Modeling and Simulation Exam

Transcription

1 Modeling and Simulation am Facult of Computers & Information Department: Computer Science Grade: Fourth Course code: CSC Total Mark: 75 Date: Time: hours Answer the following questions: - a Define the following terms, in the contet of modeling and simulation: - Verification - Validation - Credibilit b Can a simulation model be verified but not valid and vice-versa? Investigate our answer with an eample for each. c Discuss 5 techniques for verification of simulation computer programs. d Discuss 5 techniques for increasing model validit and credibilit. e List 5 major Pitfalls in simulation modeling. - a Define the following terms: - periment - Sample space - Probabilit mass function of discrete random variable - Joint probabilit mass function of two discrete random variables and b Suppose that is a discrete random variable with the probabilit mass function i given b: pi =, i =,,,, Plot p - Compute and plot F - Compute P Compute - Compute Var See the net page

2 - a Briefl describe the following concepts: - Trace-driven simulation - mpirical distributions - Fitting theoretical distributions b Mention the advantages and disadvantages of each of the methods in -a. - Suppose that and are jointl continuous random variables with for and f, otherwise - Compute and plot f and f - Are and independent? - Compute and plot F and F - Compute, Var,, Var, Cov,, and Cor, 5 For the following sequence of RNs, showing the steps, determine whether or not it passes the Runs Test of Independence. Read rows first

3 Model Answer Modeling and Simulation am Facult of Computers & Information Department: Computer Science Course code: CSC Total Mark: 8 Date: Time: hours - a Solution: Verification is to determine whether the conceptual simulation model has been correctl translated into a computer program Validation is the process of determining whether a simulation model is an accurate representation of the real sstem Credibilit: A simulation model and its results have credibilit if the manager and other ke project personnel accept them as correct b Solution: es, a model can be verified but not validated and vice-versa. For eample, a model that simulates the operations of an airport ma be valid such that it reall represents the airport sstem; however, it contains an internal defect which means it is not verified for eample, it fails after running 5 times, or uses a wrong random number generator function. On the other hand, another model ma be verified such that it doesn t contain an defects; however, it doesn t represent the airport sstem ver accuratel doesn t consider the flights schedule for eample c Solution: An 5 techniques of the techniques below shall be correct and complete answer: Technique : Divide the program into subprograms and then debug these subprograms individuall. Sometimes computer simulation programs ma go to, statements Start b a moderate simulation model then graduall increase compleit as needed.

4 Technique : Make a structured walk-through of the program b other persons as one ma not able to criticize himself. Technique : Run the simulation model under several settings of the input parameters. Tr it first for known sstem performance. Technique : One of the powerful techniques is to trace the state of the simulated sstem and compare with a hand simulation. Technique 5: Run the model under simplified assumptions for which its true characteristics are known. ample: replace the M queuing model b MM etc. Technique 6: If it is possible, use animation to trace entities in the model. Technique 7: Compute a sample mean and sample variance for each simulation input probabilit and compare with the desired known mean and variance. Technique 8: Use commercial simulation packages carefull to reduce the amount of programming time. d Technique : Collect high qualit information and data on the sstem. To develop such a model, it should make use of the eisting information including: A. Conversation with Subject Mater perts SM s Analst not working in isolation. The modeler should work with some people Analst will have to be resourceful B. Observations of the sstem: Data which used in building the model must be correct contain no recording error isting Theor: The interval times of costumers are quite likel to be IID eponential random variable Relevant Results from similar simulation model: Use previous data that have been introduced from similar simulation studies. perienceintuition: Use the eperience and intuition of the modelers to hpothesize how certain components of a comple sstem operation. Technique : Interact with the manager on a regular basis

5 Technique : Maintain assumptions of document and perform a structural walk-through: Record all assumptions that have been taken in the simulation model including Project goals Detailed description of each subsstem What simplifing assumptions were made and wh Summar of data such as mean, histogram, etc. Sources of important and controversial information. Technique : Validate components of the model b using quantitative techniques. Use sensitivit analsis to determine model factors that have a significant impact on the desired measures of performance. amples include The value of a parameter The choice of a distribution that the entit moving in the sstem The level of detail of subsstems What data are the most crucial to collect Technique 5: Validate output from the overall simulation model. Compare the output with a similar eisting sstem to check whether the output of the simulation model reflects the real life performance or not. Model ma suggest improvements Increasing the credibilit. Compared with eisting sstem e An 5 points of the following will be sufficient: - Failure to have a well-defined set of objectives at the beginning of the stud. - Misunderstanding of simulation b management - Failure to communicate with management on a regular basis - Treating a simulation stud as if it were primaril an eercise in computer programming - Lack of knowledge of simulation methodolog, operations research, probabilit, and statistics - Failure to collect good sstem data - Inappropriate level of model detail - Misuse of animation

6 - Failure to model sstem randomness appropriatel - Failure to perform a proper output-data analsis

7 - a Solution: - periment is a process whose outcome is not known with certaint - Sample space S is the set of all possible outcome of an eperiment - Probabilit mass function of discrete random variable The probabilit that random variable takes on value i is given b p i = P= i for i=,, p is the probabilit mass function of discrete random variable - Joint probabilit mass function of two discrete random variables and : p, P, for all, b - Plot p p Compute and plot F F p i for 5 i F = 5 F = = 5

8 F = = 65 F = = 5 F5 = = 55 F Compute P P = p + p + p = = 95 - Compute 5 i i p i fordiscrete i = = Compute Var Var i i = i i ² = = 55 ² = 555² Hence, Var = ² = 9.556

9 - a Trace-driven simulation: The data on the input random variables of interest are used directl in the simulation without making an change. In other words, we use historical data as is without making an modifications or additions to it. mpirical Distributions: The data values could be used to define an empirical distribution function in some wa. The historical data and cumulative frequenc are used as input to the model so that an value between minimum and maimum can be generated. For instance, assume a picked a random number as F doesn t correspond to an eisting ; however, it s located between two other values, then interpolation is used to calculate its. Fitting theoretical distributions: Standard techniques of statistical inferences are used to fit a theoretical distribution form to the data. In this technique, data inputs are observed and a curve is plotted to determine to which distribution famil these inputs belong.

10 b Advantages Disadvantages Trace Driven mpirical distrib. Fitting ditrsib. Simple Allows the smooth out the Reproduces generation of data irregularities observed behavior inputs within the Allow generation of eactl range that have not values that have not been originall been observed and observed outside their range Not ver comple generates a wider range of values as to change Traces don t allow ma be based on a Usuall more us to generate small sample size comple than Trace values outside of ma have and mpirical our sample i.e., we irregularities distributions ma not have can t work outside observed the sstem the observed data in all states range can t test the can t test the performance of the performance of the simulated sstem simulated sstem under etreme under etreme conditions conditions

11 -a f d d d f d d d

12 - dependent are and f f.. - d F d F 5 d d d f 9 8 d d d f

13 6 d d d f 6 6 d d d f 5 Var 9 Var

14 , d d d d d d d d f *.,, 9 5 *., Var Var Cov Cor Cov

15 5. N = number of RNs =. let a to be the number of runs. Runs are: and hence, a =. Calculate N a 6N 9 a 9 9 a 9 a. 9. Calculate a a Z ~ N, a Z If -z.5 <= Z <= z.5 ; where α is the significance level, we will accept H and our sequence passes the independence test. Otherwise, we reject it Z.5 =.96, - = -.96, and Z =.556. Z lies between Z.5 and - Z.5 and Z.5 hence, H is accepted and the sequence of RNs passes the test of independence