Fundamentals of Quantitative Design and Analysis - Computer Architecture: A Quantitative Approach - page 67

e. [10] <1.4> The rate of growth for DRAM capacity has also slowed down. For 20 years,
DRAM capacity improved by 60% each year. That rate dropped to 40% each year and
now improvement is 25 to 40% per year. If this trend continues, what will be the ap-
proximate rate of growth for DRAM capacity by 2020?
1.9 [10/10] <1.5> You are designing a system for a real-time application in which speciic
deadlines must be met. Finishing the computation faster gains nothing. You find that your
system can execute the necessary code, in the worst case, twice as fast as necessary.
a. [10] <1.5> How much energy do you save if you execute at the current speed and turn
of the system when the computation is complete?
b. [10] <1.5> How much energy do you save if you set the voltage and frequency to be
half as much?
1.10 [10/10/20/20] <1.5> Server farms such as Google and Yahoo! provide enough compute ca-
pacity for the highest request rate of the day. Imagine that most of the time these servers
operate at only 60% capacity. Assume further that the power does not scale linearly with
the load; that is, when the servers are operating at 60% capacity, they consume 90% of max-
imum power. The servers could be turned of, but they would take too long to restart in
response to more load. A new system has been proposed that allows for a quick restart but
requires 20% of the maximum power while in this “barely alive” state.
a. [10] <1.5> How much power savings would be achieved by turning of 60% of the serv-
ers?
b. [10] <1.5> How much power savings would be achieved by placing 60% of the servers
in the “barely alive” state?
c. [20] <1.5> How much power savings would be achieved by reducing the voltage by
20% and frequency by 40%?
d. [20] <1.5> How much power savings would be achieved by placing 30% of the servers
in the “barely alive” state and 30% of?
1.11 [10/10/20] <1.7> Availability is the most important consideration for designing servers,
followed closely by scalability and throughput.
a. [10] <1.7> We have a single processor with a failures in time (FIT) of 100. What is the
mean time to failure (MTTF) for this system?
b. [10] <1.7> If it takes 1 day to get the system running again, what is the availability of
the system?
c. [20] <1.7> Imagine that the government, to cut costs, is going to build a supercomputer
out of inexpensive computers rather than expensive, reliable computers. What is the
MTTF for a system with 1000 processors? Assume that if one fails, they all fail.
1.12 [20/20/20] <1.1, 1.2, 1.7> In a server farm such as that used by Amazon or eBay, a single
failure does not cause the entire system to crash. Instead, it will reduce the number of re-
quests that can be satisfied at any one time.
a. [20] <1.7> If a company has 10,000 computers, each with a MTTF of 35 days, and it ex-
periences catastrophic failure only if 1/3 of the computers fail, what is the MTTF for
the system?
b. [20] <1.1, 1.7> If it costs an extra $1000, per computer, to double the MTTF, would this
be a good business decision? Show your work.