Allocating Independent Subtasks on Parallel Processors
IEEE Transactions on Software Engineering
Handbook of algorithms and data structures: in Pascal and C (2nd ed.)
Handbook of algorithms and data structures: in Pascal and C (2nd ed.)
Stochastic Bounds on Execution Times of Parallel Programs
IEEE Transactions on Software Engineering
Performance of Synchronous Parallel Algorithms with Regular Structures
IEEE Transactions on Parallel and Distributed Systems
Lower and Upper Bounds on Time for Multiprocessor Optimal Schedules
IEEE Transactions on Parallel and Distributed Systems
Stochastic Prediction of Execution Time for Dynamic Bulk Synchronous Computations
The Journal of Supercomputing
Stochastic Prediction of Execution Time for Dynamic Bulk Synchronous Computations
IPDPS '01 Proceedings of the 15th International Parallel & Distributed Processing Symposium
Optimal periodic remapping of dynamic bulk synchronous computations
Journal of Parallel and Distributed Computing
Journal of Parallel and Distributed Computing - Special issue on parallel bioinspired algorithms
Statistical Performance Analysis and Estimation for Parallel Multimedia Processing
Journal of Signal Processing Systems
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A parallel program can be modeled as an acyclic directed graph, where a node represents a task, which is the smallest grain of computation to be assigned to a processor, and arcs stand for precedence (synchronization) constraints among the tasks. Due to different input data and unpredictable dynamic run time environments, the execution times of tasks as well as the entire program can be treated as random variables. In this paper, we develop some stochastic lower and upper bounds for parallel program execution times when there are limited processors. Such analysis can provide important information for job scheduling and resource allocation. For several typical classes of parallel programs, we derive very accurate closed form approximations for the bounds. Examples are also given to demonstrate the quality of the bounds derived.