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Questions and Answers
What distinguishes uniform arrival times from uniform interarrivals?
What distinguishes uniform arrival times from uniform interarrivals?
- Uniform interarrivals refer to the frequency of arrivals rather than their timing. (correct)
- Uniform arrival times are consistent over time, while interarrivals can vary.
- Uniform arrival times are only applicable in real-time systems.
- There is no difference; they are terms used interchangeably.
Which of the following is true about simulation validation?
Which of the following is true about simulation validation?
- It focuses on improving the efficiency of the simulation.
- It assesses whether the simulation accurately models the real-world system. (correct)
- It only applies to agent-based simulations.
- It is the process of ensuring that the simulation is built correctly.
What are consistency checks used for in V&V?
What are consistency checks used for in V&V?
- To measure the variability of input parameters.
- To confirm the simulation's behavior matches expected results. (correct)
- To ensure compatibility with external software.
- To identify computational inefficiencies in the simulation.
Which of the following represents an acceptable way to validate a simulation?
Which of the following represents an acceptable way to validate a simulation?
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Which phase of simulation development can be skipped without consequences?
Which phase of simulation development can be skipped without consequences?
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Which describes the service rate in the context of traffic intensity in SSQ?
Which describes the service rate in the context of traffic intensity in SSQ?
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Which statement is true about Little's Equation in the context of SSQ?
Which statement is true about Little's Equation in the context of SSQ?
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What technique is essential for uniformly random point generation in simulations?
What technique is essential for uniformly random point generation in simulations?
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Why is it important to use multiple seeds in Monte Carlo simulations?
Why is it important to use multiple seeds in Monte Carlo simulations?
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Which characteristic is unique to Monte Carlo simulations?
Which characteristic is unique to Monte Carlo simulations?
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What is the relationship between a seed for a pRNG and the sequence of values generated?
What is the relationship between a seed for a pRNG and the sequence of values generated?
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What is a primary flaw of the traditional one-pass variance equation in computer simulation?
What is a primary flaw of the traditional one-pass variance equation in computer simulation?
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How do empirical cumulative distribution functions (CDFs) compare to histograms?
How do empirical cumulative distribution functions (CDFs) compare to histograms?
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What does the Random() routine provide to a simulation writer?
What does the Random() routine provide to a simulation writer?
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In terms of binning continuous data, how many bins are generally needed for a sample of size n?
In terms of binning continuous data, how many bins are generally needed for a sample of size n?
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Study Notes
Exam 1 Learning Goals Summary
- Monte Carlo Simulations
- Know accept/reject techniques for generating uniformly random points.
- Write Monte Carlo simulations for estimating the probability of an event.
- Understand common pitfalls of naive random point generation.
- Recognize the unique features that define a Monte Carlo simulation.
- Identify faulty point generation algorithms by analyzing spatial plots.
- Understand the importance of using a random number generator for generating radial values in a circle.
- Explain why using various seeds and multiple replications is essential in Monte Carlo simulations.
- Know the function of the Random() API routine in a simulation.
- Identify the purpose of a seed in a pseudo-random number generator (pRNG) and its connection to the generated values.
- Define ρ (rho) in the context of pRNGs.
- Understand the conditions under which the sequence of values generated by the Random() function repeats.
- Probability Distributions
- Understand how to derive the cumulative distribution function (CDF) from the probability density function (PDF) of continuous probability distributions.
- Calculate the probability of an event for both discrete and continuous distributions.
- Calculate the mean and standard deviation of discrete data.
- Recognize the limitations of traditional one-pass variance equations in computer simulations.
- Explain empirical CDFs and their advantages over histograms.
- Define histograms and their relation to CDFs.
- Understand the general approach to binning continuous data and the estimated number of bins needed for a sample size of n.
- Apply Welford's discrete and integral mean and variance equations (Theorems 4.1.2 and 4.1.4) to a data set.
- Recognize the superiority of Welford's equations over traditional one-pass algorithms.
- Identify the flawed non-Welford equations for calculating variance.
- Explain why integrals and anti-differentiation are not necessary for integrating sample paths.
- Distinguish between uniform arrival times and uniform interarrivals.
- Understand that valid computer simulations should not produce outliers.
- Simulation Validation and Verification (V&V)
- Define consistency checks and their application in V&V.
- Understand the five phases of simulation development proposed by the authors: conceptual, specification, computational, and V&V.
- Define validation and verification in the context of simulation.
- Understand the concepts of computational model, conceptual model, and specification model in simulation.
- Identify two acceptable methods for validating a simulation.
- Explain when specific stages of simulation development can be skipped.
- Simple Inventory System (SIS) Case Study
- Understand the SIS, its assumptions, and simplifications.
- Analyze the experimental design of the SIS case study, including how an optimal value for s was determined.
- Describe the effect of traffic intensity on the expected behavior and performance of a single-server queue (SSQ).
- Calculate traffic intensity and its relation to service rate.
- Understand how to write a FIFO SSQ simulation using a simple while loop and how to manipulate ai and si for simple experiments.
- Appreciate the broad applicability of the canonical SSQ to computer simulation.
- Distinguish between job-averaged and time-averaged statistics in an SSQ.
- Identify the four different queuing disciplines that can be used in an SSQ simulation.
- Understand the conditions required for applying Little's equations to the statistical measures of an SSQ.
- Differentiate timestamps and time intervals within the six time measures used in an SSQ.
- Random Variates
- Understand the parameters, probability mass function (pmf), and CDF of the Equilikely(a,b) random variate.
- Understand the Exponential(mu) random variate and the interpretation of its parameter mu in the context of arrival times.
- Explain the F(x) inversion technique for constructing random variates and its requirement on F(x).
- Understand the parameters, PDF, and CDF of the Uniform(a,b) random variate.
- Recognize the limitations of the RandomInteger() mod SIZE programming pattern.
- Explain the role of the parameter u in random variates.
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