New competitive algorithms for online job scheduling

Abstract

Job scheduling, which greatly impacts on the system performance, is a fundamental problem in computer science. In this thesis, we study three kinds of scheduling problems, that is, deadline scheduling, due date scheduling, and flow time scheduling. Traditionally, the major concern for scheduling problems is the system performance, i.e. the “Quality of Service" (QoS). Different scheduling problems use different QoS measurements. For deadline scheduling, the most common QoS to optimize is the throughput; for due date scheduling, it is the total quoted lead time; and for flow time scheduling, it is the total (weighted) flow time.

Recently, energy efficiency is becoming more and more important. Many modern processors adopt technologies like dynamic speed scaling and sleep management to reduce energy usage. Much work is done on energy efficient scheduling. In this thesis, we study this topic for all three kinds of scheduling mentioned above.

Meanwhile, we also revisit the traditional flow time scheduling problem to optimize the QoS. However, we consider the problem in a more realistic model that makes the problem much more challenging.

Below is the summary of the problems studied in the thesis. First, we consider the tradeoff between energy and throughput for deadline scheduling. Specifically, each job is associated with a value (or importance) and a deadline. A scheduling algorithm is allowed to discard some of the jobs, and the objective is to minimize total energy usage plus total value of discarded jobs. When processor's maximum speed is unbounded, we propose an O(1)-competitive algorithm. When processor's maximum speed is bounded, we show a strong lower bound and give an algorithm with a competitive ratio close to that lower bound.

Second, we study energy efficient due date scheduling. Jobs arrive online with different sizes and weights. An algorithm needs to assign a due date to each job once it arrives, and complete the job by the due date. The quoted lead time of a job equals its due date minus its arrival time, multiplied by its weight. We propose a competitive algorithm for minimizing the sum of the total quoted lead time and energy usage.

Next, we consider flow time scheduling with power management on multiple machines. Jobs with arbitrary sizes and weights arrive online. Each machine consumes different amount of energy when processing a job, idling or sleeping. A scheduler has to maintain a good balance of the states of the machines to avoid energy wastage and, meanwhile, guarantee high QoS. Our result is an O(1)-competitive algorithm to minimize total weighted flow time plus energy usage.

Finally, we consider the traditional preemptive scheduling to minimize total flow time. Previous theoretical results often assume preemption is free, which is not true for most systems. We investigate the complexity of the problem when a processor has to perform a certain amount of overhead before it resumes the execution of a job preempted before. We first show an Ω(n^(1/4)) lower bound, and then, propose a (1+ε)-speed (1+ 1/ε )-competitive algorithm in resource augmentation model.