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Resources are allocated to tasks based on task weight calculated using analysis hierarchy process.
In Fig. 3 a, the task weight range is set to [ 1,50].
The equation uses a series of lifting multipliers (parameters) to calculate corresponding recommended task weight limits.
The reason is, with the increasing range of task weight, some tasks with large task weight could not migrate to other users, since no user would admit the migration for such a big job for some rounds in our simulation.
Similarly, in Fig. 3 b, c, the task weight range is set to [ 1,100] and [ 1,500], respectively.
We set different task weight values to each task, such that the tasks could be migrated among users.
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First, we rank the task weights in descending order.
where W(x j ) is the sum of task weights on machine j.
Fig. 3 Load balancing performance comparisons between proportional allocation and best response, when the task weights are concerned.
If the task weights are randomly selected from a larger range, the diversities among users would be more significant.
Also, it is worth noting that we have not shown the convergence property of the max-weight best response method, because it could get immediate convergence property once task weights are ordered and tasks are allocated sequentially, which has been proved in [23].
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com