IE306Lec9 - IE306 SYSTEMS SIMULATION Ali Rıza Kaylan...

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Unformatted text preview: IE306 SYSTEMS SIMULATION Ali Rıza Kaylan kaylan@boun.edu.tr 1 LECTURE 9 OUTLINE Lifecycle of a Simulation Project Model Verification Model Validation Validation Techniques Subjective Statistical M/M/1 Example 2 LIFECYCLE OF A SIMULATION PROJECT VERIFICATION Conceptual Model VALIDATION System VALIDATION Simulation Program Simulation Output CREDIBILITY Implementation MODEL CREDIBILITY: When a simulation model and its results are accepted by the model user as being valid and are used as a decision aid. 3 MODEL VERIFICATION Checking the transformation of the conceptual simulation model into a computer program with sufficient accuracy. BUILDING THE MODEL RIGHT VERIFICATION Conceptual Model Simulation Program 4 MODEL VALIDATION Determining whether the conceptual simulation model is an accurate representation of the system under study. BUILDING THE RIGHT MODEL (I , I ,..., I ) s 1 s 2 s n INPUT VARIABLES (I m 1 m m , I2 ,..., In ) INPUT VARIABLES (P , P ,..., P ) s 1 s 2 (P m 1 s l SYSTEM MODEL RESPONSE VARIABLES (R , R ,..., R ) s 1 s 2 m , P2 ,..., Plm ) s k RESPONSE VARIABLES (R m 1 m , R2 ,..., Rkm ) 5 VALIDATION TECHNIQUES SUBJECTIVE Event Validation Face Validation Field Tests Graphical Comparisons Hypothesis Validation Predictive Validation Sensitivity Analysis Submodel Testing Turing Test STATISTICAL Analysis of Variance Confidence Intervals Factor Analysis Hotelling's T2 Tests Multivariate Analysis Nonparametric Tests Regression Analysis Theil's Inequality Coefficient Time Series Analysis 6 t-tests VALIDATION TECHNIQUES EVENT VALIDATION Employs identifiable events or event patterns as criteria against which to compare model and system behaviours. FACE VALIDATION People knowledge about the system under study, based upon their estimates and intuition, compare model and system behaviours to judge whether the model and its results are reasonable. 7 VALIDATION TECHNIQUES FIELD TESTS The model is put in an operational situation for the purpose of collecting as much information as possible for model validation. GRAPHICAL COMPARISONS The graphs of model and system variables are compared to investigate similarities and discrepancies. Characteristics such as periodicities, skewness, trend lines, inflection points are checked. 8 VALIDATION TECHNIQUES HYPOTHESIS VALIDATION Hypothesized input output relationships for the system under study and the developed model are compared. PREDICTIVE VALIDATION The model is driven by past system input data and its forecasts are compared with the corresponding past system output data to test the predictive ability of the model. 9 VALIDATION TECHNIQUES SENSITIVITY ANALYSIS Performed by systematically changing the values of model input variables and parameters over some range of interest and observing the effect upon model behaviour. 10 VALIDATION TECHNIQUES TURING TEST 1. Find experts about the system under study, 2. Present them with two sets of output data one from the model and one from the system obtained under the same input conditions, 3. Without identifying which one is which, ask them to differentiate between the two, 4. If they succeed, get feedback for correcting model, 5. If they can not differentiate, our confidence in model validity is increased. 11 VALIDATION TECHNIQUES M/M/1 QUEUEING SYSTEM ANALYTICAL SOLUTIONS 1 E(W ) = µ−λ λ E(Wq ) = µ (µ − λ ) E ( N ) = λ * E (W ) E(N q )= λ * E (W q ) E(W ) = E(W q )+ E(S) 1 − ρ F( t ) = 1 − ρ * exp[− µ (1 − ρ )t ] t =0 t>0 12 VALIDATION TECHNIQUES M/M/1 QUEUEING SYSTEM EXAMPLE E( Interarrival Time ) = 10 min utes λ = 0.1 arrivals / min ute E(Service Time) = 5 min utes µ = 0.2 services / min ute ρ = λ / µ = 0.5 1 E( W ) = = 10 0.2 − 0.1 E(Wq ) = 0.5 =5 0.2 − 0.1 E(N ) = 0.1*10 = 1 E(N q )= 0.1* 5 = 0.5 13 VALIDATION TECHNIQUES M/M/1 QUEUEING SYSTEM EXAMPLE Arrival Service Mean 10 Simulation End Time= Server Utilization= IA 9,84 S 5,09 Wq 4,531 W 9,634 Lq 0,458 L 0,974 ID 9,89 5 989 0.515 No 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 IA 9 1 6 5 10 6 26 5 4 1 4 40 6 16 24 5 8 18 12 6 S 2 21 3 5 8 1 5 8 8 2 0 2 28 1 2 1 1 1 17 4 A 9 9 16 21 32 37 63 69 73 74 78 118 124 140 164 169 177 195 207 214 SS 9 11 32 35 40 47 63 69 76 85 87 118 124 152 164 169 177 195 207 225 SE 11 32 35 40 47 49 68 76 85 87 87 120 152 153 167 171 178 196 225 228 Wq 0 0 16 13 8 10 0 0 4 11 9 0 0 12 0 0 0 0 0 11 W 2 22 19 19 16 12 5 8 12 13 9 2 28 13 2 1 1 1 17 15 I 9 0 0 0 0 0 15 1 0 0 0 31 4 0 11 3 7 17 11 0 ID 11 21 3 5 8 1 19 9 8 2 0 32 32 1 13 4 7 18 29 4 99 100 3 8 6 5 976 984 977 984 983 989 1 0 7 5 0 1 6 6 14 VALIDATION TECHNIQUES M/M/1 QUEUEING SYSTEM EXAMPLE System Model E(W) 10 9.634 E(Wq) 5 4.531 E(N) 1 0.974 E(Nq) 0.5 0.458 15 VALIDATION TECHNIQUES M/M/1 QUEUEING SYSTEM EXAMPLE Experiment End Time Utilization IA S Wq W Lq L ID 1 2 3 4 5 Mean St.Dev. 989 0,515 9,84 5,09 4,531 9,634 0,458 0,974 9,89 1103 0,471 11 5,19 5,435 10,647 0,493 0,965 11,03 973 0,52 9,68 5,06 5,317 10,373 0,546 1,066 9,73 1067 0,474 10,57 5,06 2,895 7,966 0,271 0,747 10,67 1096 0,43 10,95 4,71 3,471 8,186 0,317 0,747 10,96 1046 0,482 10,41 5,02 4,33 9,361 0,417 0,9 10,46 61 0,037 0,62 0,18 1,122 1,233 0,118 0,145 0,61 16 VALIDATION TECHNIQUES M/M/1 QUEUEING SYSTEM EXAMPLE CONFIDENCE INTERVAL (α=5%) for W X ± t n-1, 1-α /2 s2 n 9.361 ± t 4, 0.975 1.2332 5 9.361 ± 2.776 1.2332 5 9.361 ± 1.531 [7.830,10.892 ] 17 ...
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This note was uploaded on 07/30/2009 for the course INDUSTRIAL ie306 taught by Professor Alirizakaylan during the Spring '09 term at Boğaziçi University.

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