Optimal time-varying load sharing for divisible loads

A load sharing problem involving the optimal load allocation of divisible loads in a distributed computing system consisting of N processors interconnected through a bus-oriented network is investigated, For a divisible load, the workload is infinitely divisible so that each fraction of the workload can be distributed and independently computed on each processor. For the first time in divisible load theory, an analysis is provided in the case when the processor speed and the channel speed are time varying due to background jobs submitted to the distributed system with nonnegligible communication delays. A numerical method to calculate the average of the time-varying processor speed and the channel speed and an algorithm to find the optimal allocation of the workload to minimize the total processing finish time are proposed via a deterministic analysis. A stochastic analysis which makes use of Markovian queueing theory is introduced for the case when arrival and departure times of the background jobs are not known.