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Ensuring Data Freshness in Multi-Rate Task Chains Scheduling

José Luis Conradi Hoffmann, Antônio Augusto Fröhlich

TL;DR

A formal methodology to decompose Data Dependency Graphs into Dominant Paths by tracing the strictest data freshness constraints backward from the actuators is introduced, and a Consensus Offset Search algorithm is proposed that synchronizes shared producers and private predecessors without the artificial latency of LET buffering.

Abstract

In safety-critical autonomous systems, data freshness presents a fundamental design challenge. While the Logical Execution Time (LET) paradigm ensures compositional determinism, it often does so at the cost of injected latency, degrading the phase margin of high-frequency control loops. Furthermore, mapping heterogeneous, multi-rate sensor fusion requirements onto rigid task-centric schedules typically implies in resource-inefficient oversampling. This paper proposes a Task-based scheduling framework extended with data freshness constraints. Unlike traditional models, scheduling decisions are driven by the lifespan of data. We introduce task offset based on the data freshness constraint to order data production in a Just-in-Time (JIT) fashion: the completion of the production of data with strictest data freshness constraint is delayed to the instant its consumers will be ready to use it. This allows for flexible task release offsets. We introduce a formal methodology to decompose Data Dependency Graphs into Dominant Paths by tracing the strictest data freshness constraints backward from the actuators. Based on this decomposition, we propose a Consensus Offset Search algorithm that synchronizes shared producers and private predecessors. This approach enforces end-to-end data freshness without the artificial latency of LET buffering. We formally prove that this offset-based alignment preserves the 100\% schedulability capacity of Global EDF, ensuring data freshness while eliminating the computational overhead of redundant sampling.

Ensuring Data Freshness in Multi-Rate Task Chains Scheduling

TL;DR

A formal methodology to decompose Data Dependency Graphs into Dominant Paths by tracing the strictest data freshness constraints backward from the actuators is introduced, and a Consensus Offset Search algorithm is proposed that synchronizes shared producers and private predecessors without the artificial latency of LET buffering.

Abstract

In safety-critical autonomous systems, data freshness presents a fundamental design challenge. While the Logical Execution Time (LET) paradigm ensures compositional determinism, it often does so at the cost of injected latency, degrading the phase margin of high-frequency control loops. Furthermore, mapping heterogeneous, multi-rate sensor fusion requirements onto rigid task-centric schedules typically implies in resource-inefficient oversampling. This paper proposes a Task-based scheduling framework extended with data freshness constraints. Unlike traditional models, scheduling decisions are driven by the lifespan of data. We introduce task offset based on the data freshness constraint to order data production in a Just-in-Time (JIT) fashion: the completion of the production of data with strictest data freshness constraint is delayed to the instant its consumers will be ready to use it. This allows for flexible task release offsets. We introduce a formal methodology to decompose Data Dependency Graphs into Dominant Paths by tracing the strictest data freshness constraints backward from the actuators. Based on this decomposition, we propose a Consensus Offset Search algorithm that synchronizes shared producers and private predecessors. This approach enforces end-to-end data freshness without the artificial latency of LET buffering. We formally prove that this offset-based alignment preserves the 100\% schedulability capacity of Global EDF, ensuring data freshness while eliminating the computational overhead of redundant sampling.
Paper Structure (32 sections, 1 theorem, 29 equations, 1 algorithm)

This paper contains 32 sections, 1 theorem, 29 equations, 1 algorithm.

Table of Contents

  1. Introduction
  2. Contributions
  3. Related Works
  4. Predictability in Task Chains
  5. Logical Execution Time (LET) and Task Chains
  6. Task Dependency and Data Freshness
  7. System and Task Model
  8. Task Model
  9. Scheduling Constraints and Operational Assumptions
  10. Baseline Constraints
  11. System Assumptions
  12. Data Freshness Constraint
  13. Adapting Start Offset to Optimize Data Freshness in Task Chains
  14. Motivating Example: The AEB Sensor Fusion Chain
  15. Dependency in Task-chains
  16. ...and 17 more sections

Key Result

Theorem 1

Let $\mathcal{T} = \{\tau_1, \dots, \tau_n\}$ be a set of periodic tasks with implicit deadlines $D_i = T_i$. The introduction of static offsets $\Phi_i \geq 0$ to satisfy data freshness constraints does not reduce the maximum schedulable utilization bound of the system under Global EDF.

Theorems & Definitions (10)

  • Definition 1: Worst-Case Communication Latency (WCCL) $L_{ij}$
  • Definition 2: Release Time $r_{i,k}$
  • Definition 3: Start Time $s_{i,k}$
  • Definition 4: Finish Time $f_{i,k}$
  • Remark 1
  • Remark 2
  • Definition 5: Critical Predecessor ($previous(\tau)$)
  • Remark 3: Data Freshness Check
  • Remark 4
  • Theorem 1