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# Chapter9 - Chapter 9 Input Modeling Banks Carson Nelson...

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1 Chapter 9 Input Modeling Banks, Carson, Nelson & Nicol Discrete-Event System Simulation 2 Purpose & Overview Input models provide the driving force for a simulation model. The quality of the output is no better than the quality of inputs. In this chapter, we will discuss the 4 steps of input model development: Collect data from the real system Identify a probability distribution to represent the input process Choose parameters for the distribution Evaluate the chosen distribution and parameters for goodness of fit.

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2 3 Data Collection One of the biggest tasks in solving a real problem. GIGO – garbage-in-garbage-out Suggestions that may enhance and facilitate data collection: Plan ahead: begin by a practice or pre-observing session, watch for unusual circumstances Analyze the data as it is being collected: check adequacy Combine homogeneous data sets, e.g. successive time periods, during the same time period on successive days Be aware of data censoring: the quantity is not observed in its entirety, danger of leaving out long process times Check for relationship between variables, e.g. build scatter diagram Check for autocorrelation Collect input data, not performance data 4 Identifying the Distribution Histograms Selecting families of distribution Parameter estimation Goodness-of-fit tests Fitting a non-stationary process
3 5 Histograms [Identifying the distribution] A frequency distribution or histogram is useful in determining the shape of a distribution The number of class intervals depends on: The number of observations The dispersion of the data Suggested: the square root of the sample size For continuous data: Corresponds to the probability density function of a theoretical distribution For discrete data: Corresponds to the probability mass function If few data points are available: combine adjacent cells to eliminate the ragged appearance of the histogram 6 Histograms [Identifying the distribution] Vehicle Arrival Example: # of vehicles arriving at an intersection between 7 am and 7:05 am was monitored for 100 random workdays. There are ample data, so the histogram may have a cell for each possible value in the data range Arrivals per Period Frequency 0 12 1 10 2 19 3 17 4 10 5 8 6 7 7 5 8 5 9 3 10 3 11 1 Same data with different interval sizes

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4 7 Selecting the Family of Distributions [Identifying the distribution] A family of distributions is selected based on: The context of the input variable Shape of the histogram Frequently encountered distributions: Easier to analyze: exponential, normal and Poisson Harder to analyze: beta, gamma and Weibull 8 Selecting the Family of Distributions [Identifying the distribution] Use the physical basis of the distribution as a guide, for example: Binomial: # of successes in n trials Poisson: # of independent events that occur in a fixed amount of time or space Normal: dist’n of a process that is the sum of a number of component processes Exponential: time between independent events, or a process time that is memoryless Weibull: time to failure for components
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