Assignment%202%202007%20Solutions

Assignment%202%202007%20Solutions - Simon Fraser University...

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1 Simon Fraser University School of Engineering Science Engineering Science 427 Problem Assignment 2 Solutions Due Date: 4pm, April 3 2007 Note: (*.*) refer to problem numbers from Leon-Garcia & Widjaja, 2 nd edition Question 1: Expedited and normal data packets are served from an M/G/1/ buffer. The ratio, of average expedited packet length to average normal packet length, is 0.1. The arrival rate of the expedited class of packets is λ 1 = 2 packets/second. The arrival rate of the normal class of packets is λ 2 = 4 packets/second. The total traffic utilization is ρ = 0.6. The service times, of each class of packets, are exponentially distributed. Find E ( w 2 ), the mean waiting time of the normal class of packets, in the following two cases: (a) Nonpreemptive priority is given to the expedited data packets. (b) Nonpriority service. Solution: Given that 1 2 12 0.6 2 packets/sec 4 packets/sec 11 1 , 10 ρ λ μμ = = = = we solve for the service rates of each class of packet to find 1 2 1 2 70 7 2 70 4 7 μ = = = =
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2 Also, since both classes of packets each have exponentially distributed service times, the variance of each class of service times is equal to the square of the mean of the service times of that class. We then find that: 22 111 11 () ( ) ( ) 2 4900 EX E X V a rX μμ =+ = Similarly, we find 2 2 2 49 = The composite second moment of service time is then 222 12 2 2.735 10 λ λλ (a)
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This note was uploaded on 10/09/2009 for the course ENSC 1156 taught by Professor Rhardy during the Spring '07 term at Simon Fraser.

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Assignment%202%202007%20Solutions - Simon Fraser University...

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