In order to explore different methods of
allocating processing power to jobs we employ a
slightly modified version of the
generalization of processor allocation policies
proposed by
Brecht
[3].
In this generalization,
is the
characteristic of job 
being used to make
the allocation decision,
P is the number of processors in the
system, N is the number of jobs currently executing,
is the control that determines the actual
allocation policy, and
is the number of processors allocated to
job as a result of the policy.
The generalization is defined as:
Different values of represent
various points on a spectrum of processor allocation
strategies.
The chosen acts as both a means of
selecting the degree of
processor sharing and as a control on
which jobs should be given larger portions of the
processors.
Different values of can be used to make
allocation decisions based on different job
characteristics.
For example, using 
, we have
policies that base allocation decisions on work.
In this case
larger positive values of
allocate a greater portion of processors to
jobs with more work (larger jobs)
while larger negative values of
allocate a greater portion of processors to
jobs with less work (smaller jobs).
Specific values of worth noting
(when using ) are:
, which allocates
processors in direct proportion to the work being
executed by each application
[3].
,
which allocates processors in proportion
to the square root of the work being
executed by each application.
This policy has been examined
by Sevcik
[32]
and Brecht
[3]
in the context of static scheduling algorithms.
,
which allocates processors
equally among all jobs
(i.e., independently of the work
being executed by each job).
This is the much studied equipartition policy
[33, 19, 36, 5].
We consider dynamic scheduling policies that allocate or reallocate processors at job arrival and departures (if required). The scheduling algorithm limits the number of jobs active at any time, N, to be less than or equal to the number of processors, P.