Consider an SMP with a distributed shared$-$address$-$space. Consider a simple cost

model in which it takes $10ns$ to access local cache, $100ns$ to access local memory, and

$400ns$ to access remote memory. A parallel program is running on this machine. The

program is perfectly load balanced with $80\%$ of all accesses going to local cache, $10\%$ to

local memory, and $10\%$ to remote memory. What is the effective memory access time for

this computation? If the computation is memory bound, what is the peak computation

rate?

Now consider the same computation running on one processor. Here, the processor hits

the cache $70\%$ of the time and local memory $30\%$ of the time. What is the effective peak

computation rate for one processor? What is the fractional computation rate of a processor

in a parallel configuration as compared to the serial configuration?

Hint: Notice that the cache hit for multiple processors is higher than that for one

processor. This is typically because the aggregate cache available on multiprocessors is

larger than on single processor systems.