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SimPro - Simulation and Modeling SYSC 5001 Project...

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Simulation and Modeling SYSC 5001 Project: Simulation of Single server Queue Topology A by Rajab Legnain 100762228 Prof.: Ioannis Lambadaris winter 2010 1
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Contents 1 1 Description of System 2 1.1 Generation of Exponential RV . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Simulation Results and Discussion 3 2.1 Average Waiting Time in The System . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Average Number of Packets in The System . . . . . . . . . . . . . . . . . . . 4 2.3 Correlation Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.4 Verification of Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3 Conclusion 8 1
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Objectives The objective of this project is to model and simulate a single server queue. The average number of packets in the system and average waiting time in the will be measured system in different cases (i.e different arrival rate and different correlation between Inter-arrival time) in order to analysis and study the behavior of system. Another objective is to verify my MATLAB code by using two-side hypothesis test. 1 Description of System The single server queue, Topology A, is simulated by using MATLAB program, version (2009b), because MATLAB is very powerful simulation program. It is contain a huge of useful function,especially in statistic. The following system is considered for the simulation: 1. A single server queue system has unlimited capacity. 2. The inter-arrival times and service times are exponentially distributed. 3. The service times packets are independent (i.e. a=0.5) and with service rate μ =10 packets/sec. 4. The arrival rate will take values (1,3,5,7,9) Packets/sec, in order to study the effect of increasing the arrival rate on the queue . 5. The correlation between inter-arrival will set to ( a=0.1, 0.3, 0.5) for each arrival rate. The value a=0.5 means that the inter-arrival times are independent of each other. 6. Number of replication, R, is set to 10 time. In other words, will run the simulation 10 times. This mean we will get 10 independent simulations [1]. 7. The number of packets to be simulated, N=100,000. 8. The observation is divided into 20 batches in each replication [1]. 2
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Table 1: Parameters of Simulation Number of Packets N=100,000 Packets Number of replication R=10 times Number of batches in a replication N b =20 batches Service Rate μ =10 Packet/sec Arrival Rate λ =1,3,5,7,8 Packet/sec Correlation [-a,a] a=0.1, 0.3, 0.5 1.1 Generation of Exponential RV The exponential random variable is generated from uniform random variable by using Inverse- Transform technique [2]. The uniform random variable with variable correlation is generated by using Transform-Expand-Sample (TES) [3]. I wrote the following program to generate exponential random variable with adjustable correlation function y = exprv (a ,mu, n) U(1)= unifrnd ( 0 , 1 , 1 , 1 ) ; f o r i =2 : n ; V=unifrnd ( a , a , 1 , 1 ) ; . U( i )=mod(U( i 1)+V, 1 ) ; end y=expinv (U,mu) ; where a is the correlation, mu is the mean of the distribution, and n is the number of packets. 2 Simulation Results and Discussion 2.1 Average Waiting Time in The System The simulation results of average waiting time in the system, ¯ W , with the 95% confidence interval half-width, H, for different arrival rate and different correlation are listed in Tables 3
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2. Table 2 and Figure 1 show that: 1. As the arrival rate, λ
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