Some Insights on Fixed-Priority Preemptive Non-Partitioned Multiprocessor Scheduling
Konferensbidrag (offentliggjort, men ej förlagsutgivet), 2000
Fixed-priority preemptive scheduling of independent periodic
tasks on a homogeneous multiprocessor is solved using
one of two different methods based on how tasks are assigned
to the processors at run-time. In the partitioned method,
all instances of a task are executed on the same processor,
where the processor used for each task is determined before
run-time by a partitioning algorithm. In the non-partitioned
method, a task is allowed to execute on any processor, even
when resuming after having been preempted. Two fundamental
properties have been shown for the addressed problem. First, the problem of deciding whether a task set is
schedulable is NP-hard for both methods. Second, there are
task sets which are schedulable with an optimal priority assignment
with the non-partitioned method, but are unschedulable
with an optimal partitioning algorithm and conversely.
Among the two methods, the non-partitioned method has
received considerably less attention, mainly because it is believed
to suffer from several scheduling-related shortcomings.
The most well-known of these is Dhall’s effect, a
scheduling dilemma wherein some task sets may be unschedulable
on multiple processors even though they have
a low utilization. Another shortcoming is that existing
necessary and sufficient schedulability tests all have exponential
time complexity, and existing sufficient tests
have polynomial complexity but are pessimistic. It has
also been shown that the RM (rate-monotonic) priorityassignment
scheme is not optimal, and no optimal
priority-assignment schemes with polynomial time complexity
have been found.
In this paper, we present an in-depth analysis of the nonpartitioned
method in terms of its scheduling-related properties.
We (i) identify a set of anomalies for preemptive
scheduling with migration, which are the first ever reported
in the open research literature, (ii) identify several difficulties
in conveying techniques from uniprocessor scheduling
to the multiprocessor case, and (iii) conjecture that there may
exist priority-assignment schemes that can contribute to circumventing
Dhall’s effect, something that has believed to be
inherently impossible with the non-partitioned method.