02LectureNotes_OutputAnalysis_SingleSystem

# 02LectureNotes_OutputAnalysis_SingleSystem - IE 305/404...

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IE 305/404 Simulation Chapter 9: Output Analysis of a Single System Output Analysis of a Single System In this section (and Chapter 9) we will learn about analyzing the results of a single simulation model. Later in Chapter 10, we will learn how to compare alternate systems (and, for example, choose the best system). This material is applied statistics.

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A common (but poor) practice: Run the simulation for a while. Obtain estimates of the system performance measures that are relevant: e.g. o Ave time in Queue o Ave Number in system o Ave throughput time o Ave % who wait less than 5 minutes in Queue o % Resource utilization Then use these results to make decisions/conclusions. There are two major things wrong with this approach.
First these estimates are only estimates. They are random variables. We do not know how much faith we can put in them (i.e. how accurate are they?) Second the system exhibits transient behavior (see below) Do we want the average number in Q from below? Num in Q Time

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Example of first problem : Consider a simulation of a 1-800 customer service center where customers call in, wait on hold, then are serviced by customer service representative. Suppose we want: - At least 67% of the customers wait on hold to be less than 11 seconds - The mean time on hold to be less than 8 seconds. (See posted ARENA example)
Suppose we ran the simulation and got the following results: - % Customers on hold for less than 11 seconds = 69% - Average time on hold = 7.17 seconds Does the system meet the performance criteria? Since both the 69% and the 7.17 seconds are outcomes of random variables, we do not know how much faith to put in them. This leads to what is perhaps the most important and basic principle of statistics: "A (statistical) estimate is worthless unless accompanied by an indication of the accuracy of the estimate."

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Two common ways of specifying estimate accuracy are: - A confidence interval of specified probability content (e.g. a 95% confidence interval) - The standard error of the estimate . (The estimate is a random variable). Standard error is (an estimate of) the standard deviation of the estimate (and not the standard deviation of the population) These two are related, as the half-width of the confidence interval is typically a multiple of the standard error Given our (single) estimate above of the % under 11 seconds = 69%, how can we estimate the standard error?
σ given a sample of size one (since we only ran one replicate of the simulation). We can’t do it. What we need are repeated observations or “ replicates ” of the estimate. Now suppose we ran the simulation 5 times (with different random number seeds of course). Why different random number seeds?

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## This note was uploaded on 02/22/2011 for the course IE 305 taught by Professor Storer during the Spring '08 term at Lehigh University .

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02LectureNotes_OutputAnalysis_SingleSystem - IE 305/404...

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