Edge Generation Scheduling for DAG Tasks Using Deep Reinforcement Learning

TL;DR

This work addresses real-time DAG scheduling on multicore platforms by introducing the trivially schedulable DAG concept, which links schedulability to the DAG length and width via L(G) ≤ D and W(G) ≤ M. It proposes Edge Generation Scheduling (EGS) to transform a given DAG into a trivially schedulable one by adding edges, and formulates edge generation as an MDP solved with Proximal Policy Optimization (PPO) using a Graphormer-based encoder. Empirical results show EGS-PPO consistently reduces processor usage compared to state-of-the-art heuristics and MILP baselines, with 3–5x improvements in optimality gaps on small instances and robustness to task characteristics. The framework shifts complexity from global timing analyses to edge-selection policies, enabling scalable scheduling that benefits federated and heterogeneous deployments, and opens avenues for future work in makespan minimization and broader platform types.

Abstract

Directed acyclic graph (DAG) tasks are currently adopted in the real-time domain to model complex applications from the automotive, avionics, and industrial domains that implement their functionalities through chains of intercommunicating tasks. This paper studies the problem of scheduling real-time DAG tasks by presenting a novel schedulability test based on the concept of trivial schedulability. Using this schedulability test, we propose a new DAG scheduling framework (edge generation scheduling -- EGS) that attempts to minimize the DAG width by iteratively generating edges while guaranteeing the deadline constraint. We study how to efficiently solve the problem of generating edges by developing a deep reinforcement learning algorithm combined with a graph representation neural network to learn an efficient edge generation policy for EGS. We evaluate the effectiveness of the proposed algorithm by comparing it with state-of-the-art DAG scheduling heuristics and an optimal mixed-integer linear programming baseline. Experimental results show that the proposed algorithm outperforms the state-of-the-art by requiring fewer processors to schedule the same DAG tasks. The code is available at https://github.com/binqi-sun/egs.

Figures (12)

• Figure 1: Example of a DAG task.
• Figure 2: Example of DAG length and node-level timing attributes. The nodes and edges of the critical path are marked in red. The numbers inside each node represent the node's WCET, LST, and EFT with corresponding colors.
• Figure 3: Example of DAG width and node-level parallelism attributes. The nodes belonging to the critical antichains are marked red, and a dotted line surrounds each antichain. The numbers inside each node represent the node's LW, IW, and OW with corresponding colors.
• Figure 4: Example of the trivial schedule with $M=3$.
• Figure 5: Example of the trivial schedule with $M=2$.

Theorems & Definitions (27)

• Example 1
• Definition 3.1: DAG length
• Example 2
• Definition 3.2: DAG width
• Example 3
• Definition 4.1: Trivial schedulability
• Lemma 4.1
• proof
• Lemma 4.2
• proof