Object Event Simulation (OES)

A New DES Paradigm with a Formal Semantics

Gerd Wagner

Brandenburg University of Technology

Germany

Overview

• Prolog: Conceptual Confusion in Discrete Event Simulation (DES)
• Part I: Discrete Dynamic Systems
• Part II: Information Modeling with UML Class Diagrams
• Part III: Process Modeling with Extended Event Graphs
• Part IV: Simulation with OESjs

Are You also Confused about...

• What is Discrete Event Simulation (DES)?
• What is an Activity?
• What is a Process?
• What is Process-Oriented Simulation?
• What is Process-Interaction Simulation?
• What is an agent, as opposed to an object? What is Agent-Based Simulation?
• Where are the objects, and why is there no OO Modeling, in DES?
• Why is there no standard modeling language in DES, except Event Graphs (Schruben 1983)?
• Why are Event Graphs hardly used?

Some Observations

• There is a lot of conceptual confusion in DES.
• DES textbooks avoid defining DES.
• Event-Based Simulation, as defined by Event Graphs, is the foundation of DES.
• All other DES languages/frameworks should extend Event-Based Simulation.
• Activities, as an important high-level modeling concept, should be defined on top of events.
• "Process-Oriented" Simulation is, in fact, about Queuing/Processing Networks.
• Processing Network models ("entities flowing through a system") are a special class of DES models.

Modeling Language Usage

Conceptual Confusion

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 state at t (as a combination of the states of all objects of the system), 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 an Extended Event Graph (or a basic DPMN Process Diagram).

Defining Object and Event Types

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 allow combining events and 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 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)

A DPMN Process Model is composed of Event Rule Models.

An event rule model for
the PartArrival Event

An event rule model for
the ProcessingStart Event

An event rule model for
the ProcessingEnd Event

A DPMN Model of
the Workstation Process

An OESjs Model of the Workstation Process

... consists of

• an object type definition: Workstation
• three event type definitions:
  PartArrival, ProcessingStart and ProcessingEnd

It can be run as an online simulation at https://sim4edu.com/sims/102.

Workstation.js

var WorkStation = new cLASS({
  Name: "WorkStation",
  supertypeName: "oBJECT",
  properties: {
    "inputBufferLength": {range: "NonNegativeInteger",
        label: "Input buffer length"},
    "status": {range: WorkstationStatusEL, label: "Status"}
  }
});

PartArrival.js

var PartArrival = new cLASS({
  Name: "PartArrival",
  supertypeName: "eVENT",
  properties: {
    "workStation": {range: "WorkStation", label:"Workstation"}
  },
  methods: {
    "onEvent": function () {
      var events=[], ws = this.workStation;
      // add part to buffer
      ws.inputBufferLength++;
      // update statistics
      sim.stat.arrivedParts++;
      // if the work station is available
      if (ws.status === WorkstationStatusEL.AVAILABLE) {
        // schedule the part's processing start event
        events.push( new ProcessingStart({ workStation: ws}));
      }
      return events;
    }
  }
});

Conclusion and Outlook

• OES is a new DES paradigm with a formal semantics and an ontological foundation.
• The preferred modeling languages for OES are UML Class Diagrams and DPMN Process Diagrams.
• OES has been implemented in JavaScript, a Python implementation will follow.
• Basic OES can be extended by adding Activities, Processing Networks, Agents, etc.

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