Job scheduling on high performance computer systems: Complexity and algorithms

The problem of job scheduling on Partitionable Massively Parallel Processor (PMPP) Systems is studied in this dissertation. The objective of the scheduling problem is to minimize the makespan or the total completion time. Key system features include the following: (1) the number of processors K is large relative to the number of jobs n (K $\ge$ 2n), (2) the processing time of a job depends on the number of processors assigned to it, and (3) unlimited repartitioning of the processors is allowed.Three types of speedup functions are considered: linear, sublinear, and superlinear. While simple rules are found to solve problems with linear and sublinear speedup functions, the superlinear rate function, which is most common, leads to an NP-hard problem. A Processor Partition Algorithm (PP) based on the results of a continuous-resource scheduling problem is developed for this problem. It is proved that Algorithm PP finds the best schedule among all parallel schedules. Moreover, Algorithm PP has a tight worst case absolute performance bound of 1 + 1/$\theta$ when the speedup function is concave and superlinear. ($\theta$ = $K\over n$ $-$ 1) Several variants of Algorithm PP are developed. Simulation shows that significant performance improvement can be obtained by using these variants. PMPP systems with a mesh-topology are also considered. Extension of Algorithm PP to this topology indicates that the absolute worst case performance bound is also 1 + 1/$\theta$. A hybrid 2-partition-Algorithm PP variant is shown to perform better than a one-dimension-fixed heuristic in simulation studies. More computational results are presented to show the effect of different parameters on the makespan.This dissertation also studies a high performance multiprocessor time-sharing computing system. A new job loading policy is developed for this system. The importance of using information on job resource requirements to prioritize and limit jobs admitted into the kernel is illustrated through simulation model. The simulation study is based on a stationary model of a computing system as well as on a model using nonstationary historical data from NCSA's Cray-YMP system.U of I OnlyETDs are only available to UIUC Users without author permissio