Simulation Modeling Exam 1

Resources

What entities compete for

CV < 1

Gamma or Weibull with alpha > 1

Skewness < 0

Triangular, beta distribution

Mean = median

Uniform, normal, triangular distribution

Skewness = 0

Uniform, normal, triangular distribution

Monte Carlo Simulation

Use random numbers and statistical sampling to approximate solutions of quantitative problems • Stochastic and static simulation • Consists of a series of random events each event unaffected by prior events • The time is not a part of the simulation

Model

a set of assumptions/approximations about how a system works

System

a set of components that act together to achieve some goal or perform some function

Dynamic simulation model

a simulation model used in situations where the state of the system affects how the system changes or evolves over time

discrete simulation

change can occur only at separated points in time

Skewness > 0

exponential, lognormal, or gamma and Weibull with 𝛼 > 1

Entities

"Players" that move around, change status, affect and are affected by other entities.

input analysis

The activity of modeling random components

static simulation model

A simulation model used in situations where the state of the system at one point in time does not affect the state of the system at future points in time.

Attributes

Characteristics of all entities: describe, differentiate.

Lexis ratio = 1 - p

Binomial distribution

Chi-square test

Compares the empirical histogram density constructed from sample data to a candidate theoretical density

Coefficient of variation = 1

Exponential Distribution

CV > 1

Lognormal distribution

Events

Instantaneous occurrence that causes the system state to change.

System state variables

Piece of information that reflects some characteristic of your system, regardless of how many or what kinds of entities might be around.

Deterministic simulation

Models that have no random input

Lexis ratio = 1/p

Negative binomial distribution

Empirical distribution

One that is based directly in observed data

Queues

Place for entities to wait when they can't move on (maybe since resource the want to seize is not available).

Lexis Ratio = 1

Poisson Distribution

Random-number generators (RNGs)

Purpose is to produce a flow of numbers that are observations drawn from a continuous uniform distribution between zero and one and are independent from each other (random numbers).

System State

Set of variables or measures used to describe the current status of a system

Simulation

process of designing a model of a real system and conducting experiments with this model

stochastic model

some model input information is random

continuous simulation

the state of the system can change continuously over time

downtime

time spent on repairing the failure

time to failure

times between instances of failure

Quantile summaries

useful for determining whether an underlying probability density function or probability mass function can be a good fit for the data.

Properties of random numbers

• A sequence of random numbers must have two important statistical properties: • Uniformity • Independence

Kolmogorov-Smirnov test

• Compares the empirical cdf to a theoretical counterpart. • Do not require grouping of the data. • Valid for any sample size. • Range of applicability is limited, because critical values are not readily available.

Events list (event calendar)

• Data structure (like a linked list) used in a discrete event system. • Ordered list of scheduled events with the first event on the list being the earliest.

Piecewise constant rate function

• Divide time frame of simulation into subintervals of time over which you think rate is fairly flat. • Compute observed rate within each subinterval. • Count number of arrivals for each period. • Compute a different rate for each period

Goodness-of-fit test

• The goodness-of-fit of a distribution to a sample is assessed by a statistical test. • The null hypothesis: candidate distribution is a sufficiently good fit to the data. • The alternative hypothesis: it is not. • Useful in providing a quantitative measure of goodness-of-fit.