M&S Midterms

simuland

A __is the real - world item of interest.

simuland

It is the object, process, or phenomenon to be simulated

Schematic model

is a representation of a simuland.

Mechanical diagram

is used to develop a mathematical model for the car suspension system

Differential equations

are programmed for computer solution using a “continuous simulation” software tool

continuous simulation

Differential equations are programmed for computer solution using a “_” software tool

Simulation

is the process of executing a model over time

Attribute

. A significant or defining property or characteristic of a model or simulation.

• Fidelity • Resolution • Scale

Three important attributes

Fidelity

. Accuracy of model’s representation or simulation’s results.

Fidelity

AKA validity.

 Reality  Representation  Requirements

Fidelity is relative to:

Reality

How consistent are the simulation results and the real world in the same scenario

Resolution

. The degree of detail with which the real-world is simulated. More detail is higher _.

Resolution

AKA granularity.

Scale

. Size of the overall scenario or event the simulation represents.

Scale

AKA level

Component  Equipment

Typical scales for manufacturing systems:

Component-

System, subsystem, or single unit of a factory

Equipment

- 1, 10 or 100 machines

directly proportional

Fidelity and resolution relate

Indirectly proportional

Fidelity and scale relate

Indirectly proportional

Resolution and scale relate

Verification, Validation, and Accreditation

The process of determining if a model is correct and usable;

Verification, Validation, and Accreditation

the process of developing and delimiting confidence that a model can be used for a specific purpose

Verification

. The process of determining that a model implementation accurately represents the developer’s conceptual description and specifications

Verification

Is it coded right? Does the implementation match the design?

Verification

This is software engineering quality. General software testing methods apply.

Validation

. The process of determining the degree to which a model (and data) is an accurate representation of the real world from the perspective of the model’s intended usage.

Validation

Is the right thing coded? Does the model match reality (i.e., fidelity)?

Validation

This is modeling quality.

Informal

-Audit

-Desk checking

-Documentation Checking

-Face validation

-Inspections

-Reviews

-Turing test

-Walkthroughs

Static

-Cause-Effect Graphing

-Control Analysis

-Data Analysis

-Fault/Failure Analysis

-Interface Analysis

-Semantic Analysis

-Structural Analysis

-Symbolic Evaluation

-Syntax Analysis

-Traceability Assessment

Dynamic

-Acceptance Testing

-Alpha Testing

-Assertion Checking

-Beta Testing

-Bottom-up Testing

-Comparison Testing

-Statistical Techniques

-Structural Testing

-Submodel/Module Testing

-Visualization/ Animation …

Formal

-Induction

-Inductive Assertions

-Inference-Logical Deduction

-Lambda Calculus

-Predicate Calculus

-Predicate Transformation

-Proof of Correctness

Informal, Static, Dynamic, Formal

Verification and validation techniques

Accreditation

. Official certification by a responsible authority that a model is acceptable for a specific purpose.

 For a specific purpose or function

 Not a blanket or general-purpose approval

 Authority is agency or person responsible for results or use of model, not developer

Accreditation notes

Authority

is agency or person responsible for results or use of model, not developer

state of a system

The _ at time t0 is the information required at t0 such that the output y(t), for all t>=t0, is uniquely determined from this information and from the input x(t) for t>=t0 .

state variables

This state information is usually represented by a vector q(t) whose components are called

state space

The __ of a system, denoted by Q, is the set of all possible values that q(t) may take

Static System

• A system in which the output depends only on the input and is independent of the system state

Static System

• A system without memory

Dynamic System

• A system in which the output depends on both the input and the system state • A system with memory

Dynamic System

event

With each state transition, we associate an __.

event

An __ is a specific instantaneous action or occurrence which results in an instantaneous change of system state. We call such systems “event-driven” systems

“event-driven” systems

An event is a specific instantaneous action or occurrence which results in an instantaneous change of system state. We call such systems __

“time-driven” systems

The system response varies as a continuous function of time, even when there is no change in the system input. Thus, the system state appears to evolve simply because time advances, We call these systems___

Deterministic System

: A system which will produce the same output from a given starting condition or initial state

Stochastic System

: A system in which one or more variables has uncertainty or variability.

Stochastic System

In this case, the system state becomes a random variable and a probabilistic framework is required to describe system behavior

Continuous-Time System

: A system in which the time variable is represented by a continuous variable; t ε R

Discrete-Time System

: A system in which the time variable is represented by a discrete variable, t ε I. Usually, the intervals between time values are equal.

Discrete Event System (DES)

A __ is a discrete-state, event-driven system

Discrete Event System (DES)

state evolution depends entirely on the initial state of the system and the occurrence of asynchronous discrete events over time.

Continuous System

is a continuous-state, time-driven system

continuous

Many physics-based systems are modeled as _ systems.

Discrete Event Systems

PacMan movement of character

Discrete Event Systems

Water cycle phase

Continuous Systems

Projectile motion

Continuous Systems

Weather forecast system

• Static or Dynamic

• Continuous-State or Discrete-State

• Time-Driven or Event-Driven

• Deterministic or Stochastic

• Continuous-Time or Discrete Time

System Classification

DES, Continuous System

System Types

Monte Carlo Simulation

Discrete Event Simulation

Continuous Simulation

Agent-Based Simulation

Simulation Paradigms

Monte Carlo Simulation

• Static systems modeled using probability

• Simulation of a random experiment

• Implemented using spreadsheets and the relative frequency interpretation of probability

Discrete Event Simulation

• Dynamic systems modeled as queuing systems

• Implemented using spreadsheets or DES tools (Arena)

Continuous Simulation

• Dynamic systems modeled using differential equations

• Simulation of continuous-state, time-driven systems

• Implemented using spreadsheets or CS tools (Matlab-Simulink)

Agent-Based Simulation

• Generally a bottom up approach to represent human and social systems

• Usually stochastic in nature

• Implemented in various ways from a computational standpoint (ex. Netlogo)

Set

• a collection of objects

elements

• the objects are called __of the set and may be anything

Equality

set A and set B contain exactly the same elements

Union

the set consisting of all elements that are either in A or in B or in both A and B

Intersection

the set consisting of all elements that are in A and in B

Difference

the set consisting of elements in A that are not elements in B

Complement

The complement of set A, denoted A’, is the set Universal set - A

Common Probability Density Functions

Common Probability Density Functions

Random Number

is a sample, selected randomly, from the distribution UNIFORM (0, 1)

Random Variate

is a sample, drawn randomly, from a distribution other than UNIFORM (0, 1)

Inverse Transform Theorem

Used to generate random variate

Monte Carlo Simulation 

Stochastic simulation of a real-world system modeled as a random experiment.

Modeling Approach of MCS

• System behavior is modeled using probability distributions

• Physics of system is not represented explicitly

Simulation Approach of MCS

• Utilize randomly generated parameter values

• Parameter values identify possible outcomes

• Usually conduct multiple trials and perform statistical analysis

• Simulation is static; there is no time advance feature

Simulation Results of MCS

• Utilize “relative frequency” definition of probability

• Conduct multiple trials to approximate limit operation

Generate a random number n = RAND( )

Determine the standard normal variate corresponding to n using Z(n)=NORM.S.INV (n)

Denormalize Z(n) to determine the point x

Repeat this process to find a point y

The point (x, y) represents the trial result

Check to see if this is a hit or a miss

Monte Carlo Solution Approach

Estimation

is the process of estimating a population parameter based upon knowledge of a sample statistic.

estimator

The sample statistic used in estimating a population parameter is called an __.

confidence interval estimate.

The most popular form of an estimate is the

Precision

• refers to the accuracy of an estimate;

better/higher

the smaller the estimate interval, the __ the precision