[Show abstract][Hide abstract] ABSTRACT: We study parallel job scheduling, where each job may be scheduled on any number of available processors in a given parallel system. We propose a mathematical model to estimate a job's execution time when assigned to multiple parallel processors. The model incorporates both the linear computation speedup achieved by having multiple processors to execute a job and the overhead incurred due to communication, synchronization, and management of multiple processors working on the same job. We show that the model is sophisticated enough to reflect the reality in parallel job execution and meanwhile also concise enough to make theoretical analysis possible. In particular, we study the validity of our overhead model by running well-known benchmarks on a parallel system with 1024 processors. We compare our fitting results with the traditional linear model without the overhead. The comparison shows conclusively that our model more accurately reflects the effect of the number of processors on the execution time. We also summarize some theoretical results for a parallel job schedule problem that uses our overhead model to calculate execution times.
[Show abstract][Hide abstract] ABSTRACT: In this paper, we study a parallel job scheduling model which takes into account both computation time and the overhead from communication between processors. As- suming that a job Jj has a processing requirement pj and is assigned to kj processors for parallel execution, then the execution time will be modeled by tj = pj/kj +(kj −1)� c, where c is the constant overhead cost associated with each processor other than the master processor. In this model, (kj −1) � c represents the cost for communication and coor- dination among the processors. This model attempts to ac- curately portray the actual execution time for jobs running in parallel on multiple processors. Using this model, we will study the online algorithm Earliest Completion Time (ECT) and show a lower bound for the competitive ratio of ECT for m ≥ 2 processors. For m ≤ 4, we show the matching upper bound to complete the competitive analysis for m = 2, 3, 4. For large m, we conjecture that the ratio approaches 30/13 ≈ 2.30769.
Preview · Article · Jan 2007 · Proceedings of the IASTED International Conference on Parallel and Distributed Computing and Systems