# An Ecient Dynamic Load Balancing using the Dimension Exchange. Ju-wook Jang. of balancing load among processors, most of the realworld

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4 case wj;i + wk;i ww;i + wv;i wk;i+1 wj;i+1 0 m+1, m even l+1,l even m m+1 1 m+1, m even l+1,l odd m m+1 m+1, m odd l,l even m+1 m 3 m+1, m odd l,l odd m+1 m 4 m, m even l+1,l even m m 5 m, m even l+1,l odd m m 6 m, m odd l,l even m m case ww;i+1 wv;i+1 Inc i Inc i+1 0 l l l+1 l 1 0 l l l l l l l+1 l l l 0 1 Table 1. The 7 possible cases of incrementing difference regarding the type of quatized loads in successive balancing phases (Inc i:increment of difference in phase i, Inc i+1:increment of difference in phase i+1) (a) before the balancing 4 6 Max Min (b) after the balancing Figure. Balancing of quantized loads on a hypercube of 3 processors using our method: a worst case ancing performance such as average queue length and speedup in processing time. SLAM II[1] is used as a simulation tool. Following parameters are used for our simulation [5]: to the proof that, in the worst case, our method will produce the maximum dierence of exactly d 1 log N e. Therefore, the maximum dierence in our scheme is only about half of the maximum dierence in the original DEM when applied to the quantized loads. In the next section, we will show how the maximum differences resulting from repeated balancing aect the total processing time. The SLAM II simulation tool[1] is employed to show how our scheme performs better in a practical sense. Average of maximum difference dem our The simulation Simulation is performed to satisfy two purposes. First is to verify the combinatorial proof that the maximum dierence in the worst case for our method does not exceed d 1 log N e.we enumerated all possible distribution using the numbers in the range as initial loads on processors in hypercube. Table shows the number of combination which produce certain maximum dierences. As expected, our method has 0 combinations that produce the maximum dierence exceeding d 1 log N e. The second and more practical purpose is to show that our method performs better especially on quantized loads than the DEM method. The purpose of this simulation is to estimate how the reduced maximum dirence of our method will aect the job bal- Figure 3. Average of the maximum difference for 1000 The number of processors in a hypercube: 8, 16, 3, 64 Architecure: loosely coupled multicomputer Number of processes() generated in each processor: 1000; 5000 Arrival time: poisson distribution Service time: exponential distribution Threshold for overload: 50-60% CPU utilization No change in load distribution during balancing

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