Modeling and Simulation Overview

• Modeling and Simulation overview

Course Information

• Required book: Banks, J., Carson, J. S., Nelson, B. L., & Nicol, D. (2010). Discrete-Event System Simulation (5th ed.).

Course Grades Breakdown

• Attendance and Participation: 5%
• Exercises: 10%
• First Test: 10%
• Second Test (Midterm): 15%
• Final Exam: 60%

Introduction to Simulation

• This course utilize computers to imitate operations of facilities or processes, called "systems."
• Modeling involves setting assumptions about how a system works, using mathematical or logical relationships to form a model.
• The model enables understanding of system behavior.

Simulation Concepts

• Simulation imitates the operation of a real-world process or system over time, can be done by hand or with a computer.
• Simulation generates an artificial history to draw inferences about the real system's operating characteristics.
• A Model represents a system to facilitate its study, taking the form of assumptions about the system's operations.
• Assumptions are expressed in mathematical or logical relationships between entities.
• Validated models help examine "what if" questions about real-world system operation
• Simulation is an "analysis tool" to predict the impact of changes on an existing system's performance.
• Simulation acts as a "design tool" in the design phase of new systems, predicting performance under various conditions.
• Modeling constructs a system surrogate, while simulation mimics the model's operation in time and space.

Applications of Modeling and Simulation

• Design and analysis of manufacturing and transportation systems like airports and subways.
• Evaluating and improving service organizations like banks and hospitals.
• Analysis of supply chains.
• Development of ordering policies for inventory systems.
• Evaluating and improving business operations.
• Risk analysis.
• Network simulation.

When to Use Simulation

• To observe the effect of environmental or potential changes on a model's behavior.
• To gain knowledge for improving real-world systems.
• To investigate new designs/policies for performance prediction before implementation.
• To set machine requirements in factories by simulating different capabilities.
• To study interactions of subsystems within complex systems.
• For training (e.g., flight simulator) and risk mitigation (e.g., flight simulator).

When Simulation Is Inappropriate

• When problems can be solved analytically or by common sense.
• When direct experiments are cheaper.
• When simulation costs exceed savings.
• When resources are unavailable.
• When system behavior is too complex (e.g., human behavior).

Advantages of Simulation

• New policies and procedures can be explored without disrupting real systems.
• New hardware designs and transportation systems can be tested without committing resources.
• Hypothesis testing about phenomena is possible.
• Insight into variable interactions and their importance to system performance can be obtained.
• Bottleneck analysis can identify excessive delays in work-in-process and information flow.
• Understanding of how systems operate, versus perceptions of how they operate, is gained.
• "What-if" questions can be answered, aiding in the design of new systems.

Disadvantages of Simulation

• Model building requires special training and experience; models by different experts may vary.
• Simulation results can be hard to interpret due to random variables and system complexities.
• Simulation modeling and analysis can be time-consuming and expensive.
• Simulation may be used when analytical solutions are possible or preferable.

Systems and System Environment

• A system is a collection of entities (e.g., people, machines) interacting to achieve a logical end (Schmidt & Taylor, 1970).
• "The system" definition depends on the objectives of a particular study.
• Changes outside a system occur in its environment [Gordon, 1978].
• Modeling requires deciding on the boundary between the system and its environment, depending on the study's purpose.
• In a factory, order arrivals may be considered outside the factory's influence, making them part of the environment.
• Considering supply's effect on demand creates a relationship and activity within the system.
• For a single bank study, an interest rate limit is an environmental constraint.
• Considering monetary laws on banking could make setting the limit an activity of the system [Gordon, 1978].

Components of a System Defined

• Entity: An object of interest
• Attribute: A property of an entity
• Activity: A time period of specified length
• State of a System: Variables describing the system at any time,relative to the study objectives
• Event: An instantaneous occurrence that may change the system's state.
• Endogenous: Activities/events occurring within a system.
• Exogenous: Activities/events in the environment affecting the system.
• In a bank study, customer arrival is exogenous; service completion is endogenous.

Examples of System Entities, Attributes, Activities, Events and State Variables

• Banking System
  • Entities are Customers while Attributes are Checking-account balances
  • Activities are Making Deposits and Events being Arrival and Departure of cutomers
  • State Variables would be number of busy tellers and customers
• Rapid Rail System
  • Entities are Riders, Attributes are Origin/Destination
  • Activities are Traveling and Events being Arrival to and from station
  • Number of riders waiting at each station is an example of a state vaiable
• Warehouse
  • Entities: Machines, Attributes: Speed, Capacity, Breakdown Rate
  • Activities: Welding, Stamping while Events are Breakdowns
  • State Variable: Status of machines
• Communication
  • Entities are Messages, Attributes: Length and destination
  • Activities: Transmitting, Events: Arrival at destination
  • State Variable: Number waiting to be transmitted

Discrete and Continuous System

• Systems classification: discrete or continuous.
• Discrete System: State variable(s) change only at discrete points in time.
• Example is a bank: the state variable (number of customers) changes only upon customer arrival or service completion.
• Continuous System: State variable(s) change continuously over time.
• Example: water head behind a dam, changes after rainstorms and decreased during flood control to produce electricity

Model of a System

• Represents a system for study purposes.
• Models are by definition a simplification of the system.
• Models should be sufficiently detailed for valid conclusions about the real system.
• Different models may be needed for different investigation purposes.
• Physical Models: larger or smaller versions of the object being modeled (example Model of an atom)
• Mathematical Models: Use Symbolic notation and mathematical equations

Classification of Simulation Models

• Static Simulation Model: represents a system at a single point in time (aka Monte Carlo simulation).
• Dynamic Simulation Model: represents systems that change over time, ex: bank simulation from 9am to 4pm
• Deterministic Simulation Model: contain no random variables, known set of inputs with unique outputs.
• Stochastic Simulation Model: Contains one or more random variables as inputs resulting in random outputs.
• Study for this course will focus on Discrete, Dynamic and Stochastic models

Steps in a Simulation Study

• Problem Formulation: Analyst ensures clear understanding of the problem from policymakers.
• Set Objectives: Decide if simulation is proper and incorporate elements such as cost
• Model Conceptualization: selecting, modifying basic assumptions that characterize systems
• Data Collection: Begin early because the complexity can change required data amount
• Model Translation: Enter model into a computer-recognizable format.
• Verification: Is the computer program performing correctly and is debugged for logical structure and proper inputs
• Validation: Compare the model against the system behavior using the discrepancies to improve the model
• Experimental Design: Length of the Initialization and number of replications
• Production Runs and Analysis: estimate for the system being simulated and can be aided in the process by software
• More Runs: Determining if additional runs are required
• Documentation and Reporting: Document Relationships between input and output( i.e Understand how the Program operates"
• Implementation: This would dictate how well that last 11 steps where performed
• Four Phases include : Discovery, Model Building and Collection, Running and Implementation