Non-Preemptive EDF Schedulability Analysis via Partition Index
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Solution Overview
Problem
Existing feasibility analysis techniques for non-preemptive tasks in real-time systems exhibit high computational complexity, making them impractical for online systems, as they are NP-Hard and require significant processor time, unlike their preemptive counterparts.
Innovation Solution
The method reduces computational complexity by analyzing the schedulability of the lowest priority task at common scheduling points generated by all higher priority tasks, employing the Earliest Deadline First (EDF) scheduling algorithm, which transforms the computational cost from O(n²pnp₁) to O(Pnp₁), allowing for efficient feasibility determination in uni-processor systems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If existing feasibility analysis techniques are used for non-preemptive tasks, then the scheduling feasibility can be determined, but the computational complexity becomes very high (NP-Hard)
Solution Approach 1:
The patent segments the feasibility analysis by introducing a partition index i that divides the task set into two groups: tasks with higher priority (j < i) and tasks with lower or equal priority (j ≥ i). This segmentation allows the complex NP-Hard problem to be broken down into manageable components that can be analyzed separately and combined, transforming the intractable problem into a polynomial-time solvable one.
Solution Approach 2:
The patent performs preliminary actions by pre-calculating and storing the workload functions W_i^j(t) for all task pairs (i, j) before conducting the feasibility analysis. These pre-computed values represent the cumulative execution time of higher-priority tasks at any time t, and are stored in a lookup table. During the actual feasibility check, these pre-computed values are directly retrieved and used, avoiding repeated complex calculations and reducing the overall computational complexity to polynomial time.
2Device complexity
If non-preemptive scheduling is implemented, then the system complexity is reduced compared to preemptive scheduling, but the computational cost for feasibility determination becomes very high
Solution Approach 1:
The patent performs preliminary actions by pre-calculating and storing the workload functions W_i^j(t) for all task pairs (i, j) before conducting the feasibility analysis. These pre-computed values represent the cumulative execution time of higher-priority tasks at any time t, and are stored in a lookup table. During the actual feasibility check, these pre-computed values are directly retrieved and used, avoiding repeated complex calculations and reducing the overall computational complexity to polynomial time.
Solution Approach 2:
The patent creates a simplified model of the scheduling problem by copying and analyzing only the critical components: the workload functions W_i^j(t) that represent the cumulative execution time of higher-priority tasks. Instead of simulating the entire non-preemptive scheduling process, the patent copies and analyzes these essential workload characteristics, which are sufficient to determine feasibility without requiring complex real-time simulation.
3Use of energy by moving object
If polynomial time approximation algorithms are used, then the power consumption is reduced, but the feasibility determination remains undetermined (NP Hard)
Solution Approach 1:
The patent segments the feasibility analysis by introducing a partition index i that divides the task set into two groups: tasks with higher priority (j < i) and tasks with lower or equal priority (j ≥ i). This segmentation allows the complex NP-Hard problem to be broken down into manageable components that can be analyzed separately and combined, transforming the intractable problem into a polynomial-time solvable one.
Solution Approach 2:
The patent creates a simplified model of the scheduling problem by copying and analyzing only the critical components: the workload functions W_i^j(t) that represent the cumulative execution time of higher-priority tasks. Instead of simulating the entire non-preemptive scheduling process, the patent copies and analyzes these essential workload characteristics, which are sufficient to determine feasibility without requiring complex real-time simulation.
Data Source
AI summary
Earliest deadline first (EDF) scheduling algorithm is the most celebrated result for dynamic priority scheduling in real-time systems for both preemptive and non-preemptive cases. From complexity point of view, EDF is polynomial for preemptive scheduling of tasks. However, it becomes pseudo-polynomial under non-preemptive case. Described herein is a technique that determines EDF feasibility of non-preemptive task set by analyzing schedulability of the lowest priority task at common scheduling points generated by all higher priority tasks in the task set. The adjustment results in improving the computational cost of an existing test from O(n2 pn/p1) to O(pn/p1), where n is the number of tasks in the system, while pn and p1 represent the task periods of largest and smallest periodic tasks respectively. With reduced computation cost, the described method of analyzing feasibility can be intergraded with online systems for testing feasibility of a special class of real-time systems under non-preemptive case.