Efficient analysis of parallel processor scheduling policies

The widespread use of parallel systems has led to a number of proposals for high performance parallel processor scheduling policies. However, due to the specific nature of the workload assumptions and the performance evaluation techniques in previous work, the performance characteristics of processor scheduling policies are not well understood. This thesis unifies and generalizes previous policy analysis and comparisons using a general workload model that captures the essential features of parallel applications and a new performance evaluation technique. Our workload model includes general distributions of job parallelism and cumulative processing demand, controlled correlation between demand and parallelism, and a general nondecreasing deterministic execution rate function that captures the impact of synchronization and communication overheads. The proposed new approach to performance modeling of parallel processor scheduling is that of interpolation approximations. The interpolation approximation approach yields closed form expressions for mean response times that provide ready insight into the functional dependence of policy performance on workload parameters, and can be easily evaluated for systems with hundreds of processors. We use interpolation approximations to evaluate and compare four policies shown in the literature to have high performance under various specific workloads. These include a dynamic spatial equipartitioning (EQS) policy, the Preemptive Smallest Available Parallelism First (PSAPF) policy, the dynamic First Come First Serve (FCFS) policy, and a run-to-completion policy called Adaptive Static Partitioning (ASP). The results show that, as in uniprocessor scheduling disciplines, the coefficient of variation of demand is a key parameter that distinguishes relative policy performance. Using the interpolation models we also derive other key parameters and delineate regions of the design space under which each policy performs best. We show that the EQS policy has highest performance over most of the expected practical regions of the workload space. Finally, we thoroughly study the behavior of the EQS policy with respect to the workload parameters using both sample path analysis as well as approximate analysis. For example, we show that under our workload model the mean response time of EQS is smallest when all jobs are fully parallel and is highest when all jobs are fully sequential.