Response Time Analysis and Optimal Priority Assignment for Global Non-Preemptive Fixed-Priority Rigid Gang Scheduling

Non-preemptive rigid gang scheduling combines the efficiency of parallel execution with the reduced overhead of non-preemptive scheduling. This approach is particularly advantageous for parallel hardware accelerators, such as Google's Edge Tensor Processing Unit (TPU), which is widely used for deep neural network (DNN) inference on embedded systems. This paper studies sporadic global non-preemptive fixed-priority (NP-FP) rigid gang scheduling, which is well-suited for DNN applications in Edge TPU pipelines. Each gang task spawns a fixed number of threads that must execute concurrently across distinct processing units. We introduce the first carry-in limitation technique specifically designed for gang task response time analysis, addressing the unique challenges posed by intra-task parallelism. This technique is formulated as a generalized knapsack problem, and we develop both a linear programming relaxation and a dynamic programming approach to solve it under different time complexities. Additionally, we propose the first optimal priority assignment policy for NP-FP gang schedulability tests. Our proposed schedulability analysis and optimal priority assignment policy are evaluated through extensive experiments, including both synthetic task sets and a case study using DNN benchmarks on commercial off-the-shelf Edge TPU accelerators. The results demonstrate that the proposed approaches effectively enhance the state-of-the-art global NP-FP gang schedulability tests, achieving improvements of up to 57.9% for synthetic task sets and 76.7% for Edge TPU benchmarks. Furthermore, we conduct an ablations study to examine the impact of different algorithmic components in the proposed technique, providing valuable insights for future research.