Schedulability of generalized multiframe task sets under static priority assignment

Abstract

The multiframe task model has been proposed recently to effectively model a task whose execution times are periodically changed according to a specified pattern. Schedulability of task sets consisting of multiframe tasks or generalized multiframe tasks ( G M F tasks) i s now being investigated under various conditions. This paper discusses the necessary and sufficient condition of the schedulability of G M F task sets under a prioritybased preemptive scheduling with static priority assignment. The critical instant theorem f o r G M F task sets is described and the necessary and sufficient condition of their schedulability is presented based on the theorem. W e also introduce the m a x i m u m interference function ( M I F ) andpropose a polynomial-time feasibility decision algorithm using the MIF.

Exact scheduling analysis of non-accumulatively monotonic multiframe tasks

“…Takada et al [13] investigated the schedulability of MF tasks and gave a scheduling condition of the MF model, under the fixed priority scheme, showing that the time complexity of the schedulability decision becomes at least i n i 2 . They introduced a sufficient feasibility decision algorithm using a maximum interference function.…”

“…Initially the worst case response time analysis of a MF task τ i requires checking all possible combinations of all frames of the MF tasks whose priorities are higher than τ i ; which means we have to consider i−1 j=1 n j different combinations of the frames [13]. However, the critical frame concept (see Section 2) leads to the requirement of only checking the critical frames of the MF tasks whose priorities are higher than τ i 's.…”

“…The first step is to find w 3,ṽ by applying Equations (13) and (14). So, r 3,(2,0,1) (q) = ξ 1 3 (q) + 2 j=1 ξṽ j j ( r 3,(2,0,1) (q) Tj ) q = 1, then r 3,(2,0,1) (1) = 7 + 2 j=1 ξṽ j j ( r 3,(2,0,1) (1)…”

Effective Scheduling Algorithms for I/O Blocking with a Multi-Frame Task Model

“…Even if f 1 is executed at time 0, it can be postponed by the length of f 2 . Based on the preemptive static priority scheduling theorem, we give a brief description of the new critical instant theorem for a GMF model [4].…”

“…By use of the maximum interference function (MIF) [4], they have calculated the interference time caused by high priority tasks within the duration time interval t. Based on this theorem, they discussed the necessary and sufficient condition for the schedulability of a set of GMF tasks under dynamic priority assignment. As described later, our algorithms presented in this paper are based on their work.…”