Modeling and Simulation of

Business Processes with DPMN

Processing Activities

Gerd Wagner

Brandenburg University of Technology


This WSC 2021 tutorial presentation is available from

This tutorial is based on the Open Access book Business Process Modeling and Simulation with DPMN, available from

DPMN = Discrete Event Process Modeling Notation

... is a diagram language for making process models for Discrete Event Simulation (DES).

It combines the intuitive flowchart modeling style of BPMN (the Business Process Modeling Notation) with the rigorous semantics provided by


  • Part I: Event Graphs and Basic DPMN
  • Part II: Modeling Activity Networks with DPMN
  • Part III: Modeling Processing Networks with DPMN


Conceptual Foundations and Key Insights

Objects and Events


(1) Objects ("endurants") and events ("perdurants") are the two most fundamental ontological categories.

(2) Objects participate in events.

(3) Events need not be atomic, nor instantaneous. They may be composite and have non-zero duration.


... are composite events that are composed of a start event and an end event.

... have a performer, which is an agent.

Resource Constrained Activities

A performer is a resource.

Processing Activities

Processing activities are performed at processing stations, such that processing objects move from one processing station to the next one.

Event Graphs ⇒ Activity Networks
⇒ Processing Networks

  1. DPMN is a conservative extension of Event Graphs allowing to model Activity Networks and Processing Networks
  2. DPMN is the first visual modeling language that provides a conceptual integration of Event Graphs + BPMN-style process models + GPSS/SIMAN/Arena-style process models

Key Insight #1

DES and BPM Should
Learn from Each Other

  1. Strengths of Discrete Event Simulation (DES): more general/advanced forms of resource modeling
  2. Strengths of Business Process Modeling (BPM): declarative resource modeling and a standardized diagram language (BPMN)
  3. DES should adopt BPMN-style Process Diagrams and declarative resource modeling from BPMN
  4. BPMN should adopt the more general resource modeling features from DES

Key Insight #2

DES Tools Lack a Scientific Foundation

  1. ArenaSimul8AnyLogic
    EntityWork ItemAgent
    CreateStart PointSource
    Process Queue+ActivityService or Seize+Delay+Release
    DisposeEnd PointSink
    Proprietary terminologies and diagram languages
  2. No common conceptual basis
  3. No formal semantics

Key Insight #3

Event Graphs Are the Most Fundamental M&S Approach

  1. Event Graphs (Schruben 1983) allow making process models in terms of events and the state changes and follow-up events triggered by them
  2. They define an intuitive diagram language (with a formal/operational semantics) for Event-Based Simulation models
  3. Other approaches should only be considered as DES, if they conservatively extend Event Graphs

Key Insight #4

Business Processes are not Petri Nets, but Event Graphs!

  1. It has been an unfortunate choice in the history of BPM to view business process models as Petri Nets.
  2. Petri Nets are an abstract low-level computational formalism without ontological foundations.
  3. Mapping business process models to Petri Nets, instead of Event Graphs, for obtaining their semantics is like mapping SQL queries to Assembler code instead of predicate logic formulas.

Key Insight #5

There Are Two Kinds of Business Processes

  1. BPMN-style Activity Networks with a flow of events, where activity nodes have task queues.
  2. GPSS/SIMAN/Arena-style Processing Networks with a flow of objects and events, where processing nodes have object and task queues.

Key Insight #6

Declarative versus Procedural Resource Modeling

In declarative resource modeling, you just state which resources are required by an activity, instead of explicitly modeling their (de-)allocation steps.

Declarative resource modeling: resource roles in BPMN/DPMN is superior to Procedural resource modeling: Seize-Delay-Release in DES

Part I: Event Graphs and Basic DPMN

Event Graphs (EGs)

... have been proposed for DES modeling by Schruben in 1983.


The integer variable L denotes the length of the input buffer.
The Boolean variable B denotes the busy/available status of the "server".

Strengths and Weaknesses of EGs


  1. EGs provide an intuitive visual modeling language:
    events cause state changes and follow-up events.
  2. EGs capture/define the semantics of Event-Based Simulation
    with event scheduling.


  1. EGs lack a visual notation for conditional and parallel branching.
  2. EGs do not support objects with attributes (OO modeling).
  3. EGs do not support activities.

Object Event Modeling and Simulation (OEM&S)

Service Desk Event Graph

... extends Event-Based Simulation by adding objects, activities, and more. Formal semantics defined in Gerd Wagner: An Abstract State Machine Semantics For Discrete Event Simulation, Proc. of WSC 2017.

Service Desk Information Model

A DPMN process model is based on an underlying OE class model defining the types of its objects and events.

The Layers of DPMN (1)

Event Graphs (Schruben 1983)Events, Event Scheduling Arrows, Assignments
Object Event Simulation Object Event Graphs (Basic DPMN)+ Objects w/ State Changes
DPMN with Resource-Constrained Activities
  • Activities
  • Resource-Dependent Activity Scheduling Arrows
  • Resource Roles
  • Resource Multiplicity Constraints
  • Resource Pools

The Layers of DPMN (2)

Object Event Simulation Object Event Graphs (Basic DPMN)+ Objects w/ State Changes
DPMN with Resource-Constrained Activities
  • Activities
  • Resource Roles
  • Resource Multiplicity Constraints
  • Resource Pools
  • Resource-Dependent Activity Scheduling Arrows
DPMN with Processing Activities
  • Processing Activities
  • Entry/Processing/Exit Nodes
  • Processing Flow Arrows

Part II: Modeling Activity Networks with DPMN

Introducing Activities
as Paired Start/End Events

Resource-Dependent Activity Scheduling Arrows

DPMN Process Design Model Pizza-Server-1

DPMN Process Design Model Pizza-Server-2

The Make-and-Deliver-Pizza Model

  • A pizza service company takes phone orders
  • for making and delivering pizzas,
  • with the help of order takers, pizza makers, ovens and a crew of pizza delivery scooter drivers.
OE Class Design Model Pizza Service

OE Class Model

«rv» = random variable

DPMN Process Model

DPMN Process Design Model Pizza Service
Run the model with OESjs
from the presentation web page

The Load-Haul-Dump Model

  • A haul service company accepts requests for hauling large quantities of earth from a loading site to a dump site,
  • using dump trucks and wheel loaders.

DPMN Process Model

process design model Load-Haul-Dump
Run the model with OESjs

Part III: Modeling Processing Networks with DPMN

Processing Networks

  1. ... generalize Queueing Networks (M/M/c, etc.)
  2. ... have been pioneered by GPSS (1961), SIMAN (1982) and Arena (1992)
  3. ... are often characterized by "entities flowing through a system"
  4. More precisely:
    1. A Processing Object enters a Processing Network via an Arrival event at an Entry Station,
    2. is subsequently routed along a chain of Processing Stations where it is subject to Processing Activities,
    3. and finally exits the network via a Departure event at an Exit Station.

A Single Workstation System as a Processing Network

A Processing Flow arrow represents a combined object and event flow.

The Real Meaning of Processing Network Nodes

Event/activity flows are complemented by corresponding flows of processing objects.

Processing Networks extend Activity Networks, which extend Event Graphs.

The Diagnostic Department Model

A diagnostic department of a hospital performs electrocardiography (ECG) and ultrasound scans (US).

Run the model with OESjs

Summary and Outlook


  • OEM&S is a new DES paradigm with a formal semantics and an ontological foundation, extending Event-Based Simulation (Event Graphs).
  • The preferred modeling languages for OEM&S are OE/UML Class Diagrams and DPMN Process Diagrams.
  • OES has been implemented in JavaScript and Java, a Python implementation is work in progress.
  • DPMN supports Activity-Based Discrete Event Simulation including
    • BPMN-style Activity Networks
    • and GPSS/SIMAN/Arena-style Processing Networks

Next Steps

  1. Extend OEM&S by adding Agents with Beliefs, Perceptions, Actions and Communication.

Provide Inspiration

  1. DPMN can inspire the improvement of BPMN
  2. DPMN can inspire the improvement and harmonization of process modeling in DES tools (Arena/Simio/AnyLogic/etc.)