3(25 points). Assume a disk subsystem with the following components and MTTF: 20
ID: 669109 • Letter: 3
Question
3(25 points). Assume a disk subsystem with the following components and MTTF:
20 disks
1 SCSI controller, 500,000-hour MTTF
1 power supply, 200,000-hour MTTF
1 fan, 200,000-hour MTTF
1 SCSI cable, 1,000,000-hour MTTF
In order to make the system work reliably more than 5 year, what is the MTTF for a single disk? Assuming 20 disks are all the same.
(25 points) Suppose you are in charge of setting up a corporate data center, and you have a total budget of $100,000 to spend on a new cluster of computers. The users of your data center need to constantly and repeatedly run a given application program “P” on the machines in this cluster. You are trying to decide what type of computers to buy for the cluster. The company’s goal is to enable the pool of users to run the program P as frequently as possible – the more often, the better. You can buy as many computers for your cluster as you can afford while staying within budget.
4a. Identify the true nature of the problem to be solved, as an engineering problem. What quantity or quantities should you really be trying to optimize, and for each one, should you be trying to maximize or minimize that particular quantity? Circle all that apply.
Number of instructions-per-second executed per machine. Max / min?
Total throughput of your data center, within budget. Max / min?
iii. Performance of each individual machine on program P. Max / min?
Cost-performance (performance per unit cost) on P Max / min?
of the type of machine that is purchased.
Execution time of each machine when running program P. Max / min?
The CPI of the type of machine that is purchased. Max / min?
4b. Now suppose that for each type of machine M, you know all of the following quantities:
The dynamic instruction count IC of machine M when running program P.
The average cycles-per-instruction CPI of the machine when running P.
The clock frequency f of the machine.
The cost C of the machine, in dollars.
Now, formulate an expression for the key figure of merit that you should be trying to maximize or minimize, in terms of the above variables. Write the expression below.
4c. Given the below data for the following three machines A,B,C (with IC and CPI as measured for program P) use your formula from part (4b) tosolve the problem of deciding which of these three types of machines you ought to buy. Show your work below the table. How many times better (according to the correct figure of merit) is the best machine, compared to the second-best alternative?
Type A computers
Type B computers
Type C computers
Instruction count
12×109
3×109
4×109
Cycles per instr.
1
1.5
2
Clock frequency
4 GHz
3 GHz
2.8 GHz
Cost
$1,000
$2,000
$200
Type A computers
Type B computers
Type C computers
Instruction count
12×109
3×109
4×109
Cycles per instr.
1
1.5
2
Clock frequency
4 GHz
3 GHz
2.8 GHz
Cost
$1,000
$2,000
$200
Explanation / Answer
3)
Failure rate of system = 20 * 1/1000000 + 1/500000 + 1/200000+1/200000+1/1000000
= (20 +2 +5 +5 +1)/1,000,000
== 33/1,000,000Failures per hour
Our required MTTF = 1/failure rate = = 1,000,000/33
=30,303 hours.
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