Optimal Fixed Priority Scheduling in Multi-Stage Multi-Resource Distributed Real-Time Systems

TL;DR

This work tackles fixed-priority real-time scheduling with end-to-end deadlines in multi-stage multi-resource (MSMR) distributed systems. It develops an OPA-compatible schedulability test based on Delay Composition Algebra ($\mathcal{S}^{DCA}$) and uses it within an Optimal Priority Assignment framework (OPDCA) to compute a global priority order; it also proves that pairwise priority assignment can be feasible even when a total order does not exist, and provides an ILP (OPT) plus a Deadline-Monotonic Repair (DMR) heuristic to compute pairwise priorities. The key contributions are: (i) a refined, OPA-compatible DCA-based schedulability bound; (ii) OPDCA for optimal FP scheduling in MSMR systems; (iii) the observation that pairwise priority assignment can outperform or enable feasibility where total orders fail; (iv) scalable methods (OPT and DMR) to obtain pairwise schedules, validated via edge-computing simulations. The results demonstrate that OPDCA and OPT achieve higher acceptance under load compared with decomposition-based baselines, enabling holistic scheduling across compute and network resources with end-to-end deadlines.

Abstract

This work studies fixed priority (FP) scheduling of real-time jobs with end-to-end deadlines in a distributed system. Specifically, given a multi-stage pipeline with multiple heterogeneous resources of the same type at each stage, the problem is to assign priorities to a set of real-time jobs with different release times to access a resource at each stage of the pipeline subject to the end-to-end deadline constraints. Note, in such a system, jobs may compete with different sets of jobs at different stages of the pipeline depending on the job-to-resource mapping. To this end, following are the two major contributions of this work. We show that an OPA-compatible schedulability test based on the delay composition algebra can be constructed, which we then use with an optimal priority assignment algorithm to compute a priority ordering. Further, we establish the versatility of pairwise priority assignment in such a multi-stage multi-resource system, compared to a total priority ordering. In particular, we show that a pairwise priority assignment may be feasible even if a priority ordering does not exist. We propose an integer linear programming formulation and a scalable heuristic to compute a pairwise priority assignment. We also show through simulation experiments that the proposed approaches can be used for the holistic scheduling of real-time jobs in edge computing systems.

Figures (4)

• Figure 1: End-to-end delay of $J_i$ in a four-stage pipeline. (a) $\Delta_i = t_1 + t_2 + t_3 + t_4$. (b) One job-additive term due to $J_b$ as it delays $J_i$ at one stage only, $\Delta_i = t_1 + t_2 + t_5 + t_3 + t_4$. (c) & (d) Two job-additive terms if $J_b$ delays $J_i$ for two or more stages. (e) $m_{i,b}=2$ and up to two job-additive terms of $J_b$ corresponding to each segment.
• Figure 2: (a). Job-to-resource mapping. (b) Pairwise priority assignment.
• Figure 3: Edge Computing System
• Figure 4: Acceptance ratios (ARs) for varying (a) $\beta$, (b) $[h_1, h_2, h_3]$, and (c) $\gamma$. The base of the stacked histogram represents the AR of DM. The increment in the AR of DMR, OPDCA, and OPT compared to the AR of DM, DMR, and OPDCA, respectively, are stacked (upward) in this sequence. (d) Performance as admission controller.

Theorems & Definitions (1)

• proof