# 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: ² Collect data from the real system ² Identify a probability distribution to represent the input process ² Choose parameters for the distribution ² 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: ² Plan ahead: begin by a practice or pre-observing session, watch for unusual circumstances ² Analyze the data as it is being collected: check adequacy ² Combine homogeneous data sets, e.g. successive time periods, during the same time period on successive days ² Be aware of data censoring: the quantity is not observed in its entirety, danger of leaving out long process times ² Check for relationship between variables, e.g. build scatter diagram ² Check for autocorrelation ² 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: ² The number of observations ² The dispersion of the data ² Suggested: the square root of the sample size ± For continuous data: ² Corresponds to the probability density function of a theoretical distribution ± For discrete data: ² 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 01 2 11 0 21 9 31 7 41 0 58 67 75 85 93 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: ² The context of the input variable ² Shape of the histogram ± Frequently encountered distributions: ² Easier to analyze: exponential, normal and Poisson ² 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: ² Binomial: # of successes in n trials ² Poisson: # of independent events that occur in a fixed amount of time or space ² Normal: dist±n of a process that is the sum of a number of component processes ²
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Chapter9 - Chapter 9 Input Modeling Banks Carson Nelson...

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