New results on online job scheduling

Abstract

This thesis presents several new results on online job scheduling. Job scheduling is a basic requirement of many practical computer systems, and the scheduling behavior directly affects a system’s performance. In theoretical aspect, scheduling scenarios are abstracted into scheduling models, which are studied mathematically. In this thesis, we look into a variety of scheduling models which are under active research. We incorporate these models and organize them into generalized pictures.

We first study non-clairvoyant scheduling to minimize weighted flow time on two different multi-processor models. In the first model, processors are all identical and jobs can possibly be speeded up by running on several processors in parallel. Under the non-clairvoyant model, the online scheduler has no information about the actual job size and degree of speed-up due to parallelism during the execution of a job, yet it has to determine dynamically when and how many processors to run the jobs. The literature contains several O(1)-competitive algorithms for this problem under the unit-weight multi-processor setting [13, 14] as well as the weighted single-processor setting [5]. This thesis shows the first O(1)-competitive algorithm for weighted flow time in the multi-processor setting.

In the second model, we consider processors with different functionalities and only processors of the same functionality can work on the same job in parallel to achieve some degree of speed up. Here a job is modeled as a sequence of non-clairvoyant demands of different functionalities. This model is derived naturally from the classical job shop scheduling; but as far as we know, there is no previous work on scheduling to minimize flow time under this multi-processor model. In this thesis we take a first step to study non-clairvoyant scheduling on this multi-processor model. Motivated by the literature on 2-machine job shop scheduling, we focus on the special case when processors are divided into two types of functionalities, and we show a non-clairvoyant algorithm that is O(1)-competitive for weighted flow time.

This thesis also initiates the study of online scheduling with rejection penalty in the non-clairvoyant setting. In the rejection penalty model, jobs can be rejected with a penalty, and the user cost of a job is defined as the weighted flow time of the job plus the penalty if it is rejected before completion. Previous work on minimizing the total user cost focused on the clairvoyant single-processor setting [3, 10] and has produced O(1)-competitive online algorithm for jobs with arbitrary weights and penalties. This thesis gives the first non-clairvoyant algorithms that are O(1)-competitive for minimizing the total user cost on a single processor and multi-processors, when using slightly faster (i.e., (1 + ∈)-speed for any ∈> 0) processors. Note that if no extra speed is allowed, no online algorithm can be O(1)-competitive even for minimizing (unweighted) flow time alone.

The above results assume a processor running at a fixed speed. This thesis shows more interesting results on extending the above study to the dynamic speed scaling model, where the processor can vary the speed dynamically and the rate of energy consumption is an arbitrary increasing function of speed. A scheduling algorithm has to decide job rejection and determine the order and speed of job execution. It is interesting to study the tradeoff between the above-mentioned user cost and energy. This thesis gives two O(1)-competitive non-clairvoyant algorithms for minimizing the user cost plus energy on a single processor and multi-processors, respectively.