Scheduling Adaptively Parallel Jobs Scheduling Adaptively Parallel Jobs

An adaptively parallel job is one in which the number of processors which can be used without waste changes during execution. When allocating processors to multiple adap-tively parallel jobs, a job scheduler should attempt to be fair|meaning that no job gets fewer processors than another, unless it demands fewer|and eecient|meaning that the scheduler does not waste processors on jobs that do not need them. Moreover, the scheduler should adapt quickly and be implementable in a distributed fashion. In this thesis, I present and analyze a randomized processor allocation algorithm, the SRLBA algorithm, which allocates processors to adaptively parallel jobs in a distributed system of P processors and J jobs. The algorithm consists of rounds of load-balancing steps in which processor migration may occur. In the case that each job has a demand which is more than its fair share P=J of the processors, I show that after O(lg P) rounds, the system is in an almost fair and eecient allocation with high probability. To analyze the algorithm, I use a two-phase analysis with a potential-function argument. In Phase 1, I show that after O(lg P) rounds every job has at least a constant fraction of P=J processors. Then I show that in Phase 2, after an additional O(lg P) rounds, the system converges to an almost fair and eecient connguration. Finally, I conclude my thesis with some directions for future work. Acknowledgments First I would like to thank my advisor, Professor Charles E. Leiserson. Charles rst introduced me to the eld of parallel job scheduling, and has guided my research in the area ever since. He has provided valuable guidance and good ideas to improve my research, in addition to always challenging me to do my best. Charles has also read my thesis over and over, helping me to present it better. The algorithm and analysis presented in this thesis are joint work with Drs. Robert Blumofe, Charles Leiserson, Aravind Shrinivason, and David Zuckerman. I have gained valuable knowledge and inspiration from working with them. I would also like to thank my family for their moral support. Finally, I want to thank my ance, Matthew Cheyney. Matt is also a computer science student. He listened to me talking about my research, and pushed me to justify or change some of the more unrealistic assumptions of my model, resulting in a stronger paper. He also helped me tremendously with the writeup …