# From Simulation to Experiment: A Case Study on Multiprocessor Task Scheduling

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7 Table II REGRESSION MODELS (INCLUDING VALUES FOR INSTANTIATION AND REGRESSION COEFFICIENTS). time to model functions regression values execution time (multilication) = {2, 4, 7, 15} = {15, 24, 31} 1 n = 2000 a 2 + b c + d (a, b, c, d) = (239.44, 3.43, 0.08, 1.93) n = 3000 a 1 + b c + d (a, b, c, d) = (537.91, 25.55, 0.09, 11.47) execution time (addition) = {2, 4, 7, 15, 24, 31} n = 2000 a 1 + b (a, b) = (22.99, 0.03) n = 3000 a 1 + b (a, b) = (73.59, 0.38) = {1, 16, 32} redistribution startu a + b (a, b) = (7.88, ) task startu time a + b (a, b) = (0.03, 0.65) rel. makesan of HCPA Exeriment rel. makesan of HCPA Exeriment DAGs (sorted by relative makesan from simulation) DAGs (sorted by relative makesan from simulation) Figure 7. HPCA makesan relative to that of MCPA using emirical models. Left-hand side: n = 2,000. Right-hand side: n = 3,000. error [%] analytic rofile emirical error [%] analytic rofile emirical than the two other versions by orders of magnitude, while the emirical version rovides a reasonable alternative to the rofile-based version. We conclude that the emirical models rovide a good trade-off between the time and effort needed to instantiate them and the rovided simulation accuracy. In the scoe of our case study, simulation based on these models is accurate enough to draw valid conclusions regarding the HCPA and MCPA algorithms. Such conclusions would simly not have been achievable with urely analytical models. Figure 8. Makesan simulation error for the three different simulation models. Left-hand side: HCPA results. Right-hand side: MCPA results. for n = 3,000, we found that the largest discreancies seen on the right-hand side of Figure 7 are for cases in which a scheduling algorithms allocates = 16 rocessors to several tasks. For this number of rocessors, recall that we have found our imlementation of matrix multilication to lead to unexectedly oor erformance (the outliers in Figure 6). Our regressive task execution time model in this case is a oor fit to exerimental results, which exlains the discreancies. To rovide a global view of simulation errors for the three versions of our simulator (analytical, rofile-based, and emirical), Figure 8 shows error statistics over all exeriments for both each scheduling algorithm in a box-and-whisker fashion. The urely analytical version leads to errors larger VIII. RELATED WORK There is a large literature on simulation techniques and models for (redicting the erformance of) arallel alications. Not surrisingly, many authors have roosed simulators for MPI alications ranging from analytical simulators (e.g., [17]) to oerational simulators (e.g., [18]). An overarching conclusion from such works is that reasonable simulation accuracy requires extensive and ossibly alicationsecific measurements on a reresentative real-world execution environment. Yet, most ublished results in the scheduling literature are obtained with urely analytical simulation models. In this work we used a case study to quantify how such models should be evolved to achieve scientifically sound results. We have roosed emirical models that rely on simle regressions, which has also been done by other authors, and recently in [16]. Beyond those authors that have roosed a

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