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    Practice Examination: OR 635 Discrete System Simulation

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    Victoria Moore
    This document contains a practice exam for a discrete system simulation course. It includes 4 questions - the first asks to develop random number generators for a given density function using two different methods, the second asks to find parameters for and generate random variables from another density function, the third asks about sample size needs for confidence intervals, and the fourth provides a description of a queueing system and asks to simulate it by filling in a table with system states and events over time.

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    Practice Examination: OR 635 Discrete System Simulation

    Uploaded by

    Victoria Moore
    20 views3 pages
    This document contains a practice exam for a discrete system simulation course. It includes 4 questions - the first asks to develop random number generators for a given density function using two different methods, the second asks to find parameters for and generate random variables from another density function, the third asks about sample size needs for confidence intervals, and the fourth provides a description of a queueing system and asks to simulate it by filling in a table with system states and events over time.

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    This document contains a practice exam for a discrete system simulation course. It includes 4 questions - the first asks to develop random number generators for a given density function using two different methods, the second asks to find parameters for and generate random variables from another density function, the third asks about sample size needs for confidence intervals, and the fourth provides a description of a queueing system and asks to simulate it by filling in a table with system states and events over time.

    Copyright:

    Attribution Non-Commercial (BY-NC)
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    20 views3 pages

    Practice Examination: OR 635 Discrete System Simulation

    Uploaded by

    Victoria Moore
    This document contains a practice exam for a discrete system simulation course. It includes 4 questions - the first asks to develop random number generators for a given density function using two different methods, the second asks to find parameters for and generate random variables from another density function, the third asks about sample size needs for confidence intervals, and the fourth provides a description of a queueing system and asks to simulate it by filling in a table with system states and events over time.

    Copyright:

    Attribution Non-Commercial (BY-NC)
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 3

    Department of Systems Engineering & Operation Research George Mason University

    OR 635 Discrete System Simulation


    Prof. Chun-Hung Chen Fall 2004

    Practice Examination
    Discussion Date: 7:20 pm, Thursday, October 28 1. Develop a generator for the following density function: f(x) 1.0 0.75 0.5 0.25 0 (a) (b) 0.5 1.0 1.5 X

    Use Acceptance-Rejection Method, Use Inverse Transform Method

    2.

    Consider a random variable X with the density function cx + 0.9, if 0 x 1 fx(x) = 0, otherwise.

    (a) (5) (b) (10) (c) (10)

    Find a suitable c for fx(x). Give an Inverse Transform method for generating X. If you generate 10,000 random variates X1, X2, .., X10000 by using the Inverse Transform method. Approximately, how many new numbers (Xi's) should be between 0.1 and 0.4 if this random number generator is a good generator?

    3. Suppose you are asked to simulate a network and analyze the mean system time. After you have obtained 1000 observations, the 90% confidence interval is [0.8, 1.2]. If our goal is to obtain a 80% confidence interval [0.9, 1.1], do you need to run more simulations for additional observations? If not, please explain. If so, approximately, how many additional observations do you have to get? (Critical points: z0.8 = 0.8, z0.9 = 1.2, z0.95 = 1.6, z0.975 = 2.0, z0.99 = 2.3).

    4. Consider a three-node system with two classes of customer arrivals shown on next page. The sizes of the waiting buffer space at all nodes are infinite. The event times are: Interarrival times for Class 1 customers: 20, Interarrival times for Class 2 customers: 21, Service times for Class 1 (at all nodes): 5, Service times for Class 2 (at all nodes): 7,

    Class 1 1 3 Class 2 2

    System state: x1: the number of customers at node 1, x2: the number of customers at node 2, x3: the number of Class 1 customers at node 3, x4: the number of Class 2 customers at node 3, Events: a1: arrival event at node 1, a2: arrival event at node 2, d1: departure event at node 1, d2: departure event at node 2, d3: departure event at node 3, Simulate this system by filling the following table. Stop this simulation when simulation clock (t) is no less than 50.

    t 0 20

    e' INI a1

    x1 0 1

    System States x2 x3

    Event List

    x4 0 0

    a1 20 40

    a2 21 21

    d1 25

    d2

    d3

    0 0

    0 0

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