Open Jackson Network Model

In this example, the model represents a a classic queuing network problem that can be formulated as an Open Jackson Network.

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

Imports

import json

import ciw
from rich import print

from json2ciw.datasets import load_jackson_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_jackson_network_model()
print(json.dumps(json_network, indent=2))

{
  "name": "Open Jackson Network",
  "description": "A simple jackson network to convert to ciw",
  "activities": [
    {
      "name": "Service 1",
      "type": "activity",
      "resource": {
        "name": "Servers 1",
        "capacity": 1
      },
      "service_distribution": {
        "type": "exponential",
        "parameters": {
          "mean": 0.1
        }
      },
      "arrival_distribution": {
        "type": "exponential",
        "parameters": {
          "rate": 1.0
        }
      }
    },
    {
      "name": "Service 2",
      "type": "activity",
      "resource": {
        "name": "Servers 2",
        "capacity": 2
      },
      "service_distribution": {
        "type": "exponential",
        "parameters": {
          "mean": 0.1
        }
      },
      "arrival_distribution": {
        "type": "exponential",
        "parameters": {
          "rate": 4.0
        }
      }
    },
    {
      "name": "Service 3",
      "type": "activity",
      "resource": {
        "name": "Servers 3",
        "capacity": 1
      },
      "service_distribution": {
        "type": "exponential",
        "parameters": {
          "mean": 0.1
        }
      },
      "arrival_distribution": {
        "type": "exponential",
        "parameters": {
          "rate": 3.0
        }
      }
    }
  ],
  "transitions": [
    {
      "from": "Service 1",
      "to": "Exit",
      "probability": 0.1
    },
    {
      "from": "Service 1",
      "to": "Service 2",
      "probability": 0.6
    },
    {
      "from": "Service 1",
      "to": "Service 3",
      "probability": 0.3
    },
    {
      "from": "Service 2",
      "to": "Exit",
      "probability": 0.6
    },
    {
      "from": "Service 2",
      "to": "Service 1",
      "probability": 0.1
    },
    {
      "from": "Service 2",
      "to": "Service 3",
      "probability": 0.3
    },
    {
      "from": "Service 3",
      "to": "Exit",
      "probability": 0.2
    },
    {
      "from": "Service 3",
      "to": "Service 2",
      "probability": 0.4
    },
    {
      "from": "Service 3",
      "to": "Service 1",
      "probability": 0.4
    }
  ]
}

Validate with ProcessModel

model_instance = ProcessModel(**json_network)

print(model_instance)

ProcessModel(
    name='Open Jackson Network',
    description='A simple jackson network to convert to ciw',
    activities=[
        Activity(
            name='Service 1',
            type='activity',
            resource=Resource(name='Servers 1', capacity=1),
            service_distribution=Distribution(type='exponential', parameters={'mean': 0.1}),
            arrival_distribution=Distribution(type='exponential', parameters={'rate': 1.0}),
            renege_distribution=None
        ),
        Activity(
            name='Service 2',
            type='activity',
            resource=Resource(name='Servers 2', capacity=2),
            service_distribution=Distribution(type='exponential', parameters={'mean': 0.1}),
            arrival_distribution=Distribution(type='exponential', parameters={'rate': 4.0}),
            renege_distribution=None
        ),
        Activity(
            name='Service 3',
            type='activity',
            resource=Resource(name='Servers 3', capacity=1),
            service_distribution=Distribution(type='exponential', parameters={'mean': 0.1}),
            arrival_distribution=Distribution(type='exponential', parameters={'rate': 3.0}),
            renege_distribution=None
        )
    ],
    transitions=[
        Transition(source='Service 1', target='Exit', probability=0.1),
        Transition(source='Service 1', target='Service 2', probability=0.6),
        Transition(source='Service 1', target='Service 3', probability=0.3),
        Transition(source='Service 2', target='Exit', probability=0.6),
        Transition(source='Service 2', target='Service 1', probability=0.1),
        Transition(source='Service 2', target='Service 3', probability=0.3),
        Transition(source='Service 3', target='Exit', probability=0.2),
        Transition(source='Service 3', target='Service 2', probability=0.4),
        Transition(source='Service 3', target='Service 1', probability=0.4)
    ]
)

model_instance.save_diagram("jackson.mmd")

flowchart TD
    Arrivals_Service_1("Time between arrivals<br/>Exponential(λ=1.0)")
    Arrivals_Service_2("Time between arrivals<br/>Exponential(λ=4.0)")
    Arrivals_Service_3("Time between arrivals<br/>Exponential(λ=3.0)")
    Service_1["Service 1<br/>Exponential(mean=0.1)"]
    Service_2["Service 2<br/>Exponential(mean=0.1)"]
    Service_3["Service 3<br/>Exponential(mean=0.1)"]
    Resource_Servers_1(("Servers 1<br/>(1)"))
    Resource_Servers_2(("Servers 2<br/>(2)"))
    Resource_Servers_3(("Servers 3<br/>(1)"))
    Exit(["Exit"])

    Arrivals_Service_1 --> Service_1
    Arrivals_Service_2 --> Service_2
    Arrivals_Service_3 --> Service_3
    Resource_Servers_1 -.Seize.-> Service_1
    Service_1 -.Release.-> Resource_Servers_1
    Resource_Servers_2 -.Seize.-> Service_2
    Service_2 -.Release.-> Resource_Servers_2
    Resource_Servers_3 -.Seize.-> Service_3
    Service_3 -.Release.-> Resource_Servers_3
    Service_1 -->|10%| Exit
    Service_1 -->|60%| Service_2
    Service_1 -->|30%| Service_3
    Service_2 -->|60%| Exit
    Service_2 -->|10%| Service_1
    Service_2 -->|30%| Service_3
    Service_3 -->|20%| Exit
    Service_3 -->|40%| Service_2
    Service_3 -->|40%| Service_1

model_instance.display_diagram(include_resources=True)

flowchart TD Arrivals_Service_1(“Time between arrivals
Exponential(λ=1.0)”) Arrivals_Service_2(“Time between arrivals
Exponential(λ=4.0)”) Arrivals_Service_3(“Time between arrivals
Exponential(λ=3.0)”) Service_1[“Service 1
Exponential(mean=0.1)”] Service_2[“Service 2
Exponential(mean=0.1)”] Service_3[“Service 3
Exponential(mean=0.1)”] Resource_Servers_1((“Servers 1
(1)”)) Resource_Servers_2((“Servers 2
(2)”)) Resource_Servers_3((“Servers 3
(1)”)) Exit([“Exit”])

Arrivals_Service_1 --> Service_1
Arrivals_Service_2 --> Service_2
Arrivals_Service_3 --> Service_3
Resource_Servers_1 -.Seize.-> Service_1
Service_1 -.Release.-> Resource_Servers_1
Resource_Servers_2 -.Seize.-> Service_2
Service_2 -.Release.-> Resource_Servers_2
Resource_Servers_3 -.Seize.-> Service_3
Service_3 -.Release.-> Resource_Servers_3
Service_1 -->|10%| Exit
Service_1 -->|60%| Service_2
Service_1 -->|30%| Service_3
Service_2 -->|60%| Exit
Service_2 -->|10%| Service_1
Service_2 -->|30%| Service_3
Service_3 -->|20%| Exit
Service_3 -->|40%| Service_2
Service_3 -->|40%| Service_1

model_instance.get_distributions_df()

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

model_instance.get_routing_matrix_df()

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

model_instance.get_resources_df()

	Resource	Activity	Count
0	Servers 1	Service 1	1
1	Servers 2	Service 2	2
2	Servers 3	Service 3	1

Convert to ciw parameters

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

{
    'number_of_servers': [1, 2, 1],
    'arrival_distributions': [Exponential(rate=1.0), Exponential(rate=4.0), Exponential(rate=3.0)],
    'service_distributions': [Exponential(rate=10.0), Exponential(rate=10.0), Exponential(rate=10.0)],
    '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	Service 1	Servers 1	1	7235	0.100526	0.101436	49.753370	0.505073
1	0	2	Service 2	Servers 2	2	14480	0.035334	0.101033	49.936752	0.355298
2	0	3	Service 3	Servers 3	1	10834	0.311941	0.101618	75.011634	2.346920
3	1	1	Service 1	Servers 1	1	7221	0.105431	0.100141	49.728757	0.528695
4	1	2	Service 2	Servers 2	2	14483	0.034044	0.100673	50.070456	0.342399

Convert to wide format

wide = tidy_to_wide_format(df_reps)
wide.head()

	mean_Lq [Service 1]	mean_Lq [Service 2]	mean_Lq [Service 3]	mean_service [Service 1]	mean_service [Service 2]	mean_service [Service 3]	mean_wait [Service 1]	mean_wait [Service 2]	mean_wait [Service 3]	n_service [Service 1]	n_service [Service 2]	n_service [Service 3]	utilisation [Service 1]	utilisation [Service 2]	utilisation [Service 3]
rep
0	0.505073	0.355298	2.346920	0.101436	0.101033	0.101618	0.100526	0.035334	0.311941	7235	14480	10834	49.753370	49.936752	75.011634
1	0.528695	0.342399	2.633773	0.100141	0.100673	0.100782	0.105431	0.034044	0.345444	7221	14483	10979	49.728757	50.070456	76.194688
2	0.498286	0.343490	2.731786	0.099994	0.098454	0.101268	0.099478	0.034136	0.364441	7213	14490	10794	49.805521	49.213628	75.446480
3	0.568632	0.361709	2.589407	0.101253	0.099272	0.100922	0.110862	0.035452	0.337382	7386	14692	11052	51.395484	50.568808	77.015357
4	0.474180	0.314434	2.454758	0.100743	0.097752	0.101118	0.098716	0.031779	0.331041	6917	14248	10678	49.078224	48.828468	74.168355

Summarise results

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

activity	Metric	Service 1 (Servers 1)	Service 2 (Servers 2)	Service 3 (Servers 3)
0	Mean completed services	7194.4	14478.6	10867.4
1	Mean waiting time	0.1	0.0	0.3
2	Mean service time	0.1	0.1	0.1
3	Mean utilisation	50.0	49.7	75.6
4	Mean queue length	0.5	0.3	2.6