BIS_3100__Modeling_and_Simulation_(lecture_one)B[1].pptx

Simulation in the modern world

1. IST 3208 Modeling and Simulation Lecturer: Dr. Tulinayo Fiona

2. Source Karagiannis,D and Kuhn, H. Meta-modeling Platforms LNCS 2455, Springer- Verlag , 2002, p.182 Halpin , T. Information modeling and relational databases; from conceptual analysis to logical design Rajendra Kumar et. al 2009 Modeling and Simulation concepts. Law. A.M. Simulation Modeling and Analysis 4th edition J.D. Sterman . Business Dynamics- Systems Thinking and Modeling for a Complex World. McGraw Hill Higher Education, edition, 2000 .

3. Course Outline System Concepts and Modeling Types of Modeling Domain/Conceptual modeling/Data modeling Modeling Methods Meta Modeling Modeling procedure Modeling Languages Examples of Modeling methods Conceptual Modeling (Data Modeling) Class exercises Test One Modeling (Dynamic) Simulation System Dynamics System Thinking (Causal Loop Diagrams) System Modeling/Mathematical Modeling (Stock and Flow Diagrams) Practical Lessons Coursework Process Modeling

4. Objectives of Modeling and Simulation Learn about the potential of modeling and simulation tools Learn to describe behavioral modeling, data modeling and object modeling. Learn how to use simple modeling and simulation software Analyze a specific site operation in order to gain insights into its design

5. PART I: MODELING A model :  is a representation of an idea, an object, a process or a system that is  used  to describe and explain phenomena that cannot be directly experienced.   i.e. I t is an abstract representation of the system. A model is similar to but simpler than the system it represents. Modeling : is the process of producing a model that represents the construction and working of some system of interest.

6. MODELING cont … There are various forms of modeling e.g. Process modeling, discrete modeling, mathematical modeling etc. These forms are essential in: Supporting complex human design activities. Development of information systems (system modeling, Information modeling, etc ), Re-engineering of work practices. Models, particularly those that offer good insight through visualization and graphs, can help companies to structure and simplify their complex and dynamic systems.

7. Existing AND PLANNED SYSTEM MODELS Models of the existing system are used during requirements engineering to clarify; W hat the existing system does What it can be used for as a basis for discussing its strengths and weaknesses (these then lead to requirements for the new system) Models of the new system are used during requirements engineering to help explain the proposed requirements to other system stakeholders. These models are used when discussing design proposals and to document the system for implementation In a model-driven engineering process, it is possible to generate a complete or partial implementation from the system model.

8. What is a model used for ? Conceptualization Simulation Prediction/Forecasting Prognostics/Diagnostics Design/Performance Evaluation Control System Design Etc QN: Explain the use and meaning of each of the above constructs?

9. Modeling Perspectives An external perspective , where you model the context or environment of the system An interaction perspective , where you model the interactions between a system and its environment, between the components of a system. A structural perspective , where you model the organization of a system or the structure of the data that is processed by the system. A behavioral perspective , where you model the dynamic behavior of the system and how it responds to events

10. Modeling Approaches There are two modeling approaches: Static modeling approaches: These approaches define the symbols for visualizing the syntactical constructs e.g. vector graphics but they do not consider the state of the modeling constructs during modeling. Dynamic modeling approaches: These consider the model state by splitting the notation in a representation part and a control part . The representation part maps to the static approach and, The control part defines rules to query the model state and to influence the representation depending on the model state .

11. Modeling Method(s ) Modeling methods consist of two components: A modeling technique which is divided into a modeling language and a modeling procedure to guide modelers in using the language to construct models. This procedure is often called the modeling process. Mechanisms and algorithms which are workings on the models described by the modeling language .

12. Modeling Language(s ) A language has associated syntax (marks), semantics (meaning), and pragmatics (use). Written languages may be graphical (diagrams) and/or textual. A modeling language contains elements with which a model can be described. It is described by its syntax, semantics and notations. The Syntax describes the elements and rules for creating models and is described by grammar. For modeling languages, two major approaches exist to describe their syntax: Graph grammars Meta-models

13. A Meta-model A Meta - model is a model of a model ( A meta-model is itself a model that is used to describe another model using a modeling language .), Meta-modeling is the process of generating such meta-models . Meta-modeling is the analysis, construction and development of the frames, rules, constraints, models and theories applicable and useful for modeling a predefined class of problems. Note: A meta-model is not an aggregated or less detailed view of another model: A meta-model is a model at a different level of abstraction that makes statements about the structure of another model (or a whole set of other models), without making statements about their content.

14. A Meta-model Cont … There are many reasons why it is desirable to formalize a modeling language using a meta-model: Formalization of a modeling language helps to ensure that everyone uses the language in a consistent way. A meta-model allows a model to be checked for syntactic correctness using automated algorithms that implement the rules and constraints defined by the meta-model. Models that are created using the same meta-model can easily be exchanged between tools that implement the same meta-model.

15. Modeling Language(s) cont … The semantic describes the meaning of a modeling language and consists of semantic domain and the semantic mapping. The semantic domain describes the meaning by using: Ontologies ( a formal naming and definition of types, properties, and interrelationships of entities that really or fundamentally exist for a particular domain of discourse. OR a formal, explicit specification of a shared conceptualization ) Mathematical expressions etc. The semantic mapping connects the syntactical constructs with their meaning defined in the semantic domain (semantic schema). ( *Assignment ( i ) : Identify the different types of modeling languages )

16. Modeling Tools Modeling tools focus on important system features; Medium of communication with users; Document the systems analyst's understanding for implementation by designers and programmers . There are a number of modeling tools. ( * Assignment (ii): Identify the different modeling tools and state how, when and where they are applied )

17. Modeling features Graphic Tools : These are used to show high level components of particular aspect of a model. Each graphic modeling tool has a set of icons used to represent specific model component. Graphic tools are preferred type of modeling tools when the connection between model components is important. Graphic tools in essential modeling are mainly of a semantic nature highlighting the meaning of the requirements. Graphic tools in implementation modeling are mainly concerned with syntax or structure.

18. Modeling features cont .. Tabular Tools : Some information is usefully laid out in tabular forms. Tabular tools may be useful in some circumstances particularly if subject matter expert finds the graphic modeling tool difficult to relate to. Frames : Frame is used informally for a certain type of specification tool. Frame specifications are used to specify all relevant information about a model component that has been declared on a diagram or another frame. Textual Tools : Textual grammar is defined formally, using meta language or set theory .

19. Modeling Procedure/Process A modeling procedure describes the steps applied by the modeling language to create results i.e. models When developing an information system, we first specify what is required and produce a design to meet these requirements. The procedure for designing a conceptual schema that is small enough to manage as a single unit is referred to as the conceptual schema design procedure (CSDP). With large applications, the universe of discourse is divided into components or subsections (which may overlap).

20. Modeling Procedure/Process cont ... When modeling as a team, a consensus on terminology should be reached on the same names to use for similar concepts. After developing these separate models (subschemas), they are integrated or merged into a global conceptual schema that covers the whole Universe of Discourse ( UoD ). This integration is often performed iteratively in a top-down design approach. The top-down design approach can be summarized as follows: Divide the universe of discourse into manageable subsections. Apply the conceptual schema design procedure (CSDP) to each subsection. Integrate the subschemas into a global conceptual schema .

21. For each manageably sized application, the conceptual schema design is performed in seven steps : Transform familiar information examples into elementary facts, and apply quality checks. Draw the fact types, and apply a population check . Check for entity types that should be combined, and note any arithmetic derivations. Add uniqueness constraints, and check arity of fact types . Add mandatory role constraints, and check for logical derivations . Add value, set comparison, and subtyping constraints . Add other constraints and perform final checks . ( For Details read Terry Halpin’s Book )

22. Types of Models Physical models State machine models e.g. Mathematical models Mental models Conceptual models or Data Models Meta-models Process Models Behavioral models Etc.

23. Physical Models A physical Model is a technical pictorial representation that depict what a system is or does and how the system is implemented . i.e. It is a smaller or larger physical copy of an object.  Physical models allow visualization, from examining the model, of information about the “thing” the model represents. A model can be a physical object such as an architectural model of a building .

24. Mathematical Models A mathematical model is an abstract model that uses mathematical language to describe the behavior of a system. Eykhoff (1974) defined a mathematical model as “a representation of the essential aspects of an existing system (or a system to be constructed) which presents knowledge of that system in usable form”. Mathematical models are used particularly in the natural sciences and engineering disciplines (such as physics, biology, and electrical engineering) but also in the social sciences (such as economics, sociology and political science); physicists, engineers, computer scientists, and economists use mathematical models most extensively.

25. Mathematical Models cont ... Mathematical models can take many forms, including but not limited to Dynamical systems Statistical models, Differential equations, Game theoretic models, Etc.

26. Mathematical Modeling Mathematical modeling seeks to gain an understanding of science through the use of mathematical models. “Mathematical modeling involves teamwork” Mathematical modeling is often used in place of experiments when experiments are too L arge , E xpensive, D angerous , or T ime consuming . It can be useful in “what if” studies; e.g. to investigate the use of pathogens (viruses, bacteria) to control an insect population. And is a modern tool for scientific investigation.

27. Classification of Mathematical Models Linear vs. Non-linear Deterministic vs. Probabilistic (Stochastic) Static vs. Dynamic Discrete vs. Continuous White box, black box and gray box

28. Linear and Nonlinear Functions Identifying functions on tables, graphs , and equations .

29. Tables: Linear or Nonlinear linear nonlinear x y 2 50 4 35 6 20 8 5 x y 1 1 4 16 7 49 10 100 Is the rate of change constant (the same)? +2 +2 +2 -15 -15 -15 +3 +3 +3 +15 +33 +51

30. Equations: Linear or Nonlinear Note : x 1 = x and x = 1 In “y = ” form, is x raised to a power of 1 or 0? Does x appear in the numerator ? y = x + 4 y = 6/x y = 4 y = x 3 + 1 y = ½ x linear nonlinear linear nonlinear linear

31. Identify : Linear or Nonlinear Equation ? y = 2/x + 5 y = x 2 + 8 y = .6x 1 y = + 1 3x 2 linear linear nonlinear nonlinear

32. Pointers to Keep in Mind A table is linear if the rate of change is constant . There is a common difference . A graph is linear if it is a straight line . An equation is linear if the power of x is either 1 or 0 and it appears in the numerator .

33. Deterministic vs. Probabilistic (Stochastic ) A system being modeled exhibits probabilistic or stochastic behavior if an element of chance exists. For example : The path of an earthquake is probabilistic. In contrast, a behavior can be deterministic , such as the position of a falling object in a vacuum. Similarly, models can be deterministic or probabilistic . A probabilistic or stochastic model exhibits random effects, while a deterministic model does not. The results of a deterministic model depend on the initial conditions ; and in the case of computer implementation with particular input, the output is the same for each program execution . Deterministic: Randomness does not affect the behavior of the system. The output of the system is not a random variable. Stochastic: Randomness affects the behavior of the system. The output of the system is a random variable.

34. DETERMINISTIC AND PROBABILISTIC MODELS Deterministic Models are models in which all relevant data are assumed to be known with certainty . can handle complex situations with many decisions and constraints . are very useful when there are few uncontrolled model inputs that are uncertain . are useful for a variety of management problems . allow for managerial interpretation of results . h elp in developing one’s ability to formulate models in general .

35. DETERMINISTIC AND PROBABILISTIC MODELS Probabilistic (Stochastic) Models are models in which some inputs to the model are not known with certainty. uncertainty is incorporated via probabilities on these “random” variables. very useful when there are only a few uncertain model inputs and few or no constraints . often used for strategic decision making involving an organization’s relationship to its environment .

36. Static vs. Dynamic A static model does not consider time, while a dynamic model changes with time . Static: A simulation of a system at one specific time, or a simulation in which time is not a relevant parameter for example, Monte Carlo & steady-state simulations. Dynamic: A simulation representing a system evolving over time for examples, the majority of simulation problems . In a static model , we do not consider time , so that the model is comparable to a snapshot or a map . While in a dynamic model , time changes, so that such a model is comparable to an animated cartoon or a movie.

37. Discrete vs. Continuous When time changes continuously and smoothly, the model is continuous . If time changes in incremental steps, the model is discrete . A discrete model is analogous to a movie . In a continuous model , time changes continuously, while in a discrete model time changes in incremental steps. Continuous: State variables change continuously as a function of time and generally analytical method like deductive mathematical reasoning is used to define and solve the system. Discrete model : the state variables change only at a countable number of points in time. These points in time are the ones at which the event occurs/change in state. Continuous : the state variables change in a continuous way, and not abruptly from one state to another (infinite number of states ).

38. Black Box Model When only input and output are known. Internal dynamics are either too complex or unknown. Easy to Model Input Output

39. Grey Box Model When input, output and some information about the internal dynamics of the system is known. Easier than white box Modelling. u(t) y(t) y[u(t), t]

40. White Box Model When input, output and internal dynamics of the system is known. One should have complete knowledge of the system to derive a white box model. u(t) y(t)

41. Mathematical modeling process

42. Real World Problem Identify Real-World Problem : Perform background research, focus on a workable problem. Conduct investigations (Labs ), if appropriate. Learn the use of a computational tool: Matlab , Mathematica , Excel, Java. Understand current activity and predict future behavior.

43. Real World Problem cont … Mathematical model of a real world system is derived using a combination of physical laws and/or experimental means Physical laws are used to determine the model structure (linear or nonlinear) and order. The parameters of the model are often estimated and/or validated experimentally. Mathematical model of a dynamic system can often be expressed as a system of differential (difference in the case of discrete-time systems) equations

44. Working Model Simplify  Working Model : Identify and select factors to describe important aspects of Real World Problem ; determine those factors that can be neglected. State simplifying assumptions. Determine governing principles, physical laws. Identify model variables and inter-relationships.

45. Mathematical Model Represent  Mathematical Model : Express the Working Model in mathematical terms; write down mathematical equations whose solution describes the Working Model . In general, the success of a mathematical model depends on how easy it is to use and how accurately it predicts.

46. Computational Model cont.. Translate  Computational Model : Change Mathematical Model into a form suitable for computational solution. Existence of unique solution Choice of the numerical method Choice of the algorithm Software Computational models include software such as Matlab , Excel, or Mathematica , or languages such as Fortran, C, C++, or Java.

47. Results/Conclusions Simulate  Results/Conclusions : Run “ Computational Model” to obtain Results ; draw Conclusions . Verify your computer program; use check cases; explore ranges of validity. Graphs, charts, and other visualization tools are useful in summarizing results and drawing conclusions.

48. Real World Problem Interpret Conclusions: Compare with Real World Problem behavior. If model results do not “agree” with physical reality or experimental data, reexamine the Working Model (relax assumptions) and repeat modeling steps. Often, the modeling process proceeds through several iterations until model is “ acceptable”.

49. Meta-models A Meta-model is a semantic information model. Meta-modeling is an activity, and this activity produces meta-models Meta-modeling identifies the underlying modeling process and provides tools and techniques for model development that will allow students and researchers to sort through the many different methods, understand them, and apply them to new problems.

50. Mental Models Craik (1943) described mental models as internal constructions of some aspect of the external world enabling predictions to be made Involves unconscious and conscious processes, where images and metaphors are activated Deep versus shallow models (e.g. how to drive a car and how it works )

51. Mental Models cont ..

52. Mental Models Users develop an understanding of a system through learning & using it. This type of understanding is often described as a mental model How to use the system (what to do next) What to do with unfamiliar systems or unexpected situations (how the system works ) People make inferences using mental models of how to carry out tasks Mental models are models people have of themselves, others, the environment, and the things with which they interact .

53. Data Models A data model is a precise description of the data content in a system Types of data models: Conceptual : describes WHAT the system contains A modeling method comprises both a language and a procedure to guide modelers in using the language to construct models. A language has associated syntax (marks), semantics (meaning) and pragmatics (use). Logical: describes HOW the system will be implemented, regardless of the Database Management System (DBMS) Physical: describes HOW the system will be implemented using a specific DBMS

54. Why do we need to create data models? To aid in the development of a sound database design that does not allow anomalies or inconsistencies Goal: to create database tables that do not contain duplicate data values that can become inconsistent

55. Types of Data Models Entity-Relationship (E-R) Models Only addresses data and relationships Classic, simplest Best for deriving a sound table design Many extensions/variations exist Basis for most other modeling approaches UML (unified modeling language) Class models Goes beyond data, also models behaviors Object Role Modeling (ORM)

56. *******END of Lecture One********** ***NEXT*** PART Il CONCEPTUAL MODELING

57. What is a Conceptual Model ? A conceptual model is a representation of a system that uses concepts and ideas to form said representation.Conceptual modeling is used across many fields, ranging from the sciences to socioeconomics to software development. conceptual modeling is used as a way to describe physical or social aspects of the world in an abstract way. For example, in the realm of software development, a conceptual model may be used to represent the relationships of entities within a database.  A conceptual model should fulfill four fundamental objectives: Enhance understanding of the representative system. Promote efficient conveyance of system details between team members. Provide a point of reference for system designers to gather system specifications. Document the system for future reference.

58. PART iI : Conceptual MODELING Conceptual modeling is described as the “activity of formally describing aspects of the physical and social world for the purposes of human understanding and communication” ( Mylopoulos 1992). It portrays the application domain at a high level, using terms and concepts familiar to the application users, ignoring logical- and physical-level aspects (e.g., the underlying database or programming structures used for implementation) and external-level aspects (e.g., the screen forms used for data entry ).