Revisiting the Schedule Graph Generation for the Exact and Sustainable Analysis of Non-preemptive Scheduling

TL;DR

A schedulability analysis is developed that constructs the schedule graph using new job-eligibility rules and is exact and sustainable for both work-conserving and enhanced formalization of non-work-conserving policies.

Abstract

This paper addresses the problem of scheduling non-preemptive tasks with release jitter and execution time variation on a uniprocessor. We show that the schedulability analysis based on schedule graph generation, proposed by Nasri and Brandenburg [RTSS 2017], produces negative results when it could be easily avoided by slightly reformalizing the notion of non-work-conserving policies. In this work, we develop a schedulability analysis that constructs the schedule graph using new job-eligibility rules and is exact and sustainable for both work-conserving and enhanced formalization of non-work-conserving policies. Besides, the experimental evaluation shows that our schedulability analysis is substantially faster.

Figures (11)

• Figure 1: A loose chart of the example instance given in Table \ref{['table:ex1_table']}. Each row represents a different task. The top row represents task $\mathcal{T}_{1}$, the middle row represents task $\mathcal{T}_{2}$ and the bottom row represents task $\mathcal{T}_{3}$.
• Figure 2: A regular chart of the example instance given in Table \ref{['table:ex1_table']} assuming the worst-case execution times and latest release times.
• Figure 3: A regular chart of the example instance given in Table \ref{['table:ex1_table']} with execution scenario that results in a deadline miss.
• Figure 4: A loose chart of the illustrative instance given in Table \ref{['table:ex3_table']}.
• Figure 5: The process of building a schedule graph using EDF policy. Each vertex $v_{k}$ contains its finish time interval $[e_{k},l_{k}]$. Each arc is labeled by the executed job. The stages are annotated with level and type of phase (either E for expansion or M for merge). The merge phases on levels 0 and 1 do not change the graph and are therefore omitted.