Balancing Flow Time and Energy Consumption

TL;DR

This paper develops dynamic programming algorithms to minimize total flow time in batch scheduling with energy constraints, focusing on agreeable deadlines, and improves runtime efficiency over previous methods.

Contribution

Introduces efficient dynamic programming solutions for flow time minimization under active time constraints, specifically for jobs with agreeable deadlines.

Findings

Achieves O(B·k·n) runtime for unit jobs

Achieves O(B·k·n^5) runtime for uniform length jobs

Outperforms previous DP approaches with higher computational complexity

Abstract

In this paper, we study the following batch scheduling model: find a schedule that minimizes total flow time for $n$ uniform length jobs, with release times and deadlines, where the machine is only actively processing jobs in at most $k$ synchronized batches of size at most $B$. Prior work on such batch scheduling models has considered only feasibility with no regard to the flow time of the schedule. However, algorithms that minimize the cost from the scheduler's perspective -- such as ones that minimize the active time of the processor -- can result in schedules where the total flow time is arbitrarily high \cite{ChangGabowKhuller}. Such schedules are not valuable from the perspective of the client. In response, our work provides dynamic programs which minimize flow time subject to active time constraints. Our main contribution focuses on jobs with agreeable deadlines; for such job instances, we introduce dynamic programs that achieve runtimes of O$(B \cdot k \cdot n)$ for unit jobs and O$(B \cdot k \cdot n^5)$ for uniform length jobs. These results improve upon our modification of a different, classical dynamic programming approach by Baptiste. While the modified DP works when deadlines are non-agreeable, this solution is more expensive, with runtime $O(B \cdot k^2 \cdot n^7)$ \cite{Baptiste00}.