markov-solver 1.0.0

Utility to solve Markov chains.

Markov Solver

Utility to solve Markov Chains.

Requirements

• Python 3.6+

Install

Install the package, running:

pip install markov-solver

Usage

Chain with constant transition rates

Let us image that we want to solve the following Markov chain:

We should create a YAML file that defines the chain:

chain:
  - from: "Sunny"
    to: "Sunny"
    value: "0.9"

  - from: "Sunny"
    to: "Rainy"
    value: "0.1"

  - from: "Rainy"
    to: "Rainy"
    value: "0.5"

  - from: "Rainy"
    to: "Sunny"
    value: "0.5"

Then, running the following command:

markov-solver solve --definition [PATH_TO_DEFINITION_FILE]

We obtain the following result:

===============================================================
                     MARKOV CHAIN SOLUTION
===============================================================

                      states probability
Rainy.........................................0.166666666666667
Sunny.........................................0.833333333333333

Chain with symbolic transition rates

Let us image that we want to solve the following Markov chain:

We should create a YAML file that defines the chain:

symbols:
  lambda: 1.5
  mu: 2.0

chain:
  - from: "0"
    to: "1"
    value: "lambda"

  - from: "1"
    to: "2"
    value: "lambda"

  - from: "2"
    to: "3"
    value: "lambda"

  - from: "3"
    to: "2"
    value: "3*mu"

  - from: "2"
    to: "1"
    value: "2*mu"

  - from: "1"
    to: "0"
    value: "mu"

Then, running the following command:

markov-solver solve --definition [PATH_TO_DEFINITION_FILE]

We obtain the following result:

===============================================================
                     MARKOV CHAIN SOLUTION
===============================================================

                      states probability
0.............................................0.475836431226766
1.............................................0.356877323420074
2.............................................0.133828996282528
3............................................0.0334572490706320

Authors

Giacomo Marciani, [e-mail]

References

• "Discrete-Event Simulation", 2006, L.M. Leemis, S.K. Park
• "Performance Modeling and Design of Computer Systems, 2013, M. Harchol-Balter

License

The project is released under the MIT License.