Suppose a program must execute $1012$ instructions in order to solve a particular

problem. Suppose further that a single processor system can solve the problem

in $106$

seconds $($about $11\mathrm{.}6$ days$).$ So$,$ on average, the single processor system executes $106$ or a million instructions per second. Now suppose that the

program has been parallelized for execution on a distributed$-$memory system.

Suppose also that if the parallel program uses p processors, each processor will

execute $1012/$p instructions and each processor must send $109$

$($p $1)$ messages. Finally, suppose that there is no additional overhead in executing the

parallel program. That is$,$ the program will complete after each processor has

executed all of its instructions and sent all of its messages, and there won$$t be

any delays due to things such as waiting for messages.