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                           <rdf:li><rdf:Description xmpDM:name="Model Validation Techniques Validation techniques for one problem may not apply to another problem." xmpDM:startTime="0" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Aspects to Validate: 1." xmpDM:startTime="0" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Assumptions 2." xmpDM:startTime="0" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Input parameter values and distributions 3." xmpDM:startTime="0" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Output values and conclusions Techniques: 1." xmpDM:startTime="0" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Expert intuition 2." xmpDM:startTime="0" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Real system measurements 3." xmpDM:startTime="0" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Theoretical results Þ 3 × 3 = 9 validation tests" xmpDM:startTime="0" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Expert Intuition Most practical and common way Experts = Involved in design, architecture, implementation, analysis, marketing, or maintenance of the" xmpDM:startTime="19100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="system Selection = fn of Life cycle stage Present assumption, input, output Better to validate one at a time See" xmpDM:startTime="19100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="if the experts can distinguish simulation vs." xmpDM:startTime="19100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="measurement" xmpDM:startTime="19100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Expert Intuition (Cont) chp_25_06-1" xmpDM:startTime="50667" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Real System Measurements Compare assumptions, input, output with the real world Often infeasible or expensive Even one or two measurements" xmpDM:startTime="77867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="add to the validity" xmpDM:startTime="77867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Theoretical Results Analysis = Simulation Used to validate analysis also Both may be invalid Use theory in conjunction with experts'" xmpDM:startTime="124333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="intuition E.g.," xmpDM:startTime="124333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Use theory for a large configuration Can show that the model is not invalid" xmpDM:startTime="124333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 25.1" xmpDM:startTime="270467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Imagine that you have been called as an expert to review a simulation study." xmpDM:startTime="270467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Which of the following simulation results would you consider non-intuitive and would want it carefully validated: 1." xmpDM:startTime="270467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The throughput of a system increases as its load increases." xmpDM:startTime="270467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="2." xmpDM:startTime="270467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The throughput of a system decreases as its load increases." xmpDM:startTime="270467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3." xmpDM:startTime="270467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The response time increases as the load increases." xmpDM:startTime="270467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4." xmpDM:startTime="270467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The response time of a system decreases as its load increases." xmpDM:startTime="270467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="5." xmpDM:startTime="270467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The loss rate of a system decreases as the load increases." xmpDM:startTime="270467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="This is not a homework." xmpDM:startTime="270467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Try but do not submit." xmpDM:startTime="270467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Check answer in the book." xmpDM:startTime="270467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="270467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Transient Removal Generally steady state performance is interesting Remove the initial part No exact definition Þ Heuristics: 1." xmpDM:startTime="331767" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Long Runs 2." xmpDM:startTime="331767" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Proper Initialization 3." xmpDM:startTime="331767" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Truncation 4." xmpDM:startTime="331767" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Initial Data Deletion 5." xmpDM:startTime="331767" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Moving Average of Independent Replications 6." xmpDM:startTime="331767" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Batch Means" xmpDM:startTime="331767" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Transient Removal Generally steady state performance is interesting Remove the initial part No exact definition Þ Heuristics: 1." xmpDM:startTime="364333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Long Runs 2." xmpDM:startTime="364333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Proper Initialization 3." xmpDM:startTime="364333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Truncation 4." xmpDM:startTime="364333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Initial Data Deletion 5." xmpDM:startTime="364333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Moving Average of Independent Replications 6." xmpDM:startTime="364333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Batch Means" xmpDM:startTime="364333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Transient Removal Techniques Long Runs: Wastes resources Difficult to insure that it is long enough Proper Initialization: Start in a" xmpDM:startTime="425933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="state close to expected steady state Þ Reduces the length and effect of transient state" xmpDM:startTime="425933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Truncation Assumes variability is lower during steady state Plot max-min of n-l observation for l =1, 2, ………." xmpDM:startTime="466200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="When (l+1)th observation is neither the minimum nor maximum Þ transient state ended At l = 9, Range = (9," xmpDM:startTime="466200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="11), next observation = 10 Sometimes incorrect result." xmpDM:startTime="466200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp TP_tmp 0 4 8 12 16 20 4 8 12 Value Observation number i Transient interval" xmpDM:startTime="466200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Terminating Simulations Transient performance is of interest E.g.," xmpDM:startTime="607833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Network traffic System shuts down Þ Do not need transient removal." xmpDM:startTime="607833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Final conditions: May need to exclude the final portion from results Techniques similar to transient removal" xmpDM:startTime="607833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Treatment of Leftover Entities Mean service time Mean waiting time Mean Queue Length TP_tmp TP_tmp TP_tmp TP_tmp" xmpDM:startTime="617367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Terminating Simulations Transient performance is of interest E.g.," xmpDM:startTime="619133" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Network traffic System shuts down Þ Do not need transient removal." xmpDM:startTime="619133" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Final conditions: May need to exclude the final portion from results Techniques similar to transient removal" xmpDM:startTime="619133" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Truncation Assumes variability is lower during steady state Plot max-min of n-l observation for l =1, 2, ………." xmpDM:startTime="619567" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="When (l+1)th observation is neither the minimum nor maximum Þ transient state ended At l = 9, Range = (9," xmpDM:startTime="619567" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="11), next observation = 10 Sometimes incorrect result." xmpDM:startTime="619567" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp TP_tmp 0 4 8 12 16 20 4 8 12 Value Observation number i Transient interval" xmpDM:startTime="619567" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Transient Removal Techniques Long Runs: Wastes resources Difficult to insure that it is long enough Proper Initialization: Start in a" xmpDM:startTime="619967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="state close to expected steady state Þ Reduces the length and effect of transient state" xmpDM:startTime="619967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Transient Removal Generally steady state performance is interesting Remove the initial part No exact definition Þ Heuristics: 1." xmpDM:startTime="620900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Long Runs 2." xmpDM:startTime="620900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Proper Initialization 3." xmpDM:startTime="620900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Truncation 4." xmpDM:startTime="620900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Initial Data Deletion 5." xmpDM:startTime="620900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Moving Average of Independent Replications 6." xmpDM:startTime="620900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Batch Means" xmpDM:startTime="620900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Transient Removal Techniques Long Runs: Wastes resources Difficult to insure that it is long enough Proper Initialization: Start in a" xmpDM:startTime="639467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="state close to expected steady state Þ Reduces the length and effect of transient state" xmpDM:startTime="639467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Truncation Assumes variability is lower during steady state Plot max-min of n-l observation for l =1, 2, ………." xmpDM:startTime="640033" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="When (l+1)th observation is neither the minimum nor maximum Þ transient state ended At l = 9, Range = (9," xmpDM:startTime="640033" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="11), next observation = 10 Sometimes incorrect result." xmpDM:startTime="640033" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp TP_tmp 0 4 8 12 16 20 4 8 12 Value Observation number i Transient interval" xmpDM:startTime="640033" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Transient Removal Techniques Long Runs: Wastes resources Difficult to insure that it is long enough Proper Initialization: Start in a" xmpDM:startTime="641633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="state close to expected steady state Þ Reduces the length and effect of transient state" xmpDM:startTime="641633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Transient Removal Generally steady state performance is interesting Remove the initial part No exact definition Þ Heuristics: 1." xmpDM:startTime="642967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Long Runs 2." xmpDM:startTime="642967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Proper Initialization 3." xmpDM:startTime="642967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Truncation 4." xmpDM:startTime="642967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Initial Data Deletion 5." xmpDM:startTime="642967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Moving Average of Independent Replications 6." xmpDM:startTime="642967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Batch Means" xmpDM:startTime="642967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Transient Removal Techniques Long Runs: Wastes resources Difficult to insure that it is long enough Proper Initialization: Start in a" xmpDM:startTime="749600" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="state close to expected steady state Þ Reduces the length and effect of transient state" xmpDM:startTime="749600" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Truncation Assumes variability is lower during steady state Plot max-min of n-l observation for l =1, 2, ………." xmpDM:startTime="750367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="When (l+1)th observation is neither the minimum nor maximum Þ transient state ended At l = 9, Range = (9," xmpDM:startTime="750367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="11), next observation = 10 Sometimes incorrect result." xmpDM:startTime="750367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp TP_tmp 0 4 8 12 16 20 4 8 12 Value Observation number i Transient interval" xmpDM:startTime="750367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Terminating Simulations Transient performance is of interest E.g.," xmpDM:startTime="750933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Network traffic System shuts down Þ Do not need transient removal." xmpDM:startTime="750933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Final conditions: May need to exclude the final portion from results Techniques similar to transient removal" xmpDM:startTime="750933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Treatment of Leftover Entities Mean service time Mean waiting time Mean Queue Length TP_tmp TP_tmp TP_tmp TP_tmp" xmpDM:startTime="795600" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Terminating Simulations Transient performance is of interest E.g.," xmpDM:startTime="800000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Network traffic System shuts down Þ Do not need transient removal." xmpDM:startTime="800000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Final conditions: May need to exclude the final portion from results Techniques similar to transient removal" xmpDM:startTime="800000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Treatment of Leftover Entities Mean service time Mean waiting time Mean Queue Length TP_tmp TP_tmp TP_tmp TP_tmp" xmpDM:startTime="898200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 25.3:" xmpDM:startTime="1119500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Treatment of Leftover Entities Three events: Arrival at t=0, departures at t=1 and t=4 Q = 2, 1, 0 at" xmpDM:startTime="1119500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="these events." xmpDM:startTime="1119500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Avg Q = (2+1+0)/3 = 1 Avg Q = Area/4 = 5/4 0 1 2 3 4 2 1 0" xmpDM:startTime="1119500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Queue length q(t) Time t" xmpDM:startTime="1119500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Treatment of Leftover Entities Mean service time Mean waiting time Mean Queue Length TP_tmp TP_tmp TP_tmp TP_tmp" xmpDM:startTime="1122733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 25.3:" xmpDM:startTime="1144200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Treatment of Leftover Entities Three events: Arrival at t=0, departures at t=1 and t=4 Q = 2, 1, 0 at" xmpDM:startTime="1144200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="these events." xmpDM:startTime="1144200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Avg Q = (2+1+0)/3 = 1 Avg Q = Area/4 = 5/4 0 1 2 3 4 2 1 0" xmpDM:startTime="1144200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Queue length q(t) Time t" xmpDM:startTime="1144200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Treatment of Leftover Entities Mean service time Mean waiting time Mean Queue Length TP_tmp TP_tmp TP_tmp TP_tmp" xmpDM:startTime="1191267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 25.3:" xmpDM:startTime="1197267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Treatment of Leftover Entities Three events: Arrival at t=0, departures at t=1 and t=4 Q = 2, 1, 0 at" xmpDM:startTime="1197267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="these events." xmpDM:startTime="1197267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Avg Q = (2+1+0)/3 = 1 Avg Q = Area/4 = 5/4 0 1 2 3 4 2 1 0" xmpDM:startTime="1197267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Queue length q(t) Time t" xmpDM:startTime="1197267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Stopping Criteria: Variance Estimation Run until confidence interval is narrow enough For Independent observations: Independence not applicable to most simulations." xmpDM:startTime="1226933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Large waiting time for ith job Þ Large waiting time for (i+1)th job For correlated observations: TP_tmp TP_tmp TP_tmp" xmpDM:startTime="1226933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Variance Estimation Methods 1." xmpDM:startTime="1396133" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Independent Replications 2." xmpDM:startTime="1396133" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Batch Means 3." xmpDM:startTime="1396133" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Method of Regeneration" xmpDM:startTime="1396133" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Independent Replications Assumes that means of independent replications are independent Conduct m replications of size n+n0 each 1." xmpDM:startTime="1433700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Compute a mean for each replication: 2." xmpDM:startTime="1433700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Compute an overall mean for all replications: TP_tmp TP_tmp" xmpDM:startTime="1433700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Independent Replications (Cont) 3." xmpDM:startTime="1496300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Calculate the variance of replicate means: 4." xmpDM:startTime="1496300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Confidence interval for the mean response is: Keep replications large to avoid waste Ten replications generally sufficient TP_tmp TP_tmp" xmpDM:startTime="1496300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Independent Replications Assumes that means of independent replications are independent Conduct m replications of size n+n0 each 1." xmpDM:startTime="1517967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Compute a mean for each replication: 2." xmpDM:startTime="1517967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Compute an overall mean for all replications: TP_tmp TP_tmp" xmpDM:startTime="1517967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Variance Estimation Methods 1." xmpDM:startTime="1564733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Independent Replications 2." xmpDM:startTime="1564733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Batch Means 3." xmpDM:startTime="1564733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Method of Regeneration" xmpDM:startTime="1564733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Independent Replications Assumes that means of independent replications are independent Conduct m replications of size n+n0 each 1." xmpDM:startTime="1566400" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Compute a mean for each replication: 2." xmpDM:startTime="1566400" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Compute an overall mean for all replications: TP_tmp TP_tmp" xmpDM:startTime="1566400" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Variance Estimation Methods 1." xmpDM:startTime="1567500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Independent Replications 2." xmpDM:startTime="1567500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Batch Means 3." xmpDM:startTime="1567500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Method of Regeneration" xmpDM:startTime="1567500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Stopping Criteria: Variance Estimation Run until confidence interval is narrow enough For Independent observations: Independence not applicable to most simulations." xmpDM:startTime="1567833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Large waiting time for ith job Þ Large waiting time for (i+1)th job For correlated observations: TP_tmp TP_tmp TP_tmp" xmpDM:startTime="1567833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Variance Estimation Methods 1." xmpDM:startTime="1576200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Independent Replications 2." xmpDM:startTime="1576200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Batch Means 3." xmpDM:startTime="1576200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Method of Regeneration" xmpDM:startTime="1576200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Independent Replications Assumes that means of independent replications are independent Conduct m replications of size n+n0 each 1." xmpDM:startTime="1576633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Compute a mean for each replication: 2." xmpDM:startTime="1576633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Compute an overall mean for all replications: TP_tmp TP_tmp" xmpDM:startTime="1576633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Independent Replications (Cont) 3." xmpDM:startTime="1577100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Calculate the variance of replicate means: 4." xmpDM:startTime="1577100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Confidence interval for the mean response is: Keep replications large to avoid waste Ten replications generally sufficient TP_tmp TP_tmp" xmpDM:startTime="1577100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Batch Means Also called method of sub-samples Run a long simulation run Discard initial transient interval, and Divide the remaining" xmpDM:startTime="1608467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="observations run into several batches or sub-samples." xmpDM:startTime="1608467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="1." xmpDM:startTime="1608467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Compute means for each batch: 2." xmpDM:startTime="1608467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Compute an overall mean: TP_tmp TP_tmp" xmpDM:startTime="1608467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Batch Means (Cont) 3." xmpDM:startTime="1608733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Calculate the variance of batch means: 4." xmpDM:startTime="1608733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Confidence interval for the mean response is: Less waste than independent replications Keep batches long to avoid correlation Check: Compute" xmpDM:startTime="1608733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="the auto-covariance of successive batch means: Double n until autocovariance is small." xmpDM:startTime="1608733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp TP_tmp TP_tmp" xmpDM:startTime="1608733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="1608967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Batch Means (Cont) 3." xmpDM:startTime="1609867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Calculate the variance of batch means: 4." xmpDM:startTime="1609867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Confidence interval for the mean response is: Less waste than independent replications Keep batches long to avoid correlation Check: Compute" xmpDM:startTime="1609867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="the auto-covariance of successive batch means: Double n until autocovariance is small." xmpDM:startTime="1609867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp TP_tmp TP_tmp" xmpDM:startTime="1609867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Batch Means Also called method of sub-samples Run a long simulation run Discard initial transient interval, and Divide the remaining" xmpDM:startTime="1610200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="observations run into several batches or sub-samples." xmpDM:startTime="1610200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="1." xmpDM:startTime="1610200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Compute means for each batch: 2." xmpDM:startTime="1610200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Compute an overall mean: TP_tmp TP_tmp" xmpDM:startTime="1610200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Independent Replications (Cont) 3." xmpDM:startTime="1612000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Calculate the variance of replicate means: 4." xmpDM:startTime="1612000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Confidence interval for the mean response is: Keep replications large to avoid waste Ten replications generally sufficient TP_tmp TP_tmp" xmpDM:startTime="1612000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Batch Means Also called method of sub-samples Run a long simulation run Discard initial transient interval, and Divide the remaining" xmpDM:startTime="1629400" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="observations run into several batches or sub-samples." xmpDM:startTime="1629400" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="1." xmpDM:startTime="1629400" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Compute means for each batch: 2." xmpDM:startTime="1629400" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Compute an overall mean: TP_tmp TP_tmp" xmpDM:startTime="1629400" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Batch Means (Cont) 3." xmpDM:startTime="1675033" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Calculate the variance of batch means: 4." xmpDM:startTime="1675033" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Confidence interval for the mean response is: Less waste than independent replications Keep batches long to avoid correlation Check: Compute" xmpDM:startTime="1675033" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="the auto-covariance of successive batch means: Double n until autocovariance is small." xmpDM:startTime="1675033" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp TP_tmp TP_tmp" xmpDM:startTime="1675033" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="1766033" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Summary Verification = Debugging Þ Software development techniques Validation Þ Simulation = Real Þ Experts involvement Transient Removal: Initial data" xmpDM:startTime="1888033" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="deletion, batch means Terminating Simulations = Transients are of interest Stopping Criteria: Independent replications, batch means, method of regeneration Variance" xmpDM:startTime="1888033" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="reduction is not for novice" xmpDM:startTime="1888033" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="1889500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Summary Verification = Debugging Þ Software development techniques Validation Þ Simulation = Real Þ Experts involvement Transient Removal: Initial data" xmpDM:startTime="1895867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="deletion, batch means Terminating Simulations = Transients are of interest Stopping Criteria: Independent replications, batch means, method of regeneration Variance" xmpDM:startTime="1895867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="reduction is not for novice" xmpDM:startTime="1895867" xmpDM:duration="1000"/></rdf:li></rdf:Seq>
                     </xmpDM:markers>
                  </rdf:Description>
               </rdf:li>
               <rdf:li>
                  <rdf:Description xmpDM:trackType="TableOfContents" xmpDM:frameRate="f1000" xmpDM:trackName="Table of Contents">
                     <xmpDM:markers>
                        <rdf:Seq>
                           <rdf:li><rdf:Description xmpDM:name="    Model Validation Techniques" xmpDM:startTime="0" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="0" tscDM:imageoffset="0" tscDM:imagerect="0, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Expert Intuition" xmpDM:startTime="19100" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="1" tscDM:imageoffset="0" tscDM:imagerect="75, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Expert Intuition (Cont)" xmpDM:startTime="50667" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="2" tscDM:imageoffset="0" tscDM:imagerect="150, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="      Real System Measurements" xmpDM:startTime="77867" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="3" tscDM:imageoffset="0" tscDM:imagerect="225, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Theoretical Results" xmpDM:startTime="124333" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="4" tscDM:imageoffset="0" tscDM:imagerect="300, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 25.1" xmpDM:startTime="270467" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="5" tscDM:imageoffset="0" tscDM:imagerect="375, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Transient Removal" xmpDM:startTime="331767" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="6" tscDM:imageoffset="0" tscDM:imagerect="450, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="End of presentation" xmpDM:startTime="356267" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="7" tscDM:imageoffset="0" tscDM:imagerect="525, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Transient Removal" xmpDM:startTime="364333" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="8" tscDM:imageoffset="0" tscDM:imagerect="600, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name=" Transient Removal Techniques" xmpDM:startTime="425933" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="9" tscDM:imageoffset="0" tscDM:imagerect="675, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Truncation" xmpDM:startTime="466200" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="10" tscDM:imageoffset="0" tscDM:imagerect="750, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Terminating Simulations" xmpDM:startTime="607833" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="11" tscDM:imageoffset="0" tscDM:imagerect="825, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="   Treatment of Leftover Entities" xmpDM:startTime="617367" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="12" tscDM:imageoffset="0" tscDM:imagerect="900, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Terminating Simulations" xmpDM:startTime="619133" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="13" tscDM:imageoffset="0" tscDM:imagerect="975, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Truncation" xmpDM:startTime="619567" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="14" tscDM:imageoffset="0" tscDM:imagerect="1050, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name=" Transient Removal Techniques" xmpDM:startTime="619967" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="15" tscDM:imageoffset="0" tscDM:imagerect="1125, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Transient Removal" xmpDM:startTime="620900" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="16" tscDM:imageoffset="0" tscDM:imagerect="1200, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name=" Transient Removal Techniques" xmpDM:startTime="639467" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="17" tscDM:imageoffset="0" tscDM:imagerect="1275, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Truncation" xmpDM:startTime="640033" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="18" tscDM:imageoffset="0" tscDM:imagerect="1350, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name=" Transient Removal Techniques" xmpDM:startTime="641633" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="19" tscDM:imageoffset="0" tscDM:imagerect="1425, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Transient Removal" xmpDM:startTime="642967" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="20" tscDM:imageoffset="0" tscDM:imagerect="1500, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name=" Transient Removal Techniques" xmpDM:startTime="749600" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="21" tscDM:imageoffset="0" tscDM:imagerect="1575, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Truncation" xmpDM:startTime="750367" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="22" tscDM:imageoffset="0" tscDM:imagerect="1650, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Terminating Simulations" xmpDM:startTime="750933" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="23" tscDM:imageoffset="0" tscDM:imagerect="1725, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="   Treatment of Leftover Entities" xmpDM:startTime="795600" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="24" tscDM:imageoffset="0" tscDM:imagerect="1800, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Terminating Simulations" xmpDM:startTime="800000" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="25" tscDM:imageoffset="0" tscDM:imagerect="1875, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="   Treatment of Leftover Entities" xmpDM:startTime="898200" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="26" tscDM:imageoffset="0" tscDM:imagerect="1950, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 25.3:  Treatment of Leftover Entities" xmpDM:startTime="1119500" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="27" tscDM:imageoffset="0" tscDM:imagerect="2025, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="   Treatment of Leftover Entities" xmpDM:startTime="1122733" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="28" tscDM:imageoffset="0" tscDM:imagerect="2100, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 25.3:  Treatment of Leftover Entities" xmpDM:startTime="1144200" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="29" tscDM:imageoffset="0" tscDM:imagerect="2175, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="   Treatment of Leftover Entities" xmpDM:startTime="1191267" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="30" tscDM:imageoffset="0" tscDM:imagerect="2250, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 25.3:  Treatment of Leftover Entities" xmpDM:startTime="1197267" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="31" tscDM:imageoffset="0" tscDM:imagerect="2325, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Stopping Criteria:  Variance Estimation" xmpDM:startTime="1226933" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="32" tscDM:imageoffset="0" tscDM:imagerect="2400, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="    Variance Estimation Methods" xmpDM:startTime="1396133" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="33" tscDM:imageoffset="0" tscDM:imagerect="2475, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Independent Replications" xmpDM:startTime="1433700" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="34" tscDM:imageoffset="0" tscDM:imagerect="2550, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name=" Independent Replications (Cont)" xmpDM:startTime="1496300" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="35" tscDM:imageoffset="0" tscDM:imagerect="2625, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Independent Replications" xmpDM:startTime="1517967" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="36" tscDM:imageoffset="0" tscDM:imagerect="2700, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="    Variance Estimation Methods" xmpDM:startTime="1564733" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="37" tscDM:imageoffset="0" tscDM:imagerect="2775, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Independent Replications" xmpDM:startTime="1566400" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="38" tscDM:imageoffset="0" tscDM:imagerect="2850, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="    Variance Estimation Methods" xmpDM:startTime="1567500" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="39" tscDM:imageoffset="0" tscDM:imagerect="2925, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Stopping Criteria:  Variance Estimation" xmpDM:startTime="1567833" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="40" tscDM:imageoffset="0" tscDM:imagerect="3000, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="    Variance Estimation Methods" xmpDM:startTime="1576200" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="41" tscDM:imageoffset="0" tscDM:imagerect="3075, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Independent Replications" xmpDM:startTime="1576633" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="42" tscDM:imageoffset="0" tscDM:imagerect="3150, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name=" Independent Replications (Cont)" xmpDM:startTime="1577100" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="43" tscDM:imageoffset="0" tscDM:imagerect="3225, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Batch Means" xmpDM:startTime="1608467" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="44" tscDM:imageoffset="0" tscDM:imagerect="3300, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Batch Means (Cont)" xmpDM:startTime="1608733" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="45" tscDM:imageoffset="0" tscDM:imagerect="3375, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Case Study 25.1:  Interconnection Networks" xmpDM:startTime="1608967" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="46" tscDM:imageoffset="0" tscDM:imagerect="3450, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Batch Means (Cont)" xmpDM:startTime="1609867" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="47" tscDM:imageoffset="0" tscDM:imagerect="3525, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Batch Means" xmpDM:startTime="1610200" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="48" tscDM:imageoffset="0" tscDM:imagerect="3600, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name=" Independent Replications (Cont)" xmpDM:startTime="1612000" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="49" tscDM:imageoffset="0" tscDM:imagerect="3675, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Batch Means" xmpDM:startTime="1629400" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="50" tscDM:imageoffset="0" tscDM:imagerect="3750, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Batch Means (Cont)" xmpDM:startTime="1675033" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="51" tscDM:imageoffset="0" tscDM:imagerect="3825, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Case Study 25.1:  Interconnection Networks" xmpDM:startTime="1766033" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="52" tscDM:imageoffset="0" tscDM:imagerect="3900, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Summary" xmpDM:startTime="1888033" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="53" tscDM:imageoffset="0" tscDM:imagerect="3975, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Case Study 25.1:  Interconnection Networks" xmpDM:startTime="1889500" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="54" tscDM:imageoffset="0" tscDM:imagerect="50, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Summary" xmpDM:startTime="1895867" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="55" tscDM:imageoffset="0" tscDM:imagerect="125, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Marker 1" xmpDM:startTime="1984800" tscDM:image="k_25asr2_Thumbnails.png" tscDM:imageindex="56" tscDM:imageoffset="0" tscDM:imagerect="200, 56, 75, 56"/></rdf:li></rdf:Seq>
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         <tscDM:controller>
            <rdf:Description xmpDM:name="tscplayer">
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                  <rdf:Bag>
                     <rdf:li xmpDM:name="autohide" xmpDM:value="true"/><rdf:li xmpDM:name="autoplay" xmpDM:value="false"/><rdf:li xmpDM:name="loop" xmpDM:value="false"/><rdf:li xmpDM:name="searchable" xmpDM:value="true"/><rdf:li xmpDM:name="captionsenabled" xmpDM:value="false"/><rdf:li xmpDM:name="sidebarenabled" xmpDM:value="false"/><rdf:li xmpDM:name="unicodeenabled" xmpDM:value="false"/><rdf:li xmpDM:name="backgroundcolor" xmpDM:value="000000"/><rdf:li xmpDM:name="sidebarlocation" xmpDM:value="left"/><rdf:li xmpDM:name="endaction" xmpDM:value="stop"/><rdf:li xmpDM:name="endactionparam" xmpDM:value="true"/><rdf:li xmpDM:name="locale" xmpDM:value="en-US"/></rdf:Bag>
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               <tscDM:controllerText>
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                  </rdf:Bag>
               </tscDM:controllerText>
            </rdf:Description>
         </tscDM:controller>
         <tscDM:contentList>
            <rdf:Description>
               <tscDM:files>
                  <rdf:Seq>
                     <rdf:li xmpDM:name="0" xmpDM:value="k_25asr2.mp4"/><rdf:li xmpDM:name="1" xmpDM:value="k_25asr2_First_Frame.png"/><rdf:li xmpDM:name="2" xmpDM:value="k_25asr2_Thumbnails.png"/></rdf:Seq>
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            </rdf:Description>
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</x:xmpmeta>