Journal of Simulation Engineering, 1:1. Available from: http://JSimE.org

# Information and Process Modeling for Simulation – Part I: Objects and Events

Gerd Wagner
G.Wagner@b-tu.de
Dept. of Informatics, Brandenburg University of Technology, Cottbus, GERMANY

# ACM Subject Categories

• Computing methodologies~Modeling methodologies

# Keywords

• Conceptual Model
• Design Model
• Information Model
• Process Model

# Abstract

In simulation engineering, a system model mainly consists of an information model and a process model. In the fields of Information Systems and Software Engineering (IS/SE) there are widely used standards such as the Class Diagrams of the Unified Modeling Language (UML) for making information models, and the Business Process Modeling Notation (BPMN) for making process models. This tutorial presents a general approach how to use UML class diagrams and BPMN process diagrams at all three levels of model-driven simulation engineering: for making conceptual domain models, for making platform-independent simulation design models, and for making platform-specific, executable simulation models. In our Object-Event Modeling (OEM) approach, object and event types are modeled as stereotyped classes, random variables are modeled as stereotyped operations constrained to comply with a specific probability distribution, and queues are modeled as ordered association ends, while event rules are modeled both as BPMN process diagrams and in pseudo-code. In Part II, we will discuss the more advanced modeling concepts of activities and GPSS/SIMAN/Arena-style Processing Networks, while in Part III we will further extend the OEM framework by adding the concepts of agents with perceptions, actions and beliefs.

# Introduction

The term simulation engineering denotes the scientific engineering discipline concerned with the development of computer simulations, which are a special class of software applications. Since a running computer simulation is a particular kind of software system, we may consider simulation engineering as a special case of software engineering.

Even though there is a common agreement that modeling is an important first step in a simulation project, at the same time it is thought to be the least understood part of simulation engineering (Tako, Kotiadis, & Vasilakis, 2010). In a panel discussion on conceptual simulation modeling (Zee, et al., 2010), the participants agreed that there is a lack of standards, on procedures, notation, and model qualities. On the other hand, there is no such lack in the field of Information Systems and Software Engineering (IS/SE) where widely used standards such as the Unified Modeling Language (UML) and the Business Process Modeling Notation (BPMN) and various modeling methodologies and model quality assurance methods have been established.

The standard view in the simulation literature, see, e.g., (Himmelspach, 2009), is that a simulation model can be expressed either in a general purpose programming language or in a specialized simulation language. This means that the term model in simulation model typically refers to a low-level computer program and not to a model expressed in a higher-level diagrammatic modeling language. In a modeling and simulation project, despite the fact that modeling is part of the discipline’s name, often no model in the sense of a conceptual model or a design model is made, but rather the modeler jumps from her mental model to its implementation in some target technology platform. Clearly, as in IS/SE, making conceptual models and design models would be important for several reasons: as opposed to a low-level computer program, a high-level model would be more comprehensible and easier to communicate, share, reuse, maintain and evolve, while it could still be used for obtaining platform-specific implementation code, possibly with the help of model transformations and code generation.

Due to their great expressivity and their wide adoption as modeling standards, UML and BPMN seem to be the best choices for making information and process models in a model-based simulation engineering approach. However, since they have not been specifically designed for this purpose, we may have to restrict, modify and extend them in a suitable way.

Several authors, e.g. (Wagner, Nicolae, & Werner, 2009), (Cetinkaya, Verbraeck, & Seck, 2011), and (Onggo & Karpat, 2011), have proposed to use BPMN for discrete event simulation modeling and for agent-based modeling. However, process modeling in general is much less understood than information modeling, and there are no guidelines and no best practices how to use BPMN for simulation modeling. Schruben (1983), with his Event Graph diagram language, has pioneered the research on process modeling languages for discrete event simulation based on the modeling concept of event types and the operational semantics concept of event scheduling with a future events list. We consider the fact that Event Graphs overlap with a fragment of BPMN as an indication that BPMN has the potential to be used as the basis of a general process modeling language for discrete event simulation.

In this tutorial article, which is extending and improving (Wagner, 2017b), we provide short introductions to model-driven engineering, to information modeling with UML class diagrams, and to process modeling with BPMN diagrams, and then show how to use a model-based simulation engineering approach for developing basic discrete event simulations (DES). In a forthcoming Part II of this tutorial, we will discuss the more advanced modeling concepts of activities and GPSS/SIMAN/Arena-style Processing Networks where work objects flow through the system by entering it through an arrival event at an entry node, then passing one or more processing nodes, participating in their processing activities, and finally leaving it through a departure event at an exit node. Finally, in Part III, we will show how to add the modeling concepts of agents with perceptions, actions and beliefs for obtaining a general agent-based DES modeling approach.

In our Object-Event Modeling (OEM) approach, object and event types are modeled as stereotyped classes that can be implemented with any object-oriented (OO) programming language or simulation library/framework. Random variables are modeled as stereotyped operations constrained to comply with a specific probability distribution such that they can be implemented as methods of an object or event class with any OO simulation technology. Queues are not modeled as objects, but rather as ordered association ends, which can be implemented as collection-valued reference properties. Finally, event rules, which include event routines, are modeled both as BPMN process diagrams and in pseudo-code such that they can be implemented in the form of special onEvent methods of event classes.

The OEM approach results in a simulation design model that has a well-defined operational semantics, as shown in (Wagner, 2017a). Such a model can, in principle, be implemented with any OO simulation technology. However, a straightforward implementation can only be expected from a technology that implements the Object-Event Simulation (OES) paradigm proposed in (Wagner, 2017a), such as the OES JavaScript (OESjs) framework presented in (Wagner, 2017c).

There are two examples of systems, which are paradigmatic for DES (and for operations research): service systems with queues (also called queuing networks) and inventory management systems. However, neither of them has yet been presented with elaborate information and process models in tutorials or textbooks. In this tutorial, we show how to make information and process models of an inventory management system and of a service system, and how to code them using the JavaScript-based simulation framework OESjs.

# What Is Discrete Event Simulation?

The term Discrete Event Simulation (DES) has been established as an umbrella term subsuming various kinds of computer simulation approaches, all based on the general idea of modeling entities/objects and events. In the DES literature, it is often stated that DES is based on the concept of entities flowing through the system (more precisely, through a queueing network). E.g., this is the paradigm of an entire class of simulation software in the tradition of GPSS (Gordon, 1961) and SIMAN/Arena (Pegden & Davis, 1992). However, this paradigm characterizes a special (yet important) class of DES only, it does not apply to all discrete dynamic systems.

In Ontology, which is the philosophical study of what there is, entities (also called individuals) are distinguished from entity types (called universals). There are three fundamental categories of entities:

1. objects,

2. tropes, which are existentially dependent entities such as the qualities and dispositions of objects and their relationships with each other, and

3. events.

These ontological distinctions are discussed, e.g., by Guizzardi and Wagner (2010a, 2010b, 2013).

While the concept of an event is often limited to instantaneous events in the area of DES, the general concept of an event, as discussed in philosophy and in many fields of computer science, includes composite events and events with non-zero duration.

A discrete event system (or discrete dynamic system) consists of

• objects (of various types),

• events (of various types),

• dispositions of objects triggered by events,

such that the states of objects may be changed by events occurring at times from a discrete set of time points, according to the dispositions of the objects triggered by the events.

For modeling a discrete event system as a state transition system, we have to describe its

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

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

3. causal regularities (disposition types) e.g., in the form of event rules.

Any discrete event simulation (DES) formalism has one or more language elements allowing to specify, at least implicitly, event rules that allow representing causal regularities. These rules specify, for any event type, the state changes of objects and the follow-up events caused by the occurrence of an event of that type, thus defining the dynamics of the transition system. Unfortunately, this is often obscured by the standard definitions of DES that are repeatedly presented in simulation textbooks and tutorials.

According to (Pegden, 2010), a simulation modeling worldview provides a framework for defining a system in sufficient detail that it can be executed to simulate the behavior of the system. It must precisely define the dynamic state transitions that occur over time. Pegden continues saying that Over the 50 year history of simulation there has been three distinct world views in use: event, process, and objects:

Event worldview: The system is viewed as a series of instantaneous events that change the state of the system over time. The modeler defines the events in the system and models the state changes that take place when those events occur. According to Pegden, the event worldview is the most fundamental worldview since the other worldviews also use events, at least implicitly.

Processing Network worldview: The system under investigation is described as a processing network where entities flow through the system (or, more precisely, work objects are routed through the network) and are subject to a series of processing steps performed at processing nodes through processing activities, possibly requiring resources and inducing queues of work objects waiting for the availability of resources (processing networks have been called queueing networks in Operations Research). This approach allows high-level modeling with semi-visual languages and is therefore the most widely used DES approach nowadays, in particular in manufacturing industries and service industries. Simulation platforms based on this worldview may or may not support object-oriented modeling and programming.

Object worldview: The system is modeled by describing the objects that make up the system. The system behavior emerges from the interaction of these objects.

All three worldviews lack important conceptual elements. The event worldview does not consider objects with their (categorical and dispositional) properties. The Processing Network worldview neither considers events nor objects. And the object worldview, while it considers objects with their categorical properties, does not consider events. None of the three worldviews includes modeling the dispositional properties of objects with a full-fledged explicit concept of event rules.

The event worldview and the object worldview can be combined in approaches that support both objects and events as first-class citizens. This seems highly desirable because (1) objects (and classes) are a must-have in today’s state-of-the-art modeling and programming, and (2) a general concept of events is fundamental in DES, as demonstrated by the classical event worldview. We use the term object-event worldview for any DES approach combining object-oriented (OO) modeling and programming with a general concept of events.

# Model-Driven Engineering

Model-Driven Engineering (MDE), also called model-driven development, is a well-established paradigm in IS/SE. Since simulation engineering can be viewed as a special case of software engineering, it is natural to apply the ideas of MDE also to simulation engineering. There have been several proposals of using an MDE approach in Modeling and Simulation (M&S), see, e.g., the overview given in (Cetinkaya & Verbraeck, 2011).

In MDE, there is a clear distinction between three kinds of models as engineering artifacts resulting from corresponding activities in the analysis, design and implementation phases:

1. domain models (also called conceptual models),

2. platform-independent design models,

3. platform-specific implementation models.

Domain models are solution-independent descriptions of a problem domain produced in the analysis phase of a software engineering project. We follow the IS/SE usage of the term ‘conceptual model’ as a synonym of ‘domain model’. However, in the M&S literature there are diverging proposals how to define the term ‘conceptual model’, see, e.g., (Guizzardi & Wagner, 2012) and (Robinson, 2013). A domain model may include both descriptions of the domain’s state structure (in conceptual information models) and descriptions of its processes (in conceptual process models). They are solution-independent, or ‘computation-independent’, in the sense that they are not concerned with making any system design choices or with other computational issues. Rather, they focus on the perspective and language of the subject matter experts for the domain under consideration.

In the design phase, first a platform-independent design model, as a general computational solution, is developed on the basis of the domain model. The same domain model can potentially be used to produce a number of (even radically) different design models. Then, by taking into consideration a number of implementation issues ranging from architectural styles, nonfunctional quality criteria to be maximized (e.g., performance, adaptability) and target technology platforms, one or more platform-specific implementation models are derived from the design model. These one-to-many relationships between conceptual models, design models and implementation models are illustrated in Figure 1.

In the implementation phase, an implementation model is coded in the programming language of the target platform. Finally, after testing and debugging, the implemented solution is then deployed in a target environment.

A model for a software (or information) system, which may be called a ‘software system model’, does not consist of just one model diagram including all viewpoints or aspects of the system to be developed (or to be documented). Rather it consists of a set of models, one (or more) for each viewpoint. The two most important viewpoints, crosscutting all three modeling levels: domain, design and implementation, are

1. information modeling, which is concerned with the state structure of the domain;

2. process modeling, which is concerned with the dynamics of the domain.

In the computer science field of database engineering, which is only concerned with information modeling, domain information models have been called ‘conceptual models’, information design models have been called ‘logical design models’, and database implementation models have been called ‘physical design models’. In the sequel, we call information implementation models data models or class models. So, from a given information design model, we may derive an SQL data model, a Java class model and a C# class model.

Examples of widely used languages for information modeling are Entity Relationship (ER) Diagrams and UML Class Diagrams. Since the latter subsume the former, we prefer using UML class diagrams for making all kinds of information models, including SQL database models. Examples of widely used languages for process modeling are (Colored) Petri Nets, UML Sequence Diagrams, UML Activity Diagrams and the BPMN. Notice that there is more agreement on the right concepts for information modeling than for process modeling, as indicated by the much larger number of different process modeling languages. We claim that this reflects a lower degree of understanding the nature of events and processes compared to understanding objects and their relationships.

Some modeling languages, such as UML Class Diagrams and BPMN, can be used on all three modeling levels in the form of tailored variants. Other languages have been designed for being used on one or two of these three levels only. E.g. Petri Nets cannot be used for conceptual process modeling, since they lack the required expressivity.

We illustrate the distinction between the three modeling levels with an example in Figure 2 below. In a simple conceptual information model of people, expressed as a UML class diagram, we require that any person has exactly one mother, expressed by a corresponding binary many-to-one association, while we represent this association with a corresponding reference property mother in the object-oriented (OO) class model. Also, we may not care about the datatypes of attributes in the conceptual model, while we do care about them in the design model, where we use platform-independent datatype names (such as Decimal), and in the C++ class model where we use C++ datatypes (such as double). Following OO programming conventions, we add get and set methods for all attributes, and we specify the visibility private (symbolically -) for attributes and public (symbolically +) for methods, in the OO class model. Finally, in the C++ class model, we use the pointer type Person* instead of Person for implementing a reference property.

Model-driven simulation engineering is based on the same kinds of models as model-driven software engineering: going from a domain model via a design model to an implementation model for the simulation platform of choice (or to several implementation models if there are several target simulation platforms). The specific concerns of simulation engineering, like, e.g., the concern to capture certain parts of the overall system dynamics with the help of random variables, do not affect the applicability of MDE principles. However, they define requirements for the modeling languages to be used.

# Information Modeling with UML Class Diagrams

Conceptual information modeling is mainly concerned with describing the relevant entity types of a real-world domain and the relationships between them, while information design and implementation modeling is concerned with describing the logical (or platform-independent) and platform-specific data structures (in the form of classes) for designing and implementing a software system or simulation. The most important kinds of relationships between entity types to be described in an information model are associations, which are called ‘relationship types’ in ER modeling, and subtype/supertype relationships, which are called ‘generalizations’ in UML. In addition, one may model various kinds of part-whole relationships between different kinds of aggregate entities and component entities, but this is an advanced topic that is not covered in this tutorial.

As explained in the introduction, we are using the visual modeling language of UML Class Diagrams for information modeling. In this language, an entity type is described with a name, and possibly with a list of properties and operations (called methods when implemented), in the form of a class rectangle with one, two or three compartments, depending on the presence of properties and operations. Integrity constraints, which are conditions that must be satisfied by the instances of a type, can be expressed in special ways when defining properties or they can be explicitly attached to an entity type in the form of an invariant box.

An association between two entity types is expressed as a connection line between the two class rectangles representing the entity types. The connection line is annotated with multiplicity expressions at both ends. A multiplicity expression has the form m..n where m is a non-negative natural number denoting the minimum cardinality, and n is a positive natural number (or the special symbol * standing for unbounded) denoting the maximum cardinality, of the sets of associated entities. Typically, a multiplicity expression states an integrity constraint. For instance, the multiplicity expression 1..3 means that there are at least 1 and at most 3 associated entities. However, the special multiplicity expression 0..* (also expressed as *) means that there is no constraint since the minimum cardinality is zero and the maximum cardinality is unbounded.

For instance, the model shown in Figure 3 below describes the entity types Shop and Delivery, and it states that

1. there are two classes: Shop and Delivery, representing entity types;

2. there is a one-to-many association between the classes Shop and Delivery, where a shop is the receiver of a delivery.

Using further compartments in class rectangles, we can add properties and operations. For instance, in the model shown in Figure 4, we have added

1. the properties name and stockQuantity to Shop and quantity to Delivery,

2. the instance-level operation onEvent to Delivery,

3. the class-level operation leadTime to Delivery.

Notice that in Figure 4, each property is declared together with a datatype as its range. Likewise, operations are declared with a (possibly empty) list of parameters, and with an optional return value type. When an operation (or property) declaration is underlined, this means that it is class-level instead of instance-level. For instance, the underlined operation declaration leadTime() : Decimal indicates that leadTime is a class-level operation that does not take any argument and returns an integer.

We may want to define various types of integrity constraints for better capturing the semantics of entity types, properties and operations. The model shown in Figure 5 contains an example of a property constraint and an example of an operation constraint. These types of constraints can be expressed within curly braces appended to a property or operation declaration. The keyword id in the declaration of the property name in the Shop class expresses an ID constraint stating that the property is a standard identifier, or primary key, attribute. The expression Exp(0.5) in the declaration of the random variable operation leadTime in the Delivery class denotes the constraint that the operation must implement the exponential probability distribution function with event rate 0.5.

UML allows defining special categories of modeling elements called stereotypes. For instance, for distinguishing between object types and event types as two different categories of entity types we can define corresponding stereotypes of UML classes («object type» and «event type») and use them for categorizing classes in class models, as shown in Figure 6 below.

Another example of using UML’s stereotype feature is the designation of an operation as a function that represents a random variable using the operation stereotype «rv» in the diagram of Figure 6.

A class may be defined as abstract by writing its name in italics, as in the example model of Figure 11 below. An abstract class cannot have direct instances. It can only be indirectly instantiated by objects that are direct instances of a subclass.

For a short introduction to UML Class Diagrams, the reader is referred to (Ambler, 2010). A good overview of the most recent version of UML (2.5) is provided by www.uml-diagrams.org/uml-25-diagrams.html

# Process Modeling with BPMN

The Business Process Modeling Notation (BPMN) is an activity-based graphical modeling language for defining business processes following the flow-chart metaphor. In 2011, the Object Management Group (OMG) has released version 2.0 of BPMN with a semi-formal token flow semantics.

BPMN process diagrams can be used for documenting existing real-world business processes and for designing new business processes, which may be partially or fully automated with the help of information technology. The most important elements of a BPMN process model are listed in Table 1 below.

Ontologically, BPMN activities (or, more precisely, activity types) are special event types. However, the subsumption of activities under events is not supported by the standard semantics of BPMN. It is one of the issues that require further improvements of BPMN as a general process modeling language.

Another severe issue of the official BPMN (token flow) semantics is its limitation to case handling processes. Each start event represents a new case and starts a new process for handling this case in isolation from other cases. This semantics disallows, for instance, to model processes where several cases are handled in parallel and interact in some way, e.g., by competing for resources. Consequently, this semantics is inadequate for capturing the overall process of a business system with many actors performing tasks related to many cases with various interdependencies, in parallel. We do therefore not adopt the official BPMN semantics, but just the visual syntax of BPMN and large parts of the informal semantics of its elements. Defining a more general semantics for BPMN that is adequate for simulation modeling is still an open research issue.

Due to these issues, it is not clear at present how to best use BPMN, and how to adapt its syntax and semantics, for simulation modeling. Our proposal how to use BPMN for simulation modeling is therefore rather experimental and still needs to be evaluated and justified, e.g., by a formal semantics.

We claim that, despite these issues, using BPMN as a basis for developing a process simulation modeling approach is the best choice of a modeling language we can make, considering the alternatives, which are either not well-defined (Flow Charts, Logic Flow Diagrams) or not sufficiently expressive (Petri Nets, UML State Transition Diagrams, UML Activity Diagrams), and which are therefore all inferior compared to BPMN.

Name of element Meaning Visual symbol(s)

Event

Something that happens during the course of a process, affecting the process flow.

A Start Event is drawn as a circle with a thin border line, while an Intermediate Event has a double border line and an End Event has a thick border line.

Activity

Work that is performed within a process.

A Task is an atomic Activity, while a Sub-Process is a composite Activity. A Sub-Process can be either in a collapsed or in an expanded view. The latter shows its internal process structure.

Gateway

For conditional or parallel branching.

A single Gateway could have multiple input and multiple output flows. A gateway with an "X" symbol denotes an Exclusive OR-Split (if there are 2 or more output flows) or an Exclusive OR-Join (if there are 2 or more input flows). A gateway with a plus symbol denotes an AND-Split (if there are 2 or more output flows) or an AND-Join (if there are 2 or more input flows).

Sequence Flow

Defines the temporal order of Events, Activities, and Gateways.

Data Object

Data Objects may be associated with Events or Activities, providing a context for reading/writing data.

Table 1. Basic elements of BPMN.

For an introductory BPMN tutorial, the reader is referred to (BPMN 2.0 Tutorial, 2017). A good modeling tool, with the advantages of an online solution, is the Signavio Process Editor, which is free for academic use.

# Example 1: Modeling an Inventory Management System

We consider a simple case of inventory management: a shop selling one product type (e.g., one model of TVs), only, such that its in-house inventory only consists of items of that type. On each business day, customers come to the shop and place their orders. If the ordered product quantity is in stock, the customer pays her order and the ordered products are handed out to her. Otherwise, the order may still be partially fulfilled, if there are still some items in stock, else the customer has to leave the shop without any item. If an order quantity is greater than the current stock level, the difference counts as a lost sale.

When the stock quantity falls below the reorder point, a replenishment order is sent to the vendor for restocking the inventory, and the ordered quantity is delivered 1-3 days later.

The purpose of the simulation is to compute the average percentage of lost sales, which is an important performance indicator.

# Information Modeling

How should we start the information modeling process? Should we first model object types and then event types, or the other way around? Here, the right order is dictated by existential dependencies. Since events existentially depend on the objects that participate in them, which is an ontological pattern that is fundamental for DES, see, e.g., (Guizzardi & Wagner, 2010b), we first model object types, together with their associations, and then add event types on top of them.

A conceptual information model describes the subject matter vocabulary used, e.g., in the system narrative, in a semi-formal way. Such a vocabulary essentially consists of names for

1. types, corresponding to classes in OO modeling, or unary predicates in formal logic;

2. properties, corresponding to binary predicates in formal logic;

3. associations, corresponding to n-ary predicates (with n > 1) in formal logic.

The main categories of types are object types and event types. A simple form of conceptual information model is obtained by providing a list of each of them, while a more elaborated model, preferably in the form of a UML class diagram, also defines properties and associations, including the participation of objects (of certain types) in events (of certain types).

An information design model is normally derived from a conceptual information model by choosing the design-relevant types of objects and events and enrich them with design details, while dropping other object types and event types not deemed relevant for the simulation design. Adding design details includes specifying property ranges as well as adding multiplicity and other types of constraints.

In addition to these general information modeling issues, there are also a few issues, which are specific for simulation modeling:

1. Due to the ontological pattern of objects participating in events, we always have special (participation) associations between object classes and event classes. Typically, they will have role names at the association ends that touch the object classes. These role names will be turned into names of corresponding reference properties of the event class in an OO class model, allowing the event rule method onEvent to access the properties of the objects participating in an event both for testing conditions and for applying state changes.

2. Certain simulation variables may be subject to random variation, so they can be considered to be random variables with an underlying probability distribution that is sampled by a corresponding method stereotyped «rv» for categorizing it as a random variate sampling method. The underlying probability distribution can be indicated in the model diagram by appending a symbolic expression, denoting a distribution (with parameter values), to the method definition clause. For instance, U(1,6) may denote the uniform distribution with lower bound 1 and upper bound 6, while Exp(1.5) may denote the exponential distribution with event rate 1.5.

3. The information design model must distinguish between exogenous and caused (or endogenous) event types. For any exogenous event type, the recurrence of events of that type must be specified, typically in the form of a random variable, but in some cases it may be a constant (like 'on each Monday'). The recurrence defines the elapsed time between two consecutive events of the given type (their inter-occurrence time). It can be specified within the event class concerned in the form of a special method with the predefined name 'recurrence'.

4. The queues of a queueing system are modeled in the form of ordered association ends, which represent ordered-collection-valued reference properties. For instance, in our service desk model shown in Figure 19 below, there is an association between the classes ServiceDesk and Customer with an ordered association end named waitingCustomers representing a queue. The annotation {ordered} means that the collection of Customer instances associated with a particular ServiceDesk is a linearly ordered set that allows to retrieve (or pop) the next customer from the waitingCustomers queue.

# Making a Solution-Independent Conceptual Information Model

We can extract the following candidates for object types from the problem description above by identifying and analyzing the domain-specific noun phrases: shops (for being more precise, we also say single product shops), products (or items), inventories, customers, customer orders, replenishment orders, and vendors. Since noun phrases may also denote events (or event types), we need to take another look at our list and drop those noun phrases. We recognize that customer orders and replenishment orders denote messages or communication events, and not ordinary objects. This leaves us with the five object types described in the diagram shown in Figure 7 below.

Later, when we make a design for a simulation model we make several simplifications based on our simulation research questions. For instance, we may abstract away from the object types products and vendors. But in a conceptual system model, we include all entity types that are relevant for understanding the real-world system, independently of the simplifications we may later make in the solution design and implementation. This approach results in a model that can be re-used in other simulation projects with the same problem domain, but with different research questions.

Notice that we have also modeled the following associations between these five object types:

1. The (named) many-to-many association customers–order-from–shops.

2. The (un-named) one-to-one association shops–have–products.

3. The (un-named) one-to-one association shops–have–inventories.

4. The (named) many-to-one association shops–order-from–vendors.

The second association is one-to-one because we are assuming that our shops only sell a single product, while the third association is one-to-one because we assume that our shops only have one inventory for their single product.

We have also added some attributes to the model’s object types, such as a name attribute for customers, shops, products and vendors, and a reorder point as well as a stock quantity attribute for inventories. Some of these attributes can be found in the problem description (such as reorder point), while others have to be inferred by commonsense reasoning (such as target inventory for the quantity to which the inventory is to be restocked).

In the next step, we add event types. We have already identified customer orders and replenishment orders as two potentially relevant event types mentioned as noun phrases in the problem description. We can try to extract the other potentially relevant event types from the text, typically by considering the verb phrases, such as pay order, hand out product, and deliver. For getting the names of our event types, we nominalize these verb phrases. So we get customer payments, product handovers and deliveries. Finally, even if this is not mentioned in the business description above, we know, using common sense, that a delivery by the vendor leads to a corresponding payment by the shop, so we also need a payments event type.

So we add these six event types to our model, together with their participation associations with involved object types, now distinguishing class rectangles that denote event types from those denoting object types with the help of UML stereotypes, as shown in Figure 8 below. For visual clarity, we use classes without a stereotype for representing object types (so we can omit the stereotype «object type» since it is the default).

Notice that a participation association between an object type and an event type is typically one-to-many, since an event of that type has typically exactly one participating object of that type, and, vice versa, an object of that type typically participates in many events of that type.

Notice that, for brevity, we omitted the event type for the shop declining a customer order. Even so, the model may seem quite large for a problem like inventory management. However, in a conceptual model, we describe a complete system including all object and event types that are relevant for understanding its dynamics.

Typically, in a simulation design model we would make several simplifications allowed by our research questions, and, for instance, abstract away from the object types products and inventories. But in a conceptual model of the system under investigation, we include all relevant entity types, independently of the simplifications we may later make in the solution design and implementation. This approach results in a conceptual model that can be re-used in other simulation projects (with different research questions).

# Making a Solution-Specific and Platform-Independent Information Design Model

We now derive an information design model from the solution-independent conceptual information model shown in Figure 8 above. Our design model is solution-specific because it is a computational design for the following specific research question: compute the percentage of lost sales (as the difference between the total number of ordered items and the total number of sold items divided by the total number of ordered items). It is platform-independent in the sense that it does not use any modeling element that is specific for a particular platform, such as a Java datatype.

In the first step, we take a decision about which object types and event types defined in the conceptual model can be dropped in the solution design model. The goal is to keep only those entity types in the model, which are needed for being able to answer the research question. One opportunity for simplification is to drop products and inventories because our assumptions imply that there is only one product and only one inventory, so we can leave them implicit and allocate their relevant attributes to the SingleProductShop class. As this class name indicates, in the design model, we follow a widely used naming convention: the name of a class is a capitalized singular noun phrase in mixed case.

Further analysis shows that we can drop the event types customer payments and vendor payments, since we don’t need any payment data, and also product handovers, since we don’t care about the point-of-sales logistics. This leaves us with three potentially relevant object types: customers, single product shops and vendors, and with three potentially relevant event types: customer orders, replenishment orders and deliveries.

There is still room for further simplification. Since for computing the percentage of lost sales, we don’t need the order quantities of individual orders, but only the total number of ordered items, it’s sufficient to model an aggregate of customer orders like, for instance, the daily demand. Consequently, we don’t need to consider individual customers and their orders. So, we can drop the object type customers and use the aggregate event type DailyDemand instead of customer orders. Since we don’t need any vendor information, we can also drop the object type vendors.

Finally, since we can now assume that replenishment orders are placed when a DailyDemand event has occurred, implying that any replenishment order event temporally coincides with a DailyDemand event, we can also drop the event type replenishment orders.

Thus, the simplifications of our first design modeling step lead to a model as shown in Figure 9.

Notice that the two associations model the participation of the shop both in DailyDemand events and in Delivery events, and the association end names shop and receiver represent the reference properties DailyDemand::shop and Delivery::receiver (as implied by the corresponding association end ownership dots). These reference properties allow to access the properties and invoke the methods of a shop from an event, which is essential for the event routine of each event type. Thus, the ontological pattern of objects participating in events and the implied software pattern of object reference properties in event types are the basis for defining event routines (and rules) in event types.

In the next step (step 2), we distinguish between two kinds of event types: exogenous event types and caused event types, and we also define for all attributes a platform-independent datatype as their range, using specific datatypes (such as PositiveInteger, instead of plain Integer, for the quantity of a delivery), as shown in Figure 10.

While exogenous events of a certain type occur again and again with some (typically random) recurrence, caused events occur at times that result from the internal causation dynamics of the simulation model. So, for any event type adopted from the conceptual model, we choose one of these two categories, and for any exogenous event type, we add a recurrence operation that is responsible for computing the time until the next event occurs.

In the model shown in Figure 10 above, we define DailyDemand as an exogenous event type with a recurrence of 1, implying that an event of this type occurs on each day, while we define Delivery as a caused event type.

# Deriving Platform-Specific Class Models from the Information Design Model

After choosing an object-oriented (OO) simulation platform based on the object-event paradigm (e.g., the JavaScript-based platform OESjs available from Sim4edu, or one of the Java-based platforms DESMO-J, JaamSim or AnyLogic), we can derive a platform-specific class model for this platform from the information design model.

In the language of such a platform, there would normally be two predefined abstract foundation classes for defining object types and event types. For instance, in OESjs, they are called oBJECT and eVENT, each with a set of generic properties and methods for implementing the two stereotypes «object type» and «event type». These two classes, with their name in italics for indicating that they are abstract, are used for deriving object types and event types in the OESjs class models shown in Figure 11 and Figure 12 below.

Notice that OESjs class models do no longer contain any explicit associations, which have been replaced with corresponding reference properties (like DailyDemand::shop and Delivery::receiver). This is the way associations are implemented in OO programing.

The onEvent operation in the eVENT class is abstract, as indicated by its name in italics. It just defines an operation signature for the event routines triggered by events. The concrete event routines are defined by the onEvent methods of the subclasses DailyDemand and Delivery. Notice that for handling the exogenous events of type DailyDemand, we have added a static createNextEvent method in DailyDemand for creating the next DailyDemand event by invoking both the demandQuantity method and the recurrence method, whenever a DailyDemand event has occurred.

# Coding a Platform-Specific Class Model

The classes defined in the OESjs class model shown in Figure 12 can be directly coded as OESjs classes. For instance, the object class SingleProductShop can be coded in the following way:

var SingleProductShop = new cLASS({
Name: "SingleProductShop",
supertypeName: "oBJECT",
properties: {
"stockQuantity": {range:"NonNegativeInteger", label:"Stock"},
"reorderPoint": {range:"NonNegativeInteger"},
"targetInventory": {range:"PositiveInteger"}
}
});

This class just has three simple data-valued properties (attributes), each defined with an integer range.

The event class DailyDemand can be coded in the following way:

var DailyDemand = new cLASS({
Name: "DailyDemand",
supertypeName: "eVENT",
properties: {
"quantity": {range: "PositiveInteger", label:"Quantity"},
"shop": {range: "SingleProductShop"}
},
methods: {
"onEvent": function () {...}
}
});
DailyDemand.recurrence = function () {...}
DailyDemand.createNextEvent = function () {...}
DailyDemand.demandQuantity = function () {...}

Notice that in the DailyDemand event class, we have a reference property shop allowing to access the properties of the shop object that participates in a DailyDemand event. We also have an onEvent method for implementing the event routine of the DailyDemand event type. In this method, the reference property shop can be used for retrieving or changing the state of the shop that participates in the DailyDemand event. We will discuss the code of this event routine below in the section on implementing the process design model.

The full code of this simulation model is available by loading the web-based simulation http://sim4edu.com/sims/4 and inspecting its JavaScript code in the browser.

# Process Modeling

We make a conceptual process model and a process design model for the inventory management system. These models can be expressed visually in the form of BPMN process diagrams and textually in the form of event rule tables.

A conceptual process model should include the event types identified in the conceptual information model, and describe in which temporal sequences events may occur, based on conditional and parallel branching. We can do this by describing, for each of the event types from the conceptual information model, the causal regularity associated with it in the form of an event rule that defines the state changes and follow-up events caused by events of that type.

For simplicity, we may merge those types of events, which can be considered to temporally coincide. This is the case whenever an event unconditionally causes an immediately succeeding follow-up event.

# Making a Conceptual Process Model

Since inventory management is part of a business system, it’s natural to make a kind of business process (BP) model describing actors and their activities, typically in response to events, as shown in Figure 13, where we model the two actors Customer and SingleProductShop, together with their interactions.

Notice that this traditional-style BP model suffers from the following BPMN deficiencies:

1. Activities/actions are not considered to be special events.

2. There is no semantic account of the activities/actions of one agent (such as Customer) being events for another agent (such as Single Product Shop). In the case of outgoing message actions (message tasks), like Place order, and their corresponding incoming message events, like CustomerOrder, this relationship can be expressed with message flow arrows between the two actors involved, but in the case of non-communicative actions and events (like Customer:Make payment and Shop:CustomerPayment), BPMN does not support expressing such a relationship.

Also, in basic DES, we do neither have an activity nor an agent concept, and therefore the BPMN pools denoting actors, and the distinction between an action/activity (like Place order) and a corresponding event (like CustomerOrder) are not useful. Consequently, for our purpose of making a conceptual process model for basic DES, we better do not use BPMN in the traditional BP modeling way, but rather develop our own style of BPMN DES models, similar to Event Graphs, without activities and without actors/pools. Below, in our discussion of a service desk model, we will show an example of activity modeling, which requires extending basic DES by adding an activity concept, as proposed in (Wagner, Nicolae, & Werner, 2009).

The purpose of a conceptual process model for simulation is to identify causal regularities and express them in the form of event rules, one for each relevant type of events, at a conceptual level. We can describe event rules textually and visually in an event rule table like Table 2.

ON (event type) DO (event routine) Conceptual Event Rule Diagram

customer order

check inventory;
if there is sufficient inventory, then product handover, else customer departure

product handover

decrement (get product from) inventory;
customer payment

customer payment

customer departure

[Notice that we do not mention the increase of the shop's cash balance due to the payment, simply because the focus is on inventory only.]

replenishment order

delivery

delivery

payment

Table 2. Conceptual event rule models.

We can integrate these conceptual event rule models in a conceptual process model, as shown in Figure 14.

Notice that the BPMN end event circles used in the event rule models may have to be converted to BPMN intermediate event circles in the integrated model.

# Making a Process Design Model

A process design model needs to provide a computationally complete specification of event rules, one for each event type defined in the information design model. An event rule for a given event type essentially defines a set of (possibly conditional) state changes and a set of (possibly conditional) follow-up events triggered by an event of that type. We will show below how event rules can be visually expressed using a variant of BPMN process diagrams, which may be viewed as generalized Event Graphs (Schruben 1983).

Since our information design model (tailored to the given research question of computing the lost sales statistics) only includes two event types, DailyDemand and Delivery, we need to model the two corresponding event rules, only, as in the event rule design Table 3, where these rules are modeled textually using pseudo-code.

ON (event expr.) DO (event routine)

DailyDemand( sh, demQ) @ t
with sh: SingleProductShop

var sQ := sh.stockQuantity
var newSQ := sQ - demQ
var rP := sh.reorderPoint
sh.stockQuantity := max( 0, newSQ)
if sQ > rP & newSQ <= rP then
if newSQ < 0 then
lostSales += demQ - sQ
newSQ := 0
var delQ := sh.targetInventory − newSQ
schedule Delivery( sh, delQ) @ t + leadTime()

Delivery( rec, delQ) @ t
with rec: SingleProductShop


rec.stockQuantity += delQ
Table 3. Event rule design with pseudo-code.

Notice the general structure of an event expression like DailyDemand( sh, demQ) @ t: it starts with the name of an event type (here: DailyDemand) followed by a comma-separated list of event parameter names (here, sh and demQ), and an occurrence time annotation @ t. The event expression is complemented with a parameter legend (here, sh: SingleProductShop) defining the type of each event parameter.

We can also express these two rules visually using a variant of BPMN, called the Discrete Process Modeling Notation (DPMN) in (Wagner, 2018), as shown in Figure 15 and Figure 16.

In general, an event rule design diagram contains a start event circle with an annotation (here: dd: DailyDemand) specifying an event variable (here: dd) and an event type (here: DailyDemand). The start event is associated with one or more data objects (here: sh: SingleProductShop). The data object rectangles contain rule variable declarations and state change statements using the event variable and the rule variable(s). The start event circle has one or more outgoing sequence flow arrows leading to end event circles representing the types of event that may be scheduled, typicallly via gateways for conditional branching.

Notice that Delivery events trigger a state change, but no follow-up events.

These two event rule design models can be merged into a process design model:

For allowing to model event rules, DPMN adapts the syntax and semantics of BPMN:

1. Data Object rectangles now have two compartments:
1. a compartment showing an object variable name and an object type name separated by a colon;
2. a second compartment containing a block of state change code (rule variable declarations and assignments, as well as state change statements such as attribute assignments.
2. Sequence Flow arrows can now be annotated by assignments.
3. Sequence Flow arrows pointing to a gateway denote "next step" control flows.
4. Sequence Flow arrows pointing to an event circle denote "schedule event" control flows. They can be annotated by event parameter settings.
5. Event circles are semantically overloaded: in the context of an incoming Sequence Flow arrow they denote a scheduled event to be added to the Future Events List (FEL), while in the context of an outgoing Sequence Flow arrow or a Data Object association, they denote an event occurrence that may trigger state changes and follow-up events. The scheduled event and the resulting event occurrence are connected by asynchronous sequencing.
6. The semi-formal case handling token flow semantics of BPMN is replaced by a formal semantics based on the operational semantics of event rules defined in (Wagner, 2017a).

Any named event circle corresponds to an event type of the information design model and may trigger both state changes (specified in the associated data object rectangles) and follow-up events specified by (possibly conditional) "schedule event" sequence flow arrows. Unnamed event circles denote pro-forma end events.

# Implementing the Process Design Model with OESjs

The process design model specifies a set of event rules, each of which can be implemented with OESjs by coding its event routine in the onEvent method of the class that represents the triggering event type. For instance, the Delivery event rule can be coded as follows:

var Delivery = new cLASS({
Name: "Delivery",
supertypeName: "eVENT",
properties: {...},
methods: {
"onEvent": function () {
return [];  // no follow-up events
}
}
});

Notice that while in the event rule diagram, we use an event variable (here: d) standing for the triggering event, in the event routine onEvent we use the special OOP variable this for the same purpose.

The DailyDemand event rule can be coded like so:

var DailyDemand = new cLASS({
Name: "DailyDemand",
supertypeName: "eVENT",
properties: {...},
methods: {
"onEvent": function () {
var sh = this.shop,
sQ = sh.stockQuantity,
newSQ = sQ - this.quantity,
rP = sh.reorderPoint;
// update stockQuantity
this.shop.stockQuantity = Math.max( 0, newSQ);
// update lostSales if demand quantity greater than stock
if (newSQ < 0) {
sim.stat.lostSales += Math.abs( newSQ);
newSQ = 0;
}
// schedule new Delivery if stock falls below reorder point
if (sQ > rP && newSQ <= rP) {
return [new Delivery({
quantity: sh.targetInventory - newSQ,
})];
} else return [];  // no follow-up events
}
}
});

The full code of this simulation model is available by loading the web-based simulation http://sim4edu.com/sims/4 and inspecting its JavaScript code in the browser.

# Example 2: Modeling a Service System

In our basic service system example, as implemented in the Sim4edu simulation library, customers arrive at random times at a service desk where they have to wait in a queue when the service desk is busy. Otherwise, when the queue is empty and the service desk is not busy, they are immediately served by the service clerk. Whenever a service is completed, the next customer from the queue, if there is any, is invited for the service.

# Making a Solution-Independent Conceptual Information Model

It is straight-forward to extract four object types from the problem description above by analyzing the noun phrases:

1. customers,

2. service desks,

3. service queues,

4. service clerks.

Thus, a first version conceptual information model of the service system may look as shown in Figure 17.

Notice that it seems preferable (more natural) to separate the service queue from the service desk and not consider the customer that is currently being served at the service desk to be part of the queue. Conceptually, a queue is a linearly ordered collection of objects of a certain type with a First-In-First-Out policy: the next object to be removed is the first object, at the front of the queue, while additional objects are added at the end of the queue.

Notice that we model customers and service clerks as subclasses of people, following a general pattern of adding a base type (or kind), such as people, for all role classes in a model, such as customers and service clerks. One of the benefits of applying this pattern is that we can see that a person playing the role of a service clerk may also play the role of a customer, which is a special case of the general possibility that an employee of an organization may also be a customer of it.

After modeling all potentially relevant object types in the first step, we model the potentially relevant event types in a second step:

1. customer arrivals,

2. customers queuing up,

3. customers being notified/invited to move forward towards the service desk,

4. service start,

5. service end,

6. customer departures.

The main type of association between events and objects is participation. When adding event types to the object types in our conceptual information model, we therefore also model the participation types between them. For instance, in Figure 18, we express that a customer arrival event has exactly one customer and one service desk as its participants.

In order to complete the model of Figure 18, we may add attributes that help describing objects and events of these types.

The reader may have noticed that, while only modeling object and event types, our model does implicitly contain an activity type composed of the two event types service start and service end. It is well-known that, conceptually, an activity is a composite event that is temporally framed by a pair of start and end events. Consequently, activity types can be implicitly included in a basic DES model by defining corresponding pairs of start and end event types. If we would make an information model for DES with activities, which will be discussed in Part II of this tutorial, we would replace these pairs of start and end event types with corresponding activity types. In our example, we would replace the two event types service start and service end with the activity type perform service.

# Making an Information Design Model

We now derive a platform-Independent information design model from the solution-independent conceptual information model shown in Figure 18 above. Our design model is solution-specific because it is a computational design for the following specific simulation research question: compute the "mean response time" statistics as the average length of time a customer spends in the system from arrival to departure, which is the average waiting time plus the average service duration.

Our research question requires that we model individual customers, since for being able to compute the time a customer spends in the system we need to know which customer is next for getting the service and what is their arrival time. For knowing which customer is next, we need to model the service queue as a First-In-First-Out (FIFO) queue, which can be expressed in the UML class diagram with the help of the ordered association end waitingCustmers. Notice that by placing a dot on the line at this end of the association, and not on the other end as well, we make the association unidirectional implying the design decision that it will be represented by a reference property with name waitingCustmers in the ServiceDesk class. For being able to easily retrieve the arrival time of a customer, which is an information item coming from the CustomerArrival event, we record it along with the customer data, so we add a corresponding attribute to the Customer class.

Concerning the event types described in the conceptual information model, the goal is to keep only those that are really needed in the design model. This question is closely related to the question, which types of state changes and follow-up event creation have to be modeled for being able to answer the research question(s).

In the case of the given research question, we need to keep track of changes of the queue length and we need to be able to add up the queue waiting time and the service duration for each customer. For keeping track of queue length changes, we need to consider all types of events that may change the queue length: customer arrivals and customer departures. For being able to add up the queue waiting time and the service duration, we need to catch service start and service end events.

After identifying the relevant event types, we can look for further simplification opportunities by analyzing their possible temporal coincidence. Clearly, we can consider customer departures to occur immediately after the corresponding service end events, without having any effects that could not be merged. Therefore, we can drop service end events, and take care of their effects when handling the related customer departure event.

In addition, we can drop service start events, since they temporally coincide with customer arrivals when the queue is empty, or otherwise (when the queue is not empty) they coincide with service end (and, hence, with customer departure) events, because each service end event causes a new service start event as long as the queue is not empty.

As a result of the above considerations, we only keep the following two types of events from the conceptual model:

1. CustomerArrival having two participation associations representing the reference properties: (a) customer with the class Customer as range, and (b) serviceDesk with the class ServiceDesk as range. As an exogenous event type, CustomerArrival has a recurrence function representing a random variable for computing the time in-between two subsequent event occurrences.

2. CustomerDeparture having one participation association with ServiceDesk representing the reference property serviceDesk.

Notice that, for simplicity, we consider the customer that is currently being served to be part of the queue. In this way, in the simulation program, we can check if the service desk is busy by testing if the length of the queue is greater than 0.

An alternative approach would be not considering the currently served customer as part of the queue, but rather use a Boolean attribute isBusy for being able to keep track if the service desk ist still busy with serving a customer.

In an information design model we distinguish between two kinds of event types: exogenous event types and caused event types. While exogenous events of a certain type occur again and again, typically with some random recurrence that can be modeled with a probability distribution, caused events occur at times that result from the internal causation dynamics of the simulation. So, for any event type adopted from the conceptual model, we have to make a decision if we model it as an exogenous or as a caused event type, and for any exogenous event type, we specify a recurrence operation (typically a random variable) in the information design model.

In our example model, shown in Figure 19 below, we define CustomerArrival as an exogenous event type with a recurrence function that implements a random variable based on the exponential distribution with event rate 0.5, symbolically expressed as Exp(0.5), while we define CustomerDeparture as a caused event type.

Notice that we have modeled the random duration of a service with the help of the random variable operation serviceDuration() shown in the third compartment of the ServiceDesk class, based on the exponential distribution function Exp(0.5). Notice also that in our design we don't need the participation association between CustomerDeparture and Customer since for any customer departure event the customer concerned can be retrieved by getting the first item from the waitingCustomers queue.

# Deriving an OESjs Class Model from the Information Design Model

We derive an OESjs class model, shown in Figure 20 and Figure 21 below, for the object types and event types defined in the design model.

Notice that in the OESjs class model, associations are represented by corresponding reference properties (like ServiceDesk::waitingCustomers and CustomerArrival::serviceDesk).

# Coding the OESjs Class Model

The object class ServiceDesk defined in the OESjs class model shown in Figure x can be coded as follows:

var ServiceDesk = new cLASS({
Name: "ServiceDesk",
supertypeName: "oBJECT",
properties: {
"waitingCustomers": { range: "Customer", label: "Waiting customers",
minCard: 0, maxCard: Infinity}
},
methods: {
"onEvent": function () {...}
}
});
ServiceDesk.serviceDuration = function () {
return rand.exponential( 0.5);
};

The full code of this simulation model is available by loading the web-based simulation http://sim4edu.com/sims/2 and inspecting its JavaScript code in the browser.

# Making a Conceptual Process Model

For brevity, we show the conceptual event rule models only for a selection of the event types from the conceptual information model.

ON (event type) DO (event routine) Conceptual Event Rule Diagram

customer arrival

if the service desk is busy, then the new customer queues up, else the service starts

service start

service end

service end

the served customer departs; if there are still customers waiting in the queue, then the next service starts

Table 4. Conceptual event rule models for the service system example.

The individual event rule models shown in Table 4 can be integrated with each other as shown in Figure 22 where we have to cast the two event types service start and service end to BPMN’s intermediate events for complying with the BPMN syntax.

If we would make a process model for DES with activities, which will be discussed in Part II of this tutorial, we would replace the two event types service start and service end with the activity type perform service resulting in the model depicted below in Figure 23.

# Making a Process Design Model

In the process design model, we only include two event rules.

ON (event expr.) DO (event routine)

CustomerArrival( c, sd) @ t
with c:Customer and sd:Servicedesk


PUSH c TO sd.waitingCustomers
IF sd.waitingCustomers.length = 1
THEN SCHEDULE CustomerDeparture( sd) @
(t + ServiceDesk.serviceDuration())

CustomerDeparture( sd) @ t
with sd:Servicedesk


POP c FROM sd.waitingCustomers
IF sd.waitingCustomers.length > 0
THEN SCHEDULE CustomerDeparture( sd) @
(t + ServiceDesk.serviceDuration())
Table 5. The event rule design table for the service system.

# Conclusions

Combining UML class diagrams and BPMN process diagrams allows making visual simulation models that can be coded with any object-oriented simulation platform. While using UML and BPMN is not yet common in modeling and simulation, both languages are well-established in information systems and software engineering.

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