prosit-pm 1.0.1

PROcess SImulation Tool — rule-aware business process simulation

Prosit — PROcess SImulation Tool

Prosit is a Python library for rule-aware business process simulation. Given an event log in XES format and a Petri net process model, it automatically discovers simulation parameters (arrival rates, execution times, waiting times, resource assignments, routing probabilities) and runs discrete-event simulations that reproduce the statistical behaviour of the original process.

Unlike basic simulation tools, Prosit builds conditional models — decision trees that learn when each resource is preferred, how long an activity takes depending on the case context, and which path is taken at decision points.

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Table of Contents

• Installation
• Quick Start
• Core Concepts
• API Reference
  • SimulatorParameters
  • SimulatorEngine
• Discovery Options
• Simulation Options
• Save and Load Parameters
• Advanced Usage
• Citation

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Installation

Requirements: Python 3.10

Option 1 — Conda (recommended)

git clone https://github.com/franvinci/prosit
cd prosit
conda env create -f environment.yml
conda activate prosit

Option 2 — pip

git clone https://github.com/franvinci/prosit
cd prosit
pip install -r requirements.txt

Dependencies

Package	Version	Purpose
pm4py	2.4.1	Event log parsing, Petri net discovery and conformance
scikit-learn	1.1.3	Decision tree models (batch discovery)
river	0.22.0	Hoeffding Adaptive Tree (incremental discovery)
scipy	1.14.1	Distribution fitting and sampling
numpy	1.26.4	Numerical operations
pandas	2.2.3	Feature DataFrame construction
tqdm	4.64.1	Progress bars
graphviz	0.20.3	Decision tree visualisation

---

Quick Start

import sys
sys.path.append("src/")

import warnings
warnings.filterwarnings("ignore")

import pm4py
import pm4py.objects.log.importer.xes.importer as xes_importer
from prosit.simulator import SimulatorParameters, SimulatorEngine

# 1. Load event log
log = xes_importer.apply("data/logs/purchasing.xes")

# 2. Discover Petri net
net, im, fm = pm4py.discover_petri_net_inductive(log)

# 3. Create and populate simulation parameters
params = SimulatorParameters(net, im, fm)
params.discover_from_eventlog(log, max_depth_tree=3)

# 4. Save for later reuse
params.to_json("params_purchasing.json")

# 5. Simulate 500 cases
sim_engine = SimulatorEngine(params)
sim_log = sim_engine.apply(n_traces=500)

print(sim_log.head())

The output is a pandas.DataFrame with columns: case:concept:name, concept:name, org:resource, enabled:timestamp, start:timestamp, time:timestamp, plus any case-level data attributes found in the original log.

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Core Concepts

What is discovered

Prosit extracts the following simulation parameters from an event log:

Parameter	What it models
Arrival time	Inter-arrival time between consecutive cases, conditional on hour and weekday
Execution time	Working-hours duration of each activity, conditional on resource and case history
Waiting time	Queue delay after a resource becomes free, conditional on workload and case context
Control flow	Routing probability at each decision point, conditional on case history and attributes
Resource selection	Which eligible resource executes each activity — one dedicated classifier per (activity, candidate resource) conditional on resource-usage history and case attributes
Calendars	Working hours per resource and for case arrivals
Multitasking	Maximum concurrent tasks per resource, derived from observed concurrent workload
Data attributes	Joint or per-attribute distribution of case-level data attributes (e.g. case type, priority)

Rules mode vs. no-rules mode

• Rules mode (max_depth_tree >= 1): Parameters are learned as Decision Trees. Time models (arrival, execution, waiting) use regression trees — each leaf has its own fitted distribution. Routing and resource selection use classification trees that score each candidate transition or resource and sample proportionally.
• No-rules mode (max_depth_tree=0): Each parameter collapses to a single fitted distribution or frequency weight — simpler, faster, less expressive.

Batch vs. incremental discovery

• Batch discovery (default): Trains Decision Trees using scikit-learn with cross-validated hyperparameters (max_depth, min_samples_leaf, max_features). Classification models (control flow, resource selection) also compare against a prior-only DummyClassifier inside the same CV grid — when no tree beats the prior, the model collapses to a single marginal probability.
• Incremental discovery (incremental_discovery=True): Uses Hoeffding Adaptive Trees from the river library. Gives more weight to recent traces, suitable for concept drift or evolving processes.

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API Reference

SimulatorParameters

SimulatorParameters(net: PetriNet, initial_marking: Marking, final_marking: Marking)

Holds all simulation parameters. Initialise with the Petri net (typically discovered via pm4py.discover_petri_net_inductive).

discover_from_eventlog

params.discover_from_eventlog(
    log,
    max_depth_tree: int = 5,
    min_samples_leaf_cv: list = [50, 100, 200],
    multitasking_thr: float = 0.05,
    enable_multitasking: bool = False,
    arrival_calendar_min_confidence: float = 0.1,
    arrival_calendar_min_support: float = 0.7,
    res_calendar_min_confidence: float = 0.1,
    res_calendar_min_support: float = 0.1,
    res_calendar_min_participation: float = 0.4,
    attribute_mode: str = 'distribution',
    incremental_discovery: bool = False,
    grace_period: int = 1000,
    random_state: int = 72,
    verbose: bool = True,
    use_workload_features: bool = False,
)

Extracts all simulation parameters from the event log.

Parameter	Type	Default	Description
log	EventLog	—	pm4py event log in XES format
max_depth_tree	int	5	Maximum depth of decision trees. Higher = more expressive rules. Set to 0 to disable rules (pure distributions)
min_samples_leaf_cv	list	[50,100,200]	Candidate values for min_samples_leaf in cross-validation. Controls the minimum number of samples per leaf — critical for reliable per-leaf distribution fitting
multitasking_thr	float	0.05	Minimum fraction of events with concurrent workload > 0 for a resource to be considered multitasking. Below this, capacity is set to 1
enable_multitasking	bool	False	If True, resources whose log exhibits concurrent workload above multitasking_thr get a capacity > 1 (parallel task execution). Default False: all resources capacity 1
arrival_calendar_min_confidence	float	0.1	Minimum per-slot confidence required to keep an (weekday, hour) slot in the arrival calendar
arrival_calendar_min_support	float	0.7	Minimum fraction of arrivals that the accepted slots must cover; slots are greedily added until this is met
res_calendar_min_confidence	float	0.1	Per-slot confidence threshold for each resource's calendar
res_calendar_min_support	float	0.1	Minimum fraction of the resource's events that the accepted slots must cover
res_calendar_min_participation	float	0.4	Minimum per-resource participation share; below it the resource falls back to a 24/7 calendar
attribute_mode	str	'distribution'	How to model case-level data attributes. 'distribution': fits each attribute independently (categorical → frequency table, continuous → best-fitting scipy distribution). 'empirical': samples from the joint observed distribution (preserves correlations)
incremental_discovery	bool	False	Use Hoeffding Adaptive Trees instead of scikit-learn. Gives more weight to recent traces
grace_period	int	1000	(Incremental only) Number of observations before the tree considers splitting a node
random_state	int	72	Seed for all random operations (reproducibility)
verbose	bool	True	Print discovery progress
use_workload_features	bool	False	If True, resource-selection and waiting-time models receive two extra features per candidate resource: current workload (concurrent tasks) and queue_length (tasks scheduled but not yet started) at the enabling time

to_json / from_json

params.to_json("params.json")   # save to file

params2 = SimulatorParameters(net, im, fm)
params2.from_json("params.json")  # restore from file

Serialises and deserialises all discovered parameters. Allows discovering once and simulating many times without re-running discovery.

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SimulatorEngine

SimulatorEngine(simulation_parameters: SimulatorParameters)

Discrete-event simulation engine. Takes a SimulatorParameters object and runs the simulation.

apply

sim_log = sim_engine.apply(
    n_traces: int = 1,
    t_start: datetime = None,
    deterministic_time: bool = False
) -> pd.DataFrame

Parameter	Type	Default	Description
n_traces	int	1	Number of process instances (cases) to simulate
t_start	datetime	datetime.now()	Start timestamp of the simulation. Cases arrive from this point onward
deterministic_time	bool	False	If True, uses the mean value of each distribution instead of sampling. Useful for deterministic analysis or debugging

Returns a pandas.DataFrame sorted by start time, with one row per simulated event.

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Discovery Options

Choosing max_depth_tree

The max_depth_tree parameter controls the complexity of conditional models:

# No rules — single distribution per activity/resource
params.discover_from_eventlog(log, max_depth_tree=0)

# Shallow rules — fast, interpretable, good for small logs
params.discover_from_eventlog(log, max_depth_tree=2)

# Standard — balances expressiveness and overfitting
params.discover_from_eventlog(log, max_depth_tree=3)

# Deep rules — for complex processes with large logs
params.discover_from_eventlog(log, max_depth_tree=5)

Cross-validation automatically selects the best depth up to max_depth_tree for each individual model.

Controlling leaf size (min_samples_leaf_cv)

This parameter is especially important for time models (execution, waiting, arrival). Each leaf of the regression tree has its own fitted distribution — if a leaf contains too few samples, the distribution fit is unreliable.

# More conservative — larger leaves, smoother distributions
params.discover_from_eventlog(log, min_samples_leaf_cv=[10, 20, 30, 50])

# Less conservative — allows finer segmentation with small logs
params.discover_from_eventlog(log, min_samples_leaf_cv=[1, 5, 10])

Incremental discovery

Use incremental discovery when the process has evolved over time and recent behaviour should dominate the model:

params.discover_from_eventlog(
    log,
    incremental_discovery=True,
    grace_period=500,   # fewer events needed before first split
    max_depth_tree=3
)

The grace_period controls how quickly the tree adapts: lower values make the model react faster to changes, higher values produce more stable trees.

---

Simulation Options

Basic simulation

from datetime import datetime

sim_engine = SimulatorEngine(params)

# Simulate 200 cases starting from a specific date
sim_log = sim_engine.apply(
    n_traces=200,
    t_start=datetime(2024, 1, 1, 8, 0, 0)
)

Deterministic simulation

Uses the mean of each distribution instead of sampling — useful for benchmarking or debugging:

sim_log = sim_engine.apply(n_traces=100, deterministic_time=True)

Multitasking

Resources that handled concurrent work in the log are automatically assigned a maximum concurrency capacity. To disable multitasking entirely (all resources serialised):

params.discover_from_eventlog(log, enable_multitasking=False)

To inspect the discovered capacities:

# {resource_name: max_concurrent_tasks}
print(params.max_concurrency)

Resources with fewer than multitasking_thr fraction of events under concurrent load are treated as non-multitasking (capacity 1) even if enable_multitasking=True.

Output format

print(sim_log.columns.tolist())
# ['case:concept:name', 'concept:name', 'org:resource',
#  'enabled:timestamp', 'start:timestamp', 'time:timestamp',
#  ... (any case-level data attributes from the original log)]

print(sim_log.dtypes)
# All timestamps are datetime objects
# case:concept:name is a string like "case_1", "case_2", ...

---

Save and Load Parameters

Discovered parameters can be saved and reused without re-running the (potentially slow) discovery phase:

# --- Discover once ---
params = SimulatorParameters(net, im, fm)
params.discover_from_eventlog(log, max_depth_tree=3)
params.to_json("my_params.json")

# --- Load and simulate later ---
params2 = SimulatorParameters(net, im, fm)
params2.from_json("my_params.json")

engine = SimulatorEngine(params2)
sim_log = engine.apply(n_traces=1000)

---

Advanced Usage

Full workflow with evaluation

import sys
sys.path.append("src/")

import warnings
warnings.filterwarnings("ignore")

import pm4py
import pm4py.objects.log.importer.xes.importer as xes_importer
from prosit.simulator import SimulatorParameters, SimulatorEngine
from datetime import datetime

# Load log
log = xes_importer.apply("data/logs/purchasing.xes")

# Split: use 80% for discovery, compare simulation against remaining 20%
n_cases = len(log)
train_log = log[:int(n_cases * 0.8)]
test_log  = log[int(n_cases * 0.8):]

# Discover from training set
net, im, fm = pm4py.discover_petri_net_inductive(train_log)
params = SimulatorParameters(net, im, fm)
params.discover_from_eventlog(
    train_log,
    max_depth_tree=3,
    min_samples_leaf_cv=[50, 100, 200],
    random_state=42,
    verbose=True
)

# Simulate the same number of cases as the test set
engine = SimulatorEngine(params)
sim_log = engine.apply(
    n_traces=len(test_log),
    t_start=datetime(2024, 1, 1, 8, 0, 0)
)

print(f"Simulated {len(sim_log)} events across {sim_log['case:concept:name'].nunique()} cases")

No-rules mode (pure distributions)

For simple processes or small logs where decision trees might overfit:

params.discover_from_eventlog(log, max_depth_tree=0)
engine = SimulatorEngine(params)
sim_log = engine.apply(n_traces=200)

Reproducible simulation

import random
random.seed(42)

params.discover_from_eventlog(log, random_state=42)
sim_log = engine.apply(n_traces=100)

Inspecting discovered parameters

# Resources discovered from the log
print(params.resources)

# Working calendar per resource (weekday -> hour -> bool)
print(params.calendars["Resource A"])

# Per-resource maximum concurrency (1 = no multitasking, >1 = multitasking)
print(params.max_concurrency)

# Which resources can perform each activity
print(params.act_to_resources)

# Whether rules mode (Decision Trees) is active
print(params.rules_mode)

# Arrival time model (DecisionRules in rules mode, distribution tuple in no-rules mode)
print(params.arrival_time_distribution)

# Execution time model per activity (DecisionRules or distribution tuple)
print(params.execution_time_distributions)

# Waiting time model per resource (DecisionRules or distribution tuple)
print(params.waiting_time_distributions)

# Resource selection: flat dict {resource: DecisionRules|float}. One binary
# classifier per resource, trained on the events where the resource was
# eligible (activity's candidate pool). At simulation time, the engine first
# filters resources via `act_to_resources[activity]`, scores each enabled
# resource with its own tree, and samples proportionally.
print(params.resource_weights)

# Control flow model per transition (DecisionRules in rules mode, float frequency in no-rules)
print(params.transition_weights)

# Case-level data attribute distribution (None if no attributes in log)
print(params.distribution_data_attributes)
# {'mode': 'empirical', 'data': {(val1, val2): frequency, ...}}
# or {'mode': 'distribution', 'data': {attr: {'type': 'categorical'|'continuous', ...}}}

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What the Models Learn

Features used per model

Model	Tree type	Conditional on
Arrival time	Regressor	Hour of day, weekday
Execution time	Regressor (per activity)	Resource identity (one-hot), hour, weekday, case attributes, activity history counts
Waiting time	Regressor (per resource)	Activity being waited for (one-hot), hour, weekday, case attributes, activity history counts; optionally workload and queue_length when use_workload_features=True
Control flow	Classifier (per transition)	Activity execution history (counts), case attributes
Resource selection	Classifier (per resource)	Per-resource history counts, activity being executed (one-hot), case attributes; optionally workload and queue_length when use_workload_features=True

History features are expressed as raw counts (number of times each activity has been executed in the case so far), so that decision tree rules are directly interpretable (e.g. "Approve" <= 2 means "Approve has been executed at most 2 times").

Before each classifier or regressor is fit, low-signal columns are pruned automatically: constant columns are dropped, and one-hot columns (resources, activities, categorical attribute values) with fewer than 20 positive observations in the current training slice are removed. This reduces noise from rare categories and keeps the CV grid compact.

For the time-regression models, cross-validation selects between every (max_depth, min_samples_leaf) combination and a no-tree baseline (global empirical distribution). If no candidate tree beats the baseline on per-leaf Wasserstein distance, the model collapses to a single unconditional distribution.

Distribution fitting

For each leaf node of a regression tree, Prosit fits the best distribution among: fixed, normal, exponential, lognormal, gamma, uniform. The best fit is selected by minimising the deterministic Wasserstein distance between the empirical and theoretical quantiles. Outliers are removed using the Median Absolute Deviation method (threshold: 20 MAD) before fitting arrival and execution times. Waiting times are fitted on the raw leaf values (no outlier removal), because they are typically zero-inflated and heavy-tailed — filtering would distort both the zero mass and the long tail needed to reproduce real cycle times.

Data attribute modeling

Case-level data attributes (e.g. case:type, case:priority) are discovered automatically and sampled at case arrival time. Two modes are available via attribute_mode:

• 'distribution' (default): fits each attribute independently (categorical → frequency table, continuous → best-fitting scipy distribution). Useful when the log is small or attributes are largely independent.
• 'empirical': samples complete attribute tuples from the observed joint distribution — preserves correlations between attributes.

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Citation

Version v0.1.0 of Prosit corresponds to the implementation presented in the following paper. Please cite it if you use Prosit in academic work:

Vinci, F., Park, G., van der Aalst, W.M.P., de Leoni, M. (2026). Reliable and Configurable Process Simulations via Probabilistic White-Box Models. In: Aiello, M., Deng, S., Murillo, JM., Georgievski, I., Benatallah, B., Wang, Z. (eds) Service-Oriented Computing. ICSOC 2025. Lecture Notes in Computer Science, vol 16321. Springer, Singapore. https://doi.org/10.1007/978-981-95-5015-9_24

BibTeX:

@inproceedings{vinci2026prosit,
  author    = {Vinci, Francesco and Park, Gyunam and van der Aalst, Wil M. P. and de Leoni, Massimiliano},
  title     = {Reliable and Configurable Process Simulations via Probabilistic White-Box Models},
  booktitle = {Service-Oriented Computing -- ICSOC 2025},
  editor    = {Aiello, Marco and Deng, Shuiguang and Murillo, Juan M. and Georgievski, Ilche and Benatallah, Boualem and Wang, Zhongjie},
  series    = {Lecture Notes in Computer Science},
  volume    = {16321},
  publisher = {Springer, Singapore},
  year      = {2026},
  doi       = {10.1007/978-981-95-5015-9_24}
}