Modeling and Simulation of

Organizations and Business Processes with

DPMN

Overview

• Setting the Scene
• Part I: Discrete Dynamic Systems
• Part II: Object-Event Modeling and Simulation (OEM&S)
• Part III: Outlook

First Things First

What's wrong with BPMN?

1. A limited concept of "business process" (e.g., only human resources)
2. Overloading/ambiguity of sequence flow arrows
3. Insufficient integration of the objects that participate in a process
4. Insufficient support of resource management
5. No support of processing activities
6. No convincing formal semantics

Baking a Blueberry Cake

Baking with Two Performers

A Haul Service Company

Compare with DPMN

BPM versus DES (1)

• When a BPM language allows simulation, it does have an execution semantics
• There are various proposals how to extend BPMN for BPS: Signavio, BIMP (Univ. Tartu), etc.)
• All of them result in quite limited forms of BPS:
  • no conditional branching
  • only human, but no other, resources
  • lack of support for important resource management features (alternative resources, pre-emption)

BPM versus DES (2)

1. In DES, there are many paradigms (and a lot of conceptual confusion)
2. The two main paradigms are Event-Based Simulation and (higher-level) Processing Network (PN) Simulation
3. There are 10+ commercial DES tools, all of them focusing on PN Simulation, but with different (proprietary) terminologies and diagram languages
4. PN Simulation is a form of BPS, but it is incompatible with BPMN

What is a Discrete Dynamic System (DDS)?

A real world system consisting of objects and a discrete flow of events such that at any moment in time, the system's past is a sequence of situations each characterized by

1. a time point t (the situation time)
2. the system's object states O at t , and
3. a set of imminent events, to occur at times greater than t.

and each situation S_t+1 is created from S_t via causal regularities triggered through the events occuring at t.

Causal Regularities

An event e@t causes:

1. state changes Δ of affected objects, and
2. follow-up events e₁@t₁, e₂@t₂,...

according to the dispositions of affected objects, which can be generalized as causal regularities of the form

with O being the set of the system's object states at time t, such that

is the resulting changed system state.

Modeling a DDS

Computationally, a DDS can be represented by an Object Event Model (OEM) consisting of:

1. object types OT, e.g., in the form of classes of an object-oriented language;

2. event types ET, e.g., in the form of classes of an object-oriented language;

3. event rules R representing causal regularities, e.g., in the form of onEvent methods of the class that implements the triggering event type.

While OT and ET can be defined by a UML Class Diagram, the set of event rules R can be defined by a DPMN Process Diagram.

Events and Discrete Processes

1. Discrete processes are governed by causal regularities, which relate events with (1) state changes of affected objects and (2) follow-up events.
2. A discrete process consists of a partially ordered set of events that happen in a spatio-temporal region determined by the events' participants and the causal regularities involved.
3. A business process is a discrete process that "happens in the context of an organization".

Modeling Objects and Events (1)

1. Since events depend on objects, we first need to model object types and then event types.
2. A process model is based on an underlying information model defining the types of its objects and events.
3. A conceptual process model describes the causal regularities of a real world process.

Modeling Objects and Events (2)

1. A simulation design model consists of an information design model and a process design model.
2. An information design model defines object types and event types (e.g., in the form of classes in a UML Class Diagram).
3. A process design model defines event rules that represent causal regularities (e.g., in a DPMN Process Diagram).

Event Graphs

Event Graphs (EGs) have been proposed for DES modeling by Schruben in 1983.

Strengths:

• EGs provide an intuitive visual modeling language.
• EGs capture the fundamental event scheduling paradigm.

Weaknesses:

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

An Event Graph Model

The integer variable L denotes the length of the input buffer.
The Boolean variable B denotes the busy/available status of the service desk or machine.

DPMN

...is the Discrete Event Process Modeling Notation, which extends Event Graphs by adding:

1. Exclusive/Inclusive/Parallel Gateways for conditional/parallel branching
2. Data Objects for replacing "state variables" (like L) with attributes (like WorkStation::inputBufferLength)
3. Activities

A DPMN Process Model is composed of Event Rule Models.

Conclusion and Outlook

• OEM&S is a new modeling and simulation paradigm with a formal semantics and an ontological foundation.
• The preferred modeling languages for OEM&S are UML Class Diagrams and DPMN Process Diagrams.
• OES has been implemented in JavaScript, a Python implementation will follow.
• DPMN allows modeling of message-based communication (with out-message and in-message events).
• OEM&S can be extended by adding Agents with Beliefs about, and Perceptions of, their environment
• How to model (DEMO) transactions in DPMN still has to be investigated.

See also

• Gerd Wagner: An Abstract State Machine Semantics For Discrete Event Simulation, Proc. of the 2017 Winter Simulation Conference.
• Gerd Wagner: Information and Process Modeling for Simulation – Part I: Objects and Events. Journal of Simulation Engineering 1:1, 2018.
• Gerd Wagner: Information and Process Modeling for Simulation – Part II: Activities and Processing Networks. 2019.
• Available on dpmn.info