EE465-USC-Fall08-Assignment9

EE465-USC-Fall08-Assignment9 - 6 Consider a closed version...

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EE 465 : Homework 9 Due : 11/25/2008, Tuesday in class. 1. Solve 8.20 (8.20) from textbook. 2. Solve 8.26 (8.26) from textbook. 3. Solve 8.32 (8.32) from textbook. 4. Solve 8.35 (8.35) from textbook. 5. Consider a model of a computer CPU connected to m I/O devices as shown in Figure 1. Jobs enter the system according to a Poisson process with rate λ , use the CPU, and with probability p i , i = 1 , . . . , m are routed to the i th I/O device, while with probability p 0 they exit the system. The service time of a job at the CPU (or the i th I/O device) is exponentially distributed with mean 1 μ 0 (or 1 μ i , respectively). We assume that all job service times at all queues are independent (including the times of successive visits to the CPU and I/O devices of the same job). Find the occupancy distribution of the system and construct an equivalent system with m + 1 queues in tandem that has the same occupancy distribution. Figure 1: Figure for Problem 5.
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Unformatted text preview: 6. Consider a closed version of the queueing system of the previous problem, shown in Figure 2. There are M jobs in the system at all times. A job uses the CPU and with probability p i , i = 1 , . . . , m is routed to the i th I/O device. The service time of a job at the CPU (or the i th I/O device) is exponentially distributed with mean 1 μ (or 1 μ i , respectively). We assume that all job service times at all queues are independent (including the times of successive visits to the CPU and I/O devices of the same job). Find the arrival rate of jobs at the CPU and the occupancy distribution of the system. Figure 2: Figure for Problem 6. Problem 7 is an optional question, those who solve it will get extra credits. 7. Solve 8.38 (8.38) from textbook. Note : 8.8 (8.7) implies problem 8.8 from the ninth edition which is the same as 8.7 in the eighth edition. 2...
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