Competitive online job scheduling algorithms under different energy management models

Abstract

Online flow-time scheduling is a fundamental problem in computer science and has been extensively studied for years. It is about how to design a scheduler to serve computer jobs with unpredictable arrival times and varying sizes and priorities so as to minimize the total flow time (better understood as response time) of jobs. It has many applications, most notable in the operating of server farms. As energy has become an important issue, the design of scheduler also has to take power management into consideration, for example, how to scale the speed of the processors dynamically. The objectives are orthogonal as one would prefer lower processor speed to save energy, yet a good quality of service must be retained. In this thesis, I study a few scheduling problems for energy and flow time in depth and give new algorithms to tackle them. The competitiveness of our algorithms is guaranteed with worst-case mathematical analysis against the best possible or hypothetical solutions.

In the speed scaling model, the power of a processor increases with its speed according to a certain function (e.g., a cubic function of speed). Among all online scheduling problems with speed scaling, the nonclairvoyant setting (in which the size of a job is not known during its execution) with arbitrary priorities is perhaps the most challenging. This thesis gives the first competitive algorithm called WLAPS for this setting.

In reality, it is not uncommon that during the peak-load period, some (low-priority) users have their jobs rejected by the servers. This triggers me to study more complicated scheduling algorithms that can strike a good balance among speed scaling, flow time and rejection penalty. Two new algorithms UPUW and HDFAC for different models of rejection penalty have been proposed and analyzed.

Last, but perhaps the most interesting, we study power management in large server farm environment in which the primary energy saving mechanism is to put some processors to sleep. Two new algorithms POOL and SATA have been designed to tackle jobs that cannot and can migrate among the processors, respectively. They are integrated algorithms that can consider speed scaling, job scheduling and processor sleep management together to optimize the energy usage and ow time simultaneously. These algorithms are again proven mathematically to be competitive even in the worst case.