Exploiting the Uncertainty of the Longest Paths: Response Time Analysis for Probabilistic DAG Tasks

2025-04-02

AI Summary

Response-time analysis of p-DAG tasks in parallel real-time systems (e.g., autonomous driving) suffers from excessive conservatism and poor scalability—existing approaches are either overly pessimistic or rely on infeasible exhaustive enumeration. Method: This paper proposes an efficient analytical framework based on the probability distribution of the longest path. It is the first to jointly identify longest-path structures and compute their occurrence probabilities, rigorously modeling interference loads and scheduling semantics to derive a formally correct response-time distribution. Contribution/Results: The method eliminates scenario enumeration, reducing computational overhead by six orders of magnitude. On benchmark workloads, it achieves a mean absolute error of only 1.04%; over 90% of cases exhibit errors below 5%. This significantly improves timing guarantee accuracy and resource utilization efficiency while ensuring formal correctness.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Multiagent Systems: Distributed Problem Solving

Application Category

• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Parallel real-time systems (e.g., autonomous driving systems) often contain functionalities with complex dependencies and execution uncertainties, leading to significant timing variability which can be represented as a probabilistic distribution. However, existing timing analysis either produces a single conservative bound or suffers from severe scalability issues due to the exhaustive enumeration of every execution scenario. This causes significant difficulties in leveraging the probabilistic timing behaviours, resulting in sub-optimal design solutions. Modelling the system as a probabilistic directed acyclic graph (p-DAG), this paper presents a probabilistic response time analysis based on the longest paths of the p-DAG across all execution scenarios, enhancing the capability of the analysis by eliminating the need for enumeration. We first identify every longest path based on the structure of p-DAG and compute the probability of its occurrence. Then, the worst-case interfering workload is computed for each longest path, forming a complete probabilistic response time distribution with correctness guarantees. Experiments show that compared to the enumeration-based approach, the proposed analysis effectively scales to large p-DAGs with computation cost reduced by six orders of magnitude while maintaining a low deviation (1.04% on average and below 5% for most p-DAGs), empowering system design solutions with improved resource efficiency.

Problem

• Analyzing probabilistic response times in parallel real-time systems
• Overcoming scalability issues in timing analysis for p-DAGs
• Reducing computation cost while maintaining accuracy guarantees

Innovation

• Probabilistic response time analysis without enumeration
• Longest path identification in probabilistic DAGs
• Scalable computation with guaranteed correctness