Some Insights on Fixed-Priority Preemptive Non-Partitioned Multiprocessor Scheduling

Other conference contribution, 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.