Real-Time Scheduling Analysis Algorithm Using Approximate Cost Estimation
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Solution Overview
Problem
Current methods for analyzing the scheduling capability of real-time systems face complexity issues, particularly with pseudo-polynomial complexity, and fail to efficiently handle tasks with varying time limits and intervals, leading to high execution times and errors.
Innovation Solution
A scalable algorithm that approximates system costs by focusing on variable error margins, allowing for a compromise between execution time and accuracy, and is applicable for both predictive and real-time analysis, enabling the determination of real-time capability and initiation of countermeasures.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If exact calculation methods are used for scheduling capability analysis, then measurement precision is improved, but algorithm complexity increases to pseudo-polynomial level
Solution Approach 1:
The patent introduces a parameter ε (epsilon) representing the acceptable error margin, and transforms the exact calculation problem into an approximate calculation problem by defining threshold values. When the calculated value differs from the exact value by less than ε, the approximate result is accepted, thus converting the complexity from pseudo-polynomial to polynomial level while maintaining acceptable precision.
Solution Approach 2:
The patent applies partial action by calculating system costs only for a subset of time intervals rather than all possible intervals. By using the formula T_i = T_(i-1) + p_j and selectively computing costs at these discrete points, the method achieves sufficient accuracy for scheduling capability analysis without performing exhaustive calculations across the entire time range.
2Measurement precision
If the number of time intervals for checking accumulated processing time is increased, then measurement precision is improved, but execution time increases
Solution Approach 1:
The patent implements periodic action by checking accumulated processing time at regular intervals defined by T_i = T_(i-1) + p_j, where p_j represents the period of task j. Instead of continuously monitoring all time points, the method performs discrete periodic checks at these structured intervals, significantly reducing the number of computations required while maintaining adequate precision through the error margin ε.
3Reliability
If system costs are calculated for all time intervals, then reliability is improved, but productivity decreases due to high computational overhead
Solution Approach 1:
The patent extracts and focuses calculation efforts only on critical time intervals where scheduling decisions are most impactful. By using the periodic interval formula T_i = T_(i-1) + p_j and comparing accumulated costs only at these extracted points, the method eliminates redundant calculations for non-critical intervals, thus maintaining reliability for real-time capability assessment while significantly improving productivity through reduced computational overhead.
Data Source
AI summary
The invention relates to a method for testing the real-time capacity of a system, especially a computer system, according to which a quantity of different tasks (τ) is to be executed, system costs being incurred by the execution of each task (τ). The aim of the invention is to provide an especially rapid and accurate method. To this end, in order to determine the total costs (Dbi(I)) for at least one time interval (I), the actual system costs (Dbi(I)) of the job of a first task are taken into account for said at least one first task, the actual system costs (Dbi(I)) of at least two jobs of the first task are taken into account for at least one first task, and other system costs are taken into account for at least one second task. The other system costs are determined by an approximation based on the actual system costs (Dbi(I)).