Open Network with lognormal service times

In this example, the model represents a simple three node network problem with lognormal service times.

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

Imports

import json

import ciw
from rich import print

from json2ciw.datasets import load_three_node_network_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_network = load_three_node_network_model()
print(json.dumps(json_network, indent=2))

{
  "name": "Three Node Network",
  "description": "A simple three node network to convert to ciw",
  "activities": [
    {
      "name": "Node 1",
      "type": "activity",
      "resource": {
        "name": "Resource 1",
        "capacity": 18
      },
      "service_distribution": {
        "type": "lognormal",
        "parameters": {
          "mean": 1,
          "std": 0.1
        }
      },
      "arrival_distribution": {
        "type": "exponential",
        "parameters": {
          "rate": 1.0
        }
      }
    },
    {
      "name": "Node 2",
      "type": "activity",
      "resource": {
        "name": "Resource 2",
        "capacity": 12
      },
      "service_distribution": {
        "type": "normal",
        "parameters": {
          "mean": 1,
          "std": 0.1
        }
      },
      "arrival_distribution": {
        "type": "exponential",
        "parameters": {
          "rate": 4.0
        }
      }
    },
    {
      "name": "Node 3",
      "type": "activity",
      "resource": {
        "name": "Resource 3",
        "capacity": 25
      },
      "service_distribution": {
        "type": "lognormal",
        "parameters": {
          "mean": 1,
          "std": 0.1
        }
      },
      "arrival_distribution": {
        "type": "exponential",
        "parameters": {
          "rate": 3.0
        }
      }
    }
  ],
  "transitions": [
    {
      "from": "Node 1",
      "to": "Exit",
      "probability": 0.1
    },
    {
      "from": "Node 1",
      "to": "Node 2",
      "probability": 0.6
    },
    {
      "from": "Node 1",
      "to": "Node 3",
      "probability": 0.3
    },
    {
      "from": "Node 2",
      "to": "Exit",
      "probability": 0.6
    },
    {
      "from": "Node 2",
      "to": "Node 1",
      "probability": 0.1
    },
    {
      "from": "Node 2",
      "to": "Node 3",
      "probability": 0.3
    },
    {
      "from": "Node 3",
      "to": "Exit",
      "probability": 0.2
    },
    {
      "from": "Node 3",
      "to": "Node 2",
      "probability": 0.4
    },
    {
      "from": "Node 3",
      "to": "Node 1",
      "probability": 0.4
    }
  ]
}

Validate with ProcessModel

model_instance = ProcessModel(**json_network)

print(model_instance)

ProcessModel(
    name='Three Node Network',
    description='A simple three node network to convert to ciw',
    activities=[
        Activity(
            name='Node 1',
            type='activity',
            resource=Resource(name='Resource 1', capacity=18),
            service_distribution=Distribution(type='lognormal', parameters={'mean': 1.0, 'std': 0.1}),
            arrival_distribution=Distribution(type='exponential', parameters={'rate': 1.0}),
            renege_distribution=None
        ),
        Activity(
            name='Node 2',
            type='activity',
            resource=Resource(name='Resource 2', capacity=12),
            service_distribution=Distribution(type='normal', parameters={'mean': 1.0, 'std': 0.1}),
            arrival_distribution=Distribution(type='exponential', parameters={'rate': 4.0}),
            renege_distribution=None
        ),
        Activity(
            name='Node 3',
            type='activity',
            resource=Resource(name='Resource 3', capacity=25),
            service_distribution=Distribution(type='lognormal', parameters={'mean': 1.0, 'std': 0.1}),
            arrival_distribution=Distribution(type='exponential', parameters={'rate': 3.0}),
            renege_distribution=None
        )
    ],
    transitions=[
        Transition(source='Node 1', target='Exit', probability=0.1),
        Transition(source='Node 1', target='Node 2', probability=0.6),
        Transition(source='Node 1', target='Node 3', probability=0.3),
        Transition(source='Node 2', target='Exit', probability=0.6),
        Transition(source='Node 2', target='Node 1', probability=0.1),
        Transition(source='Node 2', target='Node 3', probability=0.3),
        Transition(source='Node 3', target='Exit', probability=0.2),
        Transition(source='Node 3', target='Node 2', probability=0.4),
        Transition(source='Node 3', target='Node 1', probability=0.4)
    ]
)

model_instance.save_diagram("urgentcare.mmd", include_resources=False)

flowchart TD
    Arrivals_Node_1("Time between arrivals<br/>Exponential(λ=1.0)")
    Arrivals_Node_2("Time between arrivals<br/>Exponential(λ=4.0)")
    Arrivals_Node_3("Time between arrivals<br/>Exponential(λ=3.0)")
    Node_1["Node 1<br/>Lognormal(mean=1.0, stdev=0)"]
    Node_2["Node 2<br/>Normal(mean=1.0, sd=0)"]
    Node_3["Node 3<br/>Lognormal(mean=1.0, stdev=0)"]
    Exit(["Exit"])

    Arrivals_Node_1 --> Node_1
    Arrivals_Node_2 --> Node_2
    Arrivals_Node_3 --> Node_3
    Node_1 -->|10%| Exit
    Node_1 -->|60%| Node_2
    Node_1 -->|30%| Node_3
    Node_2 -->|60%| Exit
    Node_2 -->|10%| Node_1
    Node_2 -->|30%| Node_3
    Node_3 -->|20%| Exit
    Node_3 -->|40%| Node_2
    Node_3 -->|40%| Node_1

model_instance.save_diagram("urgentcare_resources.mmd", include_resources=True)

flowchart TD
    Arrivals_Node_1("Time between arrivals<br/>Exponential(λ=1.0)")
    Arrivals_Node_2("Time between arrivals<br/>Exponential(λ=4.0)")
    Arrivals_Node_3("Time between arrivals<br/>Exponential(λ=3.0)")
    Node_1["Node 1<br/>Lognormal(mean=1.0, stdev=0)"]
    Node_2["Node 2<br/>Normal(mean=1.0, sd=0)"]
    Node_3["Node 3<br/>Lognormal(mean=1.0, stdev=0)"]
    Resource_Resource_1(("Resource 1<br/>(18)"))
    Resource_Resource_2(("Resource 2<br/>(12)"))
    Resource_Resource_3(("Resource 3<br/>(25)"))
    Exit(["Exit"])

    Arrivals_Node_1 --> Node_1
    Arrivals_Node_2 --> Node_2
    Arrivals_Node_3 --> Node_3
    Resource_Resource_1 -.Seize.-> Node_1
    Node_1 -.Release.-> Resource_Resource_1
    Resource_Resource_2 -.Seize.-> Node_2
    Node_2 -.Release.-> Resource_Resource_2
    Resource_Resource_3 -.Seize.-> Node_3
    Node_3 -.Release.-> Resource_Resource_3
    Node_1 -->|10%| Exit
    Node_1 -->|60%| Node_2
    Node_1 -->|30%| Node_3
    Node_2 -->|60%| Exit
    Node_2 -->|10%| Node_1
    Node_2 -->|30%| Node_3
    Node_3 -->|20%| Exit
    Node_3 -->|40%| Node_2
    Node_3 -->|40%| Node_1

model_instance.get_distributions_df()

	Activity	Phase	Distribution Type	Parameters
0	Node 1	Arrival	Exponential	rate=1.0
1	Node 1	Service	Lognormal	mean=1.0, std=0.1
2	Node 2	Arrival	Exponential	rate=4.0
3	Node 2	Service	Normal	mean=1.0, std=0.1
4	Node 3	Arrival	Exponential	rate=3.0
5	Node 3	Service	Lognormal	mean=1.0, std=0.1

model_instance.get_routing_matrix_df()

	Node 1	Node 2	Node 3	Exit
Source Activity
Node 1	0.0	0.6	0.3	0.1
Node 2	0.1	0.0	0.3	0.6
Node 3	0.4	0.4	0.0	0.2

model_instance.get_resources_df()

	Resource	Activity	Count
0	Resource 1	Node 1	18
1	Resource 2	Node 2	12
2	Resource 3	Node 3	25

Convert to ciw parameters

adapter = CiwConverter(model_instance)
network_params = adapter.generate_params()
print(network_params)

{
    'number_of_servers': [18, 12, 25],
    'arrival_distributions': [Exponential(rate=1.0), Exponential(rate=4.0), Exponential(rate=3.0)],
    'service_distributions': [
        Lognormal(mean=-0.0049751654265839124, sd=0.0997513451195916),
        Normal(mean=1.0, sd=0.1),
        Lognormal(mean=-0.0049751654265839124, sd=0.0997513451195916)
    ],
    'reneging_time_distributions': [None, None, None],
    'routing': [[0.0, 0.6, 0.3], [0.1, 0.0, 0.3], [0.4, 0.4, 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	Node 1	Resource 1	18	7216	0.000000	1.000161	28.238367	0.000000
1	0	2	Node 2	Resource 2	12	14546	0.138830	1.000103	83.861598	1.402375
2	0	3	Node 3	Resource 3	25	10838	0.000000	0.999720	30.372911	0.000000
3	1	1	Node 1	Resource 1	18	7365	0.000000	1.001236	27.770561	0.000000
4	1	2	Node 2	Resource 2	12	14515	0.182148	1.000512	83.455292	1.836026

Convert to wide format

wide = tidy_to_wide_format(df_reps)
wide.head()

	mean_Lq [Node 1]	mean_Lq [Node 2]	mean_Lq [Node 3]	mean_service [Node 1]	mean_service [Node 2]	mean_service [Node 3]	mean_wait [Node 1]	mean_wait [Node 2]	mean_wait [Node 3]	n_service [Node 1]	n_service [Node 2]	n_service [Node 3]	utilisation [Node 1]	utilisation [Node 2]	utilisation [Node 3]
rep
0	0.0	1.402375	0.0	1.000161	1.000103	0.999720	0.0	0.138830	0.0	7216	14546	10838	28.238367	83.861598	30.372911
1	0.0	1.836026	0.0	1.001236	1.000512	1.001197	0.0	0.182148	0.0	7365	14515	10841	27.770561	83.455292	29.982137
2	0.0	1.806245	0.0	1.000565	1.000158	0.999756	0.0	0.178762	0.0	7210	14550	10678	27.542854	83.531804	29.792481
3	0.0	1.291956	0.0	0.998776	0.999506	1.001227	0.0	0.129872	0.0	7160	14325	10713	27.765163	83.631392	29.968283
4	0.0	1.483820	0.0	0.999830	1.000044	1.000370	0.0	0.148063	0.0	7056	14431	10793	27.990271	83.738731	30.265584

Summarise results

summary = summarise_results(df_reps)
summary.round(1)

activity	Metric	Node 1 (Resource 1)	Node 2 (Resource 2)	Node 3 (Resource 3)
0	Mean completed services	7201.4	14473.4	10772.6
1	Mean waiting time	0.0	0.2	0.0
2	Mean service time	1.0	1.0	1.0
3	Mean utilisation	27.9	83.6	30.1
4	Mean queue length	0.0	1.6	0.0