DiscreteEventSimulation-example

DiscreteEventSimulation-example - CDA6530: Performance...

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CDA6530: Performance Models of Computers and Networks Chapter 8: Discrete Event Simulation Example --- Three callers problem in homwork 2
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Problem Description Two lines services three callers. Each caller makes calls that are exponentially distributed in length, with mean 1/ μ . If both lines are in service by two callers and the third one requests service, the third caller will be blocked. A caller whose previous attempt to make a call was successful has an exponentially distributed time before attempting the next call, with rate λ . A caller whose previous call attempt was blocked is impatient and tries to call again at twice that rate (2 λ ), also according to exponential distribution. The callers make their calls independent of one another. 2
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Analysis Results Steady state prob: π Matlab code: Q = [………]; Pi = zeros(1, 6); Q_m = [Q(:, 1:5) ones(6,1)]; B = [0 0 0 0 0 1]; Pi = B * inv(Q_m); 3 π Q =0 π 1 =1
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Simulation based on Markov Model 4
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Pre Simulation Strictly refer to the state transition diagram Remember current state: currentState Determine next state: nextState This is a continuous-time Markov Chain Method #1: State duration time (for the transition node in the right): Exp. distr. with rate ( λ + μ ) Determine the next transition event time At the time of transition event: Use discrete r.v. simulation method to determine nextState: Transit first path with prob. of λ /( λ + μ ) Transit second path with prob. of μ /( λ + μ ) 5 λ μ
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Pre Simulation Method #2: Should jump to 1 by exp. distr. Time with rate λ find jump time t 1 Should jump to 2 by exp. distr. Time with rate μ find jump time t 2 If t 1 < t 2 , the actual jump is to 1 at even time t 1 If t 2 < t 1 , the actual jump is to 2 at even time t 2 6 λ μ 1 2
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This note was uploaded on 01/14/2012 for the course CDA 6530 taught by Professor Zou during the Fall '11 term at University of Central Florida.

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DiscreteEventSimulation-example - CDA6530: Performance...

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