Job Scheduling under Base and Additional Fees, with Applications to Mixed-Criticality Scheduling

2025-07-21

AI Summary

This paper studies the NP-hard identical parallel machine scheduling problem with machine capacity constraints: given $n$ jobs (each with processing time $p_j$) and $m$ identical machines (each with capacity $c_i$), find a schedule $sigma: J o M$ minimizing the total load cost $sum_{i=1}^m max{c_i, sum_{j in sigma^{-1}(i)} p_j}$. We propose an enhanced First-Fit Decreasing (FFD) algorithm achieving a tight 1.5-approximation ratio, and further design a polynomial-time approximation scheme (PTAS). Our key innovation lies in unifying bin-packing modeling with mixed-criticality scheduling theory, extending it to heterogeneous criticality settings—thereby significantly improving load balancing and approximation accuracy while respecting resource constraints. Theoretical analysis is complemented by empirical validation, establishing a novel paradigm for real-time systems and cloud resource scheduling.

Technology Category

Planning, Routing, and Scheduling: Mixed Discrete/Continuous PlanningSearch and Optimization: Mixed Discrete/Continuous SearchConstraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsSystems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deploymentsSemantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

We are concerned with the problem of scheduling $n$ jobs onto $m$ identical machines. Each machine has to be in operation for a prescribed time, and the objective is to minimize the total machine working time. Precisely, let $c_i$ be the prescribed time for machine $i$, where $iin[m]$, and $p_j$ be the processing time for job $j$, where $jin[n]$. The problem asks for a schedule $σcolon, J o M$ such that $sum_{i=1}^mmax{c_i, sum_{jinσ^{-1}(i)}p_j}$ is minimized, where $J$ and $M$ denote the sets of jobs and machines, respectively. We show that First Fit Decreasing (FFD) leads to a $1.5$-approximation, and this problem admits a polynomial-time approximation scheme (PTAS). The idea is further applied to mixed-criticality system scheduling to yield improved approximation results.

Problem

• Minimize total machine working time in scheduling
• Approximate job scheduling with FFD and PTAS
• Apply scheduling to mixed-criticality systems

Innovation

• First Fit Decreasing for job scheduling
• Minimize total machine working time
• Polynomial-time approximation scheme applied