

Imports

import json

import ciw
from rich import print

from json2ciw.datasets import load_call_centre_model
from json2ciw.engine import CiwConverter, multiple_replications
from json2ciw.results import summarise_results, tidy_to_wide_format
from json2ciw.schema import ProcessModel

Load JSON

json_call_centre = load_call_centre_model()
print(json.dumps(json_call_centre, indent=2))
{
  "name": "Call Handling Process",
  "description": "Discrete Event Simulation of a Patient call handling process.",
  "activities": [
    {
      "name": "Call Triage",
      "type": "activity",
      "resource": {
        "name": "Operator",
        "capacity": 13
      },
      "service_distribution": {
        "type": "triangular",
        "parameters": {
          "min": 5,
          "mode": 7,
          "max": 10
        }
      },
      "arrival_distribution": {
        "type": "exponential",
        "parameters": {
          "mean": 0.6
        }
      }
    },
    {
      "name": "Nurse Consultation",
      "type": "activity",
      "resource": {
        "name": "Nurse",
        "capacity": 9
      },
      "service_distribution": {
        "type": "uniform",
        "parameters": {
          "min": 10,
          "max": 20
        }
      }
    }
  ],
  "transitions": [
    {
      "from": "Call Triage",
      "to": "Nurse Consultation",
      "probability": 0.4
    },
    {
      "from": "Call Triage",
      "to": "Exit",
      "probability": 0.6
    },
    {
      "from": "Nurse Consultation",
      "to": "Exit",
      "probability": 1.0
    }
  ]
}

Validate with ProcessModel

model_instance = ProcessModel(**json_call_centre)
print(model_instance)
ProcessModel(
    name='Call Handling Process',
    description='Discrete Event Simulation of a Patient call handling process.',
    activities=[
        Activity(
            name='Call Triage',
            type='activity',
            resource=Resource(name='Operator', capacity=13),
            service_distribution=Distribution(
                type='triangular',
                parameters={'min': 5.0, 'mode': 7.0, 'max': 10.0}
            ),
            arrival_distribution=Distribution(type='exponential', parameters={'mean': 0.6}),
            renege_distribution=None
        ),
        Activity(
            name='Nurse Consultation',
            type='activity',
            resource=Resource(name='Nurse', capacity=9),
            service_distribution=Distribution(type='uniform', parameters={'min': 10.0, 'max': 20.0}),
            arrival_distribution=None,
            renege_distribution=None
        )
    ],
    transitions=[
        Transition(source='Call Triage', target='Nurse Consultation', probability=0.4),
        Transition(source='Call Triage', target='Exit', probability=0.6),
        Transition(source='Nurse Consultation', target='Exit', probability=1.0)
    ]
)

model_instance.save_diagram("callcentre.mmd")

flowchart TD
    Arrivals_Call_Triage("Time between arrivals<br/>Exponential(mean=0.6)")
    Call_Triage["Call Triage<br/>('Triangular(5.0, 7.0, 10.0)',)"]
    Nurse_Consultation["Nurse Consultation<br/>Uniform(10.0, 20.0)"]
    Resource_Operator(("Operator<br/>(13)"))
    Resource_Nurse(("Nurse<br/>(9)"))
    Exit(["Exit"])

    Arrivals_Call_Triage --> Call_Triage
    Resource_Operator -.Seize.-> Call_Triage
    Call_Triage -.Release.-> Resource_Operator
    Resource_Nurse -.Seize.-> Nurse_Consultation
    Nurse_Consultation -.Release.-> Resource_Nurse
    Call_Triage -->|40%| Nurse_Consultation
    Call_Triage -->|60%| Exit
    Nurse_Consultation --> Exit

model_instance.get_distributions_df()
Activity Phase Distribution Type Parameters
0 Call Triage Arrival Exponential mean=0.6
1 Call Triage Service Triangular min=5.0, mode=7.0, max=10.0
2 Nurse Consultation Service Uniform min=10.0, max=20.0 
model_instance.get_routing_matrix_df()
Call Triage Nurse Consultation Exit
Source Activity
Call Triage 0.0 0.4 0.6
Nurse Consultation 0.0 0.0 1.0 
model_instance.get_resources_df()
Resource Activity Count
0 Operator Call Triage 13
1 Nurse Nurse Consultation 9

Convert to ciw parameters

adapter = CiwConverter(model_instance)
network_params = adapter.generate_params()
print(network_params)
{
    'number_of_servers': [13, 9],
    'arrival_distributions': [Exponential(rate=1.6666666666666667), None],
    'service_distributions': [Triangular(lower=5.0, mode=7.0, upper=10.0), Uniform(lower=10.0, upper=20.0)],
    'reneging_time_distributions': [None, None],
    'routing': [[0.0, 0.4], [0.0, 0.0]]
}

Build and run the ciw model

network = ciw.create_network(**network_params)
sim = ciw.Simulation(network)
sim.simulate_until_max_time(50)
print("Quick simulation run worked!")
Quick simulation run worked!

Run the model for multiple replications

df_reps = multiple_replications(
    network,
    model_instance,
    num_reps=5,
    runtime=2880,
    warmup=1440,
    n_jobs=-1,
)

df_reps.head()
rep node_id activity_name resource_name resource_capacity n_service mean_wait mean_service utilisation mean_Lq
0 0 1 Call Triage Operator 13 2409 2.543220 7.309819 95.129252 4.254594
1 0 2 Nurse Consultation Nurse 9 765 206.954675 14.990006 99.164671 109.944671
2 1 1 Call Triage Operator 13 2370 2.795481 7.321618 93.117043 4.600896
3 1 2 Nurse Consultation Nurse 9 773 224.244232 14.981693 99.525047 120.375549
4 2 1 Call Triage Operator 13 2426 4.816395 7.323897 95.099958 8.114287

Convert to wide format

wide = tidy_to_wide_format(df_reps)
wide.head()
mean_Lq [Call Triage] mean_Lq [Nurse Consultation] mean_service [Call Triage] mean_service [Nurse Consultation] mean_wait [Call Triage] mean_wait [Nurse Consultation] n_service [Call Triage] n_service [Nurse Consultation] utilisation [Call Triage] utilisation [Nurse Consultation]
rep
0 4.254594 109.944671 7.309819 14.990006 2.543220 206.954675 2409 765 95.129252 99.164671
1 4.600896 120.375549 7.321618 14.981693 2.795481 224.244232 2370 773 93.117043 99.525047
2 8.114287 120.976784 7.323897 14.812186 4.816395 228.917962 2426 761 95.099958 99.342764
3 5.008256 122.556602 7.351322 15.043528 3.124735 243.422767 2308 725 92.053435 99.140463
4 7.162318 128.947937 7.334381 14.992293 4.211408 246.921582 2449 752 94.982781 99.548895

Summarise results

summary = summarise_results(df_reps)
summary.round(1)
activity Metric Call Triage (Operator) Nurse Consultation (Nurse)
0 Mean completed services 2392.4 755.2
1 Mean waiting time 3.5 230.1
2 Mean service time 7.3 15.0
3 Mean utilisation 94.1 99.3
4 Mean queue length 5.8 120.6