In this chapter, data$-$level parallelism has been discussed as a

way for WSCstoachieve high performance on large problems. Conceivably, even

greater performance can be obtained by using high$-$end servers; however, higher

performance servers often come with a nonlinear price increase.

aAssuming servers that are $10\%$ faster at the same utilization, but are

$20\%$ more expensive, what is the CAPEX for the WSC$?$

bIf those servers also use $15\%$ more power, what is the OPEX of the

warehouse$-$scale computer?

cGiven the speed improvement and power increase, what must

the cost of the new servers be to be comparable to the original cluster? $($Hint:

Based on this TCO model, you may have to change the critical load of the

facility.$)$

Servers that have different operating modes offer opportuni

ties for dynamically running different configurations in the cluster to match work

load usage. Use the data in Figure $6\mathrm{.}35$ for the power$/$performance modes for a

given low$-$power server.

aIf a server operator decided to save power costs by running all

servers at medium performance, how many servers would be needed to achieve

the same level of performance?

MapReduce enables large amounts of parallelism by

having data$-$independent tasks run on multiple nodes, often using commodity hard

ware; however, there are limits to the level of parallelism. For example, for redun

dancy MapReduce will write data blocks to multiple nodes, consuming disk and,

potentially, network bandwidth. Assume a total dataset size of $300$ GB$,$ a network

bandwidth of $1$ Gb$/$s$,$ a $10$ s$/$GB map rate, and a $20$ s$/$GB reduce rate. Also assume

that $30\%$ofthedata must beread fromremotenodes,andeachoutput fileis written

to two other nodes for redundancy. Use Figure $6\mathrm{.}6$ for all other parameters.

aAssume that all nodes are in the same rack. What is the

expected runtime with $5$ nodes? $10$ nodes? $100$ nodes? $1000$ nodes? Discuss

the bottlenecks at each node size.

Figure $6\mathrm{.}6$ Latency, bandwidth, and capacity of the memory hierarchy of a WSC $[$Barroso and H$$lzle $2009].$ Figure $6\mathrm{.}7$ plots this same information.