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?

They cannot analyze complex systems Signup and view all the answers

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

A conference for simulation applications and theory Signup and view all the answers

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

Eight years Signup and view all the answers

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

Fork lift trucks and conveyors Signup and view all the answers

What organization sponsors the Winter Simulation Conference (WSC)?

Six technical societies and the National Institute of Standards and Technology (NIST) 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?

Arrivals occur one at a time Signup and view all the answers

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

The mean and variance are equal 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?

Poisson distribution with mean λs 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?

e^(−λt) (λt)^n / n! 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?

Independent increments 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?

Poisson distribution with mean λ(t-s) Signup and view all the answers

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

Z = (X - μ) / σ 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)?

0.1587 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?

Additivity property Signup and view all the answers

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

Normal distribution 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?

μ = ∑i=1n aiμi 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?

σ2 = ∑i=1n ai2σi2 Signup and view all the answers

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

To estimate measures of performance for the system designs being simulated Signup and view all the answers

What is the primary goal of the experimental design phase?

To decide which alternatives to simulate Signup and view all the answers

What is the purpose of program documentation?

To facilitate modification of the program by the same or a different analyst Signup and view all the answers

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

To make decisions about the simulation runs Signup and view all the answers

What is the primary goal of simulation experiments?

To estimate measures of performance for the system designs Signup and view all the answers

What is the purpose of Chapter 11 and 12?

To discuss issues associated with the experimental design Signup and view all the answers

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

To determine if additional runs are needed and what design those additional experiments should follow Signup and view all the answers

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

To discuss issues associated with the experimental design and software to aid in the analysis of simulation experiments Signup and view all the answers

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

They are aware of the problem, but not of its exact nature. Signup and view all the answers

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

Whether simulation is the appropriate methodology for the problem. Signup and view all the answers

What is a key aspect of model conceptualization?

Ability to abstract the essential features of a problem. Signup and view all the answers

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

Some general guidelines to follow. Signup and view all the answers

What is the best approach to building a model?

Start with a simple model and build towards greater complexity. Signup and view all the answers

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

To reduce model-building and computer expenses. Signup and view all the answers

What is not necessary when building a model?

A one-to-one mapping between the model and the real system. Signup and view all the answers

Who should be involved in model conceptualization?

The model user and the model builder. Signup and view all the answers

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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Description

Learn about the role of simulation in waiting lines, especially when analytical solutions are available. Discover how simulation software can offset its disadvantages.