{"paper":{"title":"k2Q: A Quadratic-Form Response Time and Schedulability Analysis Framework for Utilization-Based Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Cong Liu, Jian-Jia Chen, Wen-Hung Huang","submitted_at":"2015-05-14T20:44:04Z","abstract_excerpt":"In this paper, we present a general response-time analysis and schedulability-test framework, called k2Q (k to Q). It provides automatic constructions of closed-form quadratic bounds or utilization bounds for a wide range of applications in real-time systems under fixed-priority scheduling. The key of the framework is a $k$-point schedulability test or a $k$-point response time analysis that is based on the utilizations and the execution times of $k-1$ higher-priority tasks. The natural condition of k2Q is a quadratic form for testing the schedulability or analyzing the response time. The resp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03883","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}