Write readme module fit and simulation

README.md

@@ -23,10 +23,12 @@
 
 <p>
     Phitter analyzes datasets and determines the best analytical probability distributions that represent them. Phitter studies over 80 probability distributions, both continuous and discrete, 3 goodness-of-fit tests, and interactive visualizations. For each selected probability distribution, a standard modeling guide is provided along with spreadsheets that detail the methodology for using the chosen distribution in data science, operations research, and artificial intelligence.
+</p>
 
+<p>
     In addition, Phitter offers the capability to perform process simulations, allowing users to graph and observe minimum times for specific observations. It also supports queue simulations with flexibility to configure various parameters, such as the number of servers, maximum population size, system capacity, and different queue disciplines, including First-In-First-Out (FIFO), Last-In-First-Out (LIFO), and priority-based service (PBS).
-
 </p>
+
 <p>
     This repository contains the implementation of the python library and the kernel of <a href="https://phitter.io">Phitter Web</a>
 </p>
@@ -45,9 +47,11 @@ python: >=3.9
 pip install phitter
 ```
 
+
+
 ## Usage
 
-### Notebook's Tutorials
+### ***1. Fit Notebook's Tutorials***
 
 |             Tutorial             |                                                                                                                  Notebooks                                                                                                                   |
 | :------------------------------: | :------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------: |
@@ -57,7 +61,28 @@ pip install phitter
 |   **Fit Specific Disribution**   | <a target="_blank" href="https://colab.research.google.com/github/phitterio/phitter-kernel/blob/main/examples/fit_specefic_distribution.ipynb"><img src="https://colab.research.google.com/assets/colab-badge.svg" alt="Open In Colab"/></a> |
 |     **Working Distribution**     |   <a target="_blank" href="https://colab.research.google.com/github/phitterio/phitter-kernel/blob/main/examples/working_distribution.ipynb"><img src="https://colab.research.google.com/assets/colab-badge.svg" alt="Open In Colab"/></a>    |
 
-### General
+### ***2. Simulation Notebook's Tutorials***
+pending
+
+## Documentation
+
+
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+
+<details>
+
+<summary style="font-size: 16px; font-weight: bold;">Documentation Fit Module</summary>
+
+
+
+### General Fit
 
 ```python
 import phitter
@@ -466,6 +491,233 @@ distribution.mode # -> 733.3333333333333
 |          poisson           | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |
 |          uniform           | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |
 
+</details>
+
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+<details>
+<summary style="font-size: 16px; font-weight: bold;">Documentation Simulation Module</summary>
+
+
+
+## Process Simulation
+
+This will help you to understand your processes. To use it, run the following line
+
+```python
+from phitter import simulation
+
+# Create a simulation process instance
+simulation = simulation.ProcessSimulation()
+
+```
+
+### Add processes to your simulation instance
+
+There are two ways to add processes to your simulation instance:
+
+-   Adding a **process _without_ preceding process (new branch)**
+-   Adding a **process _with_ preceding process (with previous ids)**
+
+#### Process _without_ preceding process (new branch)
+
+```python
+# Add a new process without preceding process
+simulation.add_process(
+    prob_distribution="normal",
+    parameters={"mu": 5, "sigma": 2},
+    process_id="first_process",
+    number_of_products=10,
+    number_of_servers=3,
+    new_branch=True,
+)
+
+```
+
+#### Process _with_ preceding process (with previous ids)
+
+```python
+# Add a new process with preceding process
+simulation.add_process(
+    prob_distribution="exponential",
+    parameters={"lambda": 4},
+    process_id="second_process",
+    previous_ids=["first_process"],
+)
+
+```
+
+#### All together and adding some new process
+
+The order in which you add each process **_matters_**. You can add as many processes as you need.
+
+```python
+# Add a new process without preceding process
+simulation.add_process(
+    prob_distribution="normal",
+    parameters={"mu": 5, "sigma": 2},
+    process_id="first_process",
+    number_of_products=10,
+    number_of_servers=3,
+    new_branch=True,
+)
+
+# Add a new process with preceding process
+simulation.add_process(
+    prob_distribution="exponential",
+    parameters={"lambda": 4},
+    process_id="second_process",
+    previous_ids=["first_process"],
+)
+
+# Add a new process with preceding process
+simulation.add_process(
+    prob_distribution="gamma",
+    parameters={"alpha": 15, "beta": 3},
+    process_id="third_process",
+    previous_ids=["first_process"],
+)
+
+# Add a new process without preceding process
+simulation.add_process(
+    prob_distribution="exponential",
+    parameters={"lambda": 4.3},
+    process_id="fourth_process",
+    new_branch=True,
+)
+
+
+# Add a new process with preceding process
+simulation.add_process(
+    prob_distribution="beta",
+    parameters={"alpha": 1, "beta": 1, "A": 2, "B": 3},
+    process_id="fifth_process",
+    previous_ids=["second_process", "fourth_process"],
+)
+
+# Add a new process with preceding process
+simulation.add_process(
+    prob_distribution="normal",
+    parameters={"mu": 15, "sigma": 2},
+    process_id="sixth_process",
+    previous_ids=["third_process", "fifth_process"],
+)
+```
+
+### Visualize your processes
+
+You can visualize your processes to see if what you're trying to simulate is your actual process.
+
+```python
+# Graph your process
+simulation.process_graph()
+```
+
+![Simulation](./multimedia/simulation_process_graph.png)
+
+### Start Simulation
+
+You can simulate and have different simulation time values or you can create a confidence interval for your process
+
+#### Run Simulation
+
+Simulate several scenarios of your complete process
+
+```python
+# Run Simulation
+simulation.run(number_of_simulations=100)
+
+# After run
+simulation: pandas.Dataframe
+```
+
+### Review Simulation Metrics by Stage
+
+If you want to review average time and standard deviation by stage run this line of code
+
+```python
+# Review simulation metrics
+simulation.simulation_metrics() -> pandas.Dataframe
+```
+
+#### Run confidence interval
+
+If you want to have a confidence interval for the simulation metrics, run the following line of code
+
+```python
+# Confidence interval for Simulation metrics
+simulation.run_confidence_interval(
+    confidence_level=0.99,
+    number_of_simulations=100,
+    replications=10,
+) -> pandas.Dataframe
+```
+
+## Queue Simulation
+
+If you need to simulate queues run the following code:
+
+```python
+from phitter import simulation
+
+# Create a simulation process instance
+simulation = simulation.QueueingSimulation(
+    a="exponential",
+    a_paramters={"lambda": 5},
+    s="exponential",
+    s_parameters={"lambda": 20},
+    c=3,
+)
+```
+
+In this case we are going to simulate **a** (arrivals) with _exponential distribution_ and **s** (service) as _exponential distribution_ with **c** equals to 3 different servers.
+
+By default Maximum Capacity **k** is _infinity_, total population **n** is _infinity_ and the queue discipline **d** is _FIFO_. As we are not selecting **d** equals to "PBS" we don't have any information to add for **pbs_distribution** nor **pbs_parameters**
+
+### Run the simulation
+
+If you want to have the simulation results
+
+```python
+# Run simulation
+simulation = simulation.run(simulation_time = 2000)
+simulation: pandas.Dataframe
+```
+
+If you want to see some metrics and probabilities from this simulation you should use::
+
+```python
+# Calculate metrics
+simulation.metrics_summary() -> pandas.Dataframe
+
+# Calculate probabilities
+number_probability_summary() -> pandas.Dataframe
+```
+
+### Run Confidence Interval for metrics and probabilities
+
+If you want to have a confidence interval for your metrics and probabilities you should run the following line
+
+```python
+# Calculate confidence interval for metrics and probabilities
+probabilities, metrics = simulation.confidence_interval_metrics(
+    simulation_time=2000,
+    confidence_level=0.99,
+    replications=10,
+)
+
+probabilities -> pandas.Dataframe
+metrics -> pandas.Dataframe
+```
+
+</details>
+
 ## Contribution
 
 If you would like to contribute to the Phitter project, please create a pull request with your proposed changes or enhancements. All contributions are welcome!