Competitive Analysis of Dynamic Multiprocessor Allocation Strategies

The subject of this thesis is to study the problem of dynamic processor allocation in parallel application scheduling. Processor allocation involves determining the number of processors to allocate to each of several simultaneously executing parallel applications and possibly dynamically adjusting the allocations during execution to improve overall system performance. We devise and analytically evaluate dynamic allocation policies that operate in environments in which full information about the jobs being executed is not known when making scheduling decisions. We use competitive analysis to compare the performance of algorithms which do not know the arrival or execution time of jobs with the performance of the optimal algorithm which uses complete information about jobs. The result of such a comparison is called a competitive ratio. The competitive ratio is indicative of the utility of different allocation policies. Our study is carried out under two performance objectives: minimizing the makespan and minimizing the mean response time respectively. Our results for minimizing the makespan consist of three parts. First we use competitive analysis to devise an allocation policy, OptComp, which yields the optimal competitive ratio for scheduling two parallel jobs. As well, we compare the dynamic equipartition (DEQ) policy with OptComp and find that the relative ratio of DEQ to OptComp is 1. 175729. This implies that the competitive ratio of DEQ is very close to optimal. Secondly we extend the results of sequential job scheduling to parallel job scheduling. Our results cover the situations when the application parallelism varies during execution as well as when applications do not arrive at the system simultaneously. Lastly we consider the case when some applications may execute infinitely because of programming errors which lead to an infinite loop. Our results show that DEQ yields the optimal competitive ratio. Our results for the problem of minimizing the mean response time assume that all applications arrive at the system simultaneously and that application parallelism does not change during execution. We show that in this case DEQ yields an optimal competitive ratio of   2 − 2 N + 1   .