PySPN

A lightweight tool for modeling and simulation of Stochastic Petri Nets (SPNs).

Getting Started

ℹ️ Tested with Python 3.11

via git

git clone https://github.com/jo-chr/pyspn.git  # 1. Clone repository
pip install -r requirements.txt  # 2. Install requirements
python3 examples/one_server.py  # 3. Run single-server queue example

Modeling

Formally, the class of SPNs that can be modeled using PySPN is defined as:

$$SPN = (P, T, A, G, m_0)$$

where:

• $P = {P_1,P_2,..,P_m}$ is the set of places, drawn as circles;
• $T = {T_1,T_2,..,T_n}$ is the set of transitions along with their distribution functions or weights, drawn as bars;
• $A = A^I \cup A^O \cup A^H$ is the set of arcs, where $A^O$ is the set of output arcs, $A^I$ is the set of input arcs and $A^H$ is the set of inhibitor arcs and each of the arcs has a multiplicity assigned to it;
• $G = {g_1,g_2,..,g_r}$ is the set of guard functions which are associated with different transitions;
• and $m_0$ is the initial marking, defining the distribution of tokens in the places.

Each transition is represented as $T_i = (type, F)$, where $type \in {timed,immediate}$ indicates the type of the transition, and $F$ is either a probability distribution function if the corresponding transition is timed, or a firing weight or probability if it is immediate.

Find sample SPNs under examples/. Currently, places, timed transitions (t_type = "T"), immediate transitions (t_type = "I"), output arcs, input arcs, inhibitor arcs, guard functions, and memory policies are supported.

Places

A place with its required arguments is defined like so:

p1 = Place(label="Place 1", n_tokens=0)

Transitions

A timed transition with its required arguments and a sample distribution function is defined like so:

t1 = Transition(label="Transition 1", t_type="T")
t1.set_distribution(distribution="expon", a=0.0, b=1.0/1.0)

An immediate transition with its required arguments and a sample weight is defined like so:

t2 = Transition(label="Transition 2", t_type="I")
t2.set_weight(weight=0.8)

For timed transitions, some of the supported distributions are:

Distribution	Parameter
Deterministic ("det")	a (fixed delay)
Exponential ("expon")	a, b
Normal ("norm")	a, b
Lognormal ("lognorm")	a, b, c
Uniform ("uniform")	a, b
Triangular ("triang")	a, b, c
Weibull ("weibull_min")	a, b, c

More distributions can be easily implemented in RNGFactory.py. See Scipy's documentation for details regarding the distributions and their parameters.

Guard Functions for Transitions

Guard functions are defined like so:

def guard_t1():
    if len(p1.n_tokens) >= 2:
        return True
    else: return False
t1.set_guard_function(guard_t1)

Memory Policies for Timed Transitions

The default setting is Race Enable ("ENABLE").

The memory policy can be set during instantiation

t1 = Transition(label="Transition_1",t_type="T",memory_policy="AGE")

or by using a function call

t1.set_memory_policy("AGE")

Join and Fork Transitions

To configure a transition that joins two or more input places, set the "Join" parameter to True. This indicates that the transition will act upon the confluence of tokens from multiple places.

t1 = Transition(label="", t_type="", Join=True)

Similarly, to set up a transition that splits its output to multiple places, utilize the "Fork" parameter. Setting split to True designates that the transition's output will be distributed to several output places.

t1 = Transition(label="", t_type="", Fork=True)

Export & Import of SPNs

Export and import SPNs as pickle files using the export_spn() and import_spn() functions of spn_io module.

Simulation

Simulate a SPN like so:

simulate(spn, max_time = 100, verbosity = 2, protocol = True)

For the verbosity there are 3 levels of what is printed in the terminal:

• 0: No information;
• 1: Only final simulation statistics;
• 2: Initial markings, firing of transitions, and final statistics;
• 3: Initial markings, firing of transitions and the resulting marking and state, and final statistics.

The simulation protocol capturing the markings throughtout the simulation can be found under output/protocol/.

Visualization

Visualize a SPN like so:

draw_spn(spn, show=False, file="sample_spn", rankdir="LR")

The graph can be found under output/graphs/.

Usage & Attribution

If you are using the tool for a scientific project please consider citing our publication:

# EAI SIMUtools 2023 - 15th EAI International Conference on Simulation Tools and Techniques (preprint, accepted for presentation)
@misc{friederich_2023,
    doi = {10.13140/RG.2.2.25334.16967},
    url = {https://www.researchgate.net/publication/375758652_PySPN_An_Extendable_Python_Library_for_Modeling_Simulation_of_Stochastic_Petri_Nets},
    year = 2023,
    month = {Nov},
    author = {Friederich, Jonas and Lazarova-Molnar, Sanja},
    title = {{PySPN}: An Extendable Python Library for Modeling & Simulation of Stochastic Petri Nets},
    conference = {EAI SIMUtools 2023 - 15th EAI International Conference on Simulation Tools and Techniques},
    note = {preprint}
} 

For questions/feedback feel free to contact me: jofr@mmmi.sdu.dk.