Introduction to modeling and simulation Engr. Hinesh Kumar Institute of Biomedical Technology, LUMHS

System A set of interacting components or entities which are related by some form of interaction and operating together to achieve a common goal or objective. Examples:  A manufacturing system with its machine centers, inventories, conveyor belts, production schedule, items produced.  A telecommunication system with its messages, communication network servers.  A theme park with rides, workers, …

3 Solar-Heated Water System Collectors Capture sun’s thermal energy Storage tank Pump Move the water through the tank Booster element Heat water Relief valve Cold water inlet Hot water outlet

4 Systems Natural vs. Artificial Systems  A natural system exists as a result of processes occurring in the natural world (e.g. river, universe)  An artificial system owes its origin to human activity (e.g. space shuttle, automobile) Static vs. Dynamic Systems  A static system has structure but no associated activity (e.g. bridge, building)  A dynamic system involves time-varying behavior (e.g. machine, U.S. economy)

5 Systems Open-loop vs. Closed-loop systems  Inputs Variables that influence the behavior of the system  e.g. wheel, accelerator, and brake of a car  Outputs Variables that are determined by the system and may influence the surrounding environment  e.g. direction and speed of a car

Systems  An open-loop system cannot control or adjust its own performance e.g. watch, car  A closed-loop system controls and adjusts its own performance in response to outputs generated by the system through feedback e.g. watch with owner, car with driver  Feedback is the system function that obtains data on system performance (outputs), compares the actual performance to the desired performance (a standard or criterion), and determines the corrective action necessary 6

7 System Controller Input Output Open-Loop System System Controller Desired Reference or Input Output Feedback Closed-Loop System - + Error Signal

How to study the System? 8 System Experiment with the actual system Experiment with a mathematical model of the system Mathematical Analysis Simulation Measure/estimate performance Improve operation Prepare for failures Experiment with a physical model of the system

COMPONENTS OF A SYSTEM Entity: is an object of interest in the system  Dynamic objects — get created, move around, change status, affect and are affected by other entities, leave (maybe)  Can have different types of entities concurrently Example: Health Center Patients Visitors

COMPONENTS OF A SYSTEM Attribute: is a characteristic of all entities, but with a specific value “local” to the entity that can differ from one entity to another. Example: Patient Type of illness, Age, Sex, Temperature, Blood Pressure

COMPONENTS OF A SYSTEM Resources: what entities compete for  Entity seizes a resource, uses it, releases it  Think of a resource being assigned to an entity, rather than an entity “belonging to” a resource Example: Health Center Doctors, Nurses X-Ray Equipment

COMPONENTS OF A SYSTEM Variable: A piece of information that reflects some characteristic of the whole system, not of specific entities  Entities can access, change some variables Example: Health Center Number of patients in the system, Number of idle doctors, Current time

State : A collection of variables that contains all the information necessary to describe the system at any time Example: Health Center {Number of patients in the system, Status of doctors (busy or idle), Number of idle doctors, Status of Lab equipment, etc} COMPONENTS OF A SYSTEM

Event: An instantaneous occurrence that changes the state of the system Example: Health Centre Arrival of a new patient, Completion of service (i.e., examination) Failure of medical equipment, etc. COMPONENTS OF A SYSTEM

Activity: represents a time period of specified length. Example: Health Center Surgery, Checking temperature, X-Ray.

16 Models What is Model  A Representation of an object, a system, or an idea in some form other than that of the entity itself.  Similar to but simpler than the system it represents Close approximation to the real system and incorporate most of its salient features Should not be so complex that it is hard to understand or experiment with it

Models Physical Model  A physical object that mimics some properties of a real system e.g. During design of buildings, it is common to construct small physical models with the same shape and appearance as the real buildings to be studied  Through prototyping process Prototyping is the process of quickly putting together a working model (a prototype) in order to test various aspects of a design, illustrate ideas or features and gather early user feedback 17

18 Models Mathematical Model  A description of a system where the relationship between variables of the system are expressed in a mathematical form e.g. Ohm's law describes the relationship between current and voltage for a resistor; Hooke's Law gives the relationship between the force applied to an unstretched spring and the amount the spring is stretched when the force is applied, etc.  Through virtual prototyping

19 F Spring = -k∙x Hooke’s Law x= -F Spring /k spring constant The amount spring is stretched F spring

20 Simulation What is Simulation  A simulation of a system is the operation of a model of the system, as an imitation of the real system  A tool to evaluate the performance of a system, existing or proposed, under different configurations of interest and over a long period of time

Reasons for Simulation Experiments on real systems are too expensive, too dangerous, or the system to be investigated does not yet exist  e.g. a simulation of an industrial process to learn about its behavior under different operating conditions in order to improve the process The time scale of the dynamics of the system is not compatible with that of the experimenter  e.g. It takes millions of years to observe small changes in the development of the universe, whereas similar changes can be quickly observed in a computer simulation of the universe Easy manipulation of parameters of models (even outside the feasible range of a particular physical system)  e.g. The mass of a body in a computer-based simulation model can be increased from 40 to 500 kg at a keystroke, whereas this change might be hard to realize in the physical system 21

22 Elements of Simulation Analysis Problem Formulation: questions for which answer are sought, the variables involved and measures of system performance to be used Data Collection and Analysis: assembling the information necessary to further refine our understanding of the problem. Model Development: building and testing the model of the real system, selecting simulation tool (programming language), coding the model and debugging it.

23 Elements of Simulation Analysis Model Verification and Validation: establish that the model is an appropriate accurate representation of the real system. Model Experimentation and Optimization: precision issues, how large sample (simulation time) is necessary to estimate the performance of the system. The design of effective experiments with which to answer the question asked in the problem formulation. Implementation and Simulation result: acceptance of the result by the users and improved decision making stemming from the analysis.

24 Elements of Simulation Analysis Problem Formulation Data Collection and Analysis Model development Model Verification and Validation Model Experimentation and Optimization Implementation of Simulation Results Major Iterative Loops in a Simulation Study

8 Advantages of Simulation Decision aid. Cause-effect relations Exploration of possibilities. Diagnosing of problems. Identification of constraints. Visualization of plans. Building consensus. Preparing for change. Cost effective investment. Training aid capability. Specification of requirements.

10 Disadvantages of Simulation Training required. Interpretation of results required. Time consuming/expensive. Inappropriately used.

11 Application Areas Manufacturing/ Materials Handling Public and Health Systems Military Natural Resource Management Transportation Computer Systems Performance Communications