Open Network with lognormal service times

On this page we will create a ciw network model from a specification in a JSON file.

The model represents a simple three node network problem with lognormal service times.

1. Imports

1.1 json2ciw imports

We will use:

• load_three_node_network_model function that loads the built in urgent care call centre JSON file.
• ProcessModel: a pydantic schema that provides automatic validation of the JSON.
• CiwConverter that accepts a valid ProcessModel that represents a DES model and returns a ciw parameter dict.
• multiple_replications:runs the network model and results a Dataframe of replication results.
• summarise_results: provides a formatted table of mean results for each node in the network.
• tidy_to_wide_format: the results from multiple_replications are returned in tidy (stacked row) format. This function converts into wide format i.e. each column is a performance measure.
• create_user_filtered_hist generates a interactive plotly chart to view replications for each performance measure. It requires replication data in wide format.

from json2ciw.datasets import load_three_node_network_model
from json2ciw.engine import (
    CiwConverter,
    multiple_replications
)
from json2ciw.results import (
    summarise_results, 
)

from json2ciw.schema import ProcessModel

1.2 Other imports

import ciw
from IPython.display import JSON
from rich import print

2. Load JSON

json_network = load_three_node_network_model()

display as collapsible JSON. Expand to view the details.

JSON(json_network)

<IPython.core.display.JSON object>

3. Convert to a ProcessModel

A ProcessModel is a pydantic schema. It is independent of ciw. This early version will automatically validate that the JSON file is correct and that all transitions add up to 1.0 when it is created.

model_instance = ProcessModel(**json_network)

The contents of the process model can be manually inspected by a developer as follows:

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.display_diagram(include_resources=False)

graph TD
    %% Three Node Network: A simple three node network to convert to ciw
    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.display_diagram(include_resources=True)

graph TD
    %% Three Node Network: A simple three node network to convert to ciw
    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

# summary of distributions
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

# summary of routing percentages
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

# resources
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

3. Convert to a ciw Network Model

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

The variable network_params is a python dict that contains all the parameters that ciw requires for a very simple queuing model. This can be passed as keyword args to the ciw.create_network function.

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]]}

# we use ciw's native `create_network` method
network = ciw.create_network(**network_params)
print(type(network))

<class 'ciw.network.Network'>

# Run a quick simulation to verify it works without crashing...
sim = ciw.Simulation(network)
sim.simulate_until_max_time(50)
print("Quick simulation run worked!")

Quick simulation run worked!

4. Run the model for multiple replications

The multiple_replications function returns a DataFrame that contains one row per activity per replication. So if there are two nodes there are two rows for each replication.

# Run replications with activity/resource names
df_reps = multiple_replications(
    network, 
    model_instance, 
    num_reps=100, 
    runtime=2880,
    warmup=1440,
    n_jobs=-1 # parallel reps
)

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

Filter the nodes with the usual pandas syntax

df_reps.loc[df_reps['activity_name'] == "Service 1"].head(3)

	rep	node_id	activity_name	resource_name	resource_capacity	n_service	mean_wait	mean_service	utilisation	mean_Lq

5. Summarise results

If needed there is a built in function to create a DataFrame that contains a mean summary of all metrics across the nodes.

# Get summary table
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	7204.1	14395.1	10785.4
1	Mean waiting time	0.0	0.1	0.0
2	Mean service time	1.0	1.0	1.0
3	Mean utilisation	27.8	83.3	30.0
4	Mean queue length	0.0	1.4	0.0