markon 1.0.0

Simple CTMC solver for Python

Markon

Continous Time Markov Chain solver for Python

Markon is a small Python utility for performing analytic solution of CTMCs. Both quantitative and symbolic analysis is possible.

Example:

from markon import solve_ctmc

# Define a CTMC as a dict of state-tuples (from_state, to_state) to a transition rate
t = {('up', 'down'): 1,  # Transition rate from 'up' to 'down' is 1
     ('down', 'up'): 5}  # Transition rate from 'down' to 'up' is 5

# Obtain steady state probabilities
p = solve_ctmc(t)
print(p)

will output

{'down': 1/6, 'up': 5/6}

Individual state probabilities can be obtained, both in exact form or as a single rounded float:

print(p['up'])
print(float(p['up']))

will output

5/6
0.8333333333333334

General symbolic analysis can also be done via Sympy:

from markon import solve_ctmc
import sympy

# Define Sympy symbols
l, m = sympy.symbols('l, m')

t = {('up', 'down'): l,
     ('down', 'up'): m}

# Obtain steady state probabilities with defined order
p = solve_ctmc(t, ['up', 'down'])
print(p)

will output

{'up': m/(l + m), 'down': l/(l + m)}

We can then use Sympy functionality to substitute values

values = [(l, 1), (m,5)]
print(p['up'].subs(values))

will output

5/6

Refer to the Sympy documentation for more on how to enable nice formatting of expressions, output to Latex, etc.