Online Scheduling of Time-Critical Tasks to Minimize the Number of Calibrations

TL;DR

This paper addresses online scheduling of time-critical jobs on machines requiring calibration, proposing algorithms that minimize calibrations and improve competitive ratios, especially for unit processing times and zero calibration time.

Contribution

It introduces an $ ext{O}( ext{lambda})$-competitive algorithm for unit processing times and enhances the competitive ratio for the zero calibration case, advancing the state of online scheduling.

Findings

Proposed an asymptotically optimal $ ext{O}( ext{lambda})$-competitive algorithm for unit processing times.

Achieved a competitive ratio of approximately 15.16 for the case $ ext{lambda}=0$, improving previous results.

Provided theoretical bounds and analysis for online calibration and scheduling problems.

Abstract

We study the online scheduling problem where the machines need to be calibrated before processing any jobs. To calibrate a machine, it will take $\lambda$ time steps as the activation time, and then the machine will remain calibrated status for $T$ time steps. The job can only be processed by the machine that is in calibrated status. Given a set of jobs arriving online, each of the jobs is characterized by a release time, a processing time, and a deadline. We assume that there is an infinite number of machines for usage. The objective is to minimize the total number of calibrations while feasibly scheduling all jobs. For the case that all jobs have unit processing times, we propose an $\mathcal{O}(\lambda)$-competitive algorithm, which is asymptotically optimal. When $\lambda=0$, the problem is degraded to rent minimization, where our algorithm achieves a competitive ratio of $3e+7(\approx 15.16)$ which improves upon the previous results for such problems.