Eager, Zahorjan, and Lazowska
[8]
point out that
where speedup is a measure of the ``benefit'' of using
some number of processors for the parallel execution of
a job, the efficiency is a measure of the ``cost'' of
using those processors.
The point at which the
ratio of efficiency to execution time,
,
is maximized
is called the knee of the
execution time - efficiency profile
and
may be useful in
determining effective processor allocations
in multiprogrammed environments.
Given our function that describes the execution rate
of parallel jobs,
the knee can be easily derived
and is 
.
Chiang, Mansharamani, and Vernon [5] also
point out that the knee, 
,
for job 
can be shown to be equal to
.
In the previous section
we based processor allocations on the efficiency of jobs
and used to characterize the
efficiency of an application.
Since the knee of the execution time - efficiency
profile for the execution rate function we have
chosen is ,
we have already, indirectly,
examined the affects of using the
knee, , to make scheduling decisions
(in the previous section).
To reiterate, the problem with such an approach is
that while small benefits can be obtained by
utilizing the knee, those benefits are limited because
the approach does not directly consider the amount of
work executed by each job.