Simulation in Waiting Lines

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Questions and Answers

Why may simulation be used even when an analytical solution is possible?

  • Because simulation provides more accurate results
  • Because of the ease of use of simulation software
  • Due to the complexity of the system
  • When closed-form models are available (correct)

What development in simulation software has offset the disadvantage of requiring extensive programming knowledge?

  • Increased use of analytical solutions
  • Advances in hardware
  • Models that require only input data for operation (correct)
  • Improved output analysis capabilities

What has contributed to the increased speed of simulation?

  • Advances in analytical solutions
  • Improvements in simulation software
  • Increased use of closed-form models
  • Advances in hardware and simulation software (correct)

What is a limitation of closed-form models?

<p>They cannot analyze complex systems (A)</p> Signup and view all the answers

What is the Winter Simulation Conference (WSC) related to?

<p>A conference for simulation applications and theory (B)</p> Signup and view all the answers

How many years of consulting practice is mentioned in the text?

<p>Eight years (D)</p> Signup and view all the answers

What type of vehicles are mentioned as being modeled in some simulation software?

<p>Fork lift trucks and conveyors (B)</p> Signup and view all the answers

What organization sponsors the Winter Simulation Conference (WSC)?

<p>Six technical societies and the National Institute of Standards and Technology (NIST) (A)</p> Signup and view all the answers

What is a condition for a counting process {N(t), t≥0} to be a Poisson process with mean rate λ?

<p>Arrivals occur one at a time (B)</p> Signup and view all the answers

What is a property of a Poisson process with mean rate λ?

<p>The mean and variance are equal (C)</p> Signup and view all the answers

What is the probability distribution of the number of arrivals during a time interval of length s in a Poisson process with mean rate λ?

<p>Poisson distribution with mean λs (B)</p> Signup and view all the answers

What is the probability of n arrivals during a time interval of length t in a Poisson process with mean rate λ?

<p>e^(−λt) (λt)^n / n! (B)</p> Signup and view all the answers

What is the property of a Poisson process that states that the number of arrivals during non-overlapping time intervals are independent random variables?

<p>Independent increments (D)</p> Signup and view all the answers

What is the distribution of the number of arrivals during a time interval [s, t] in a Poisson process with mean rate λ?

<p>Poisson distribution with mean λ(t-s) (B)</p> Signup and view all the answers

What is the transformation of variables used to evaluate the distribution of a normal random variable X?

<p>Z = (X - μ) / σ (A)</p> Signup and view all the answers

What is the probability that the vessel is loaded in less than 10 hours, given that X ~ N(12, 4)?

<p>0.1587 (D)</p> Signup and view all the answers

What is the property of the normal distribution that states the sum of n independent normal variates is a normal variate?

<p>Additivity property (C)</p> Signup and view all the answers

What is the distribution of the sum of a large number of independent observations from any distribution?

<p>Normal distribution (B)</p> Signup and view all the answers

What is the mean of the sum of n independent normal variates, given that Xi ~ N(μi, σi) and X = ∑i=1n ai Xi?

<p>μ = ∑i=1n aiμi (D)</p> Signup and view all the answers

What is the variance of the sum of n independent normal variates, given that Xi ~ N(μi, σi) and X = ∑i=1n ai Xi?

<p>σ2 = ∑i=1n ai2σi2 (B)</p> Signup and view all the answers

What is the primary purpose of production runs and their subsequent analysis?

<p>To estimate measures of performance for the system designs being simulated (A)</p> Signup and view all the answers

What is the primary goal of the experimental design phase?

<p>To decide which alternatives to simulate (C)</p> Signup and view all the answers

What is the purpose of program documentation?

<p>To facilitate modification of the program by the same or a different analyst (C)</p> Signup and view all the answers

What is the purpose of determining the length of the initialization period?

<p>To make decisions about the simulation runs (B)</p> Signup and view all the answers

What is the primary goal of simulation experiments?

<p>To estimate measures of performance for the system designs (C)</p> Signup and view all the answers

What is the purpose of Chapter 11 and 12?

<p>To discuss issues associated with the experimental design (B)</p> Signup and view all the answers

What is the primary goal of the 'More Runs?' phase?

<p>To determine if additional runs are needed and what design those additional experiments should follow (C)</p> Signup and view all the answers

What is the purpose of Chapters 4 and 11-12?

<p>To discuss issues associated with the experimental design and software to aid in the analysis of simulation experiments (C)</p> Signup and view all the answers

What is often the case with policy makers and analysts regarding a problem?

<p>They are aware of the problem, but not of its exact nature. (C)</p> Signup and view all the answers

What should be determined during the setting of objectives and overall project plan?

<p>Whether simulation is the appropriate methodology for the problem. (A)</p> Signup and view all the answers

What is a key aspect of model conceptualization?

<p>Ability to abstract the essential features of a problem. (C)</p> Signup and view all the answers

According to Morris, what can be provided to help with model building?

<p>Some general guidelines to follow. (A)</p> Signup and view all the answers

What is the best approach to building a model?

<p>Start with a simple model and build towards greater complexity. (B)</p> Signup and view all the answers

Why should the model's complexity not exceed that required to accomplish its purpose?

<p>To reduce model-building and computer expenses. (D)</p> Signup and view all the answers

What is not necessary when building a model?

<p>A one-to-one mapping between the model and the real system. (D)</p> Signup and view all the answers

Who should be involved in model conceptualization?

<p>The model user and the model builder. (C)</p> Signup and view all the answers

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Study Notes

Simulation Advantages and Disadvantages

  • Simulation can be used when an analytical solution is possible or preferable, especially in cases where closed-form queueing models are available.
  • Four disadvantages of simulation can be offset by:
    • Using simulation software with pre-built models that require only input data.
    • Utilizing output analysis capabilities within simulation software for thorough analysis.
    • Taking advantage of advances in hardware and software that enable faster simulation.
    • Recognizing that closed-form models are not able to analyze complex systems that are often encountered in practice.

Areas of Application

  • The applications of simulation are vast and can be explored through the Winter Simulation Conference (WSC) and its tutorials.
  • Policy makers and analysts often identify problems before understanding their nature, and simulation can help answer questions and set objectives.

Simulation Process

  • Setting objectives and overall project plan:
    • Determine if simulation is the appropriate methodology for the problem.
    • Define the alternative systems to be considered and a method for evaluating their effectiveness.
    • Plan the study, including the number of people involved, cost, and timeline.
  • Model conceptualization:
    • Building a model of a system is both an art and a science.
    • Start with a simple model and build towards complexity.
    • Involve the model user in the conceptualization process.
  • Experimental design:
    • Determine the alternatives to be simulated.
    • Decide on the length of the initialization period, simulation runs, and number of replications.
  • Production runs and analysis:
    • Use simulation runs to estimate measures of performance for system designs.
    • Analyze the results to determine if additional runs are needed.
  • Documentation and reporting:
    • Document the program and progress to facilitate understanding and modification.
    • Evaluate the distribution of results using the standard normal distribution.

Normal Distribution

  • The normal distribution is important because it is the most commonly used distribution in data analysis.
  • The sum of n independent normal variates is a normal variate.
  • The sum of a large number of independent observations from any distribution has a normal distribution.

Example: Normal Distribution

  • The time required to load an ocean-going vessel is distributed as N(12, 4).
  • The probability that the vessel is loaded in less than 10 hours can be calculated using the standard normal distribution.

Poisson Process

  • A Poisson process is a counting process that satisfies certain conditions:
    • Arrivals occur one at a time.
    • The process has stationary increments.
    • The process has independent increments.
  • Properties of the Poisson process:
    • Equal mean and variance.
    • Stationary increment: The number of arrivals in time s to t is also Poisson distributed with mean λ(t-s).

Example: Poisson Process

  • The time to pass through a queue to begin self-service at a cafeteria is found to be N(15, 9).
  • The Poisson process is used to model arrivals in various contexts, such as arrival of jobs, e-mails to a server, boats to a dock, and calls to a call center.

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