Design and Performance Analysis of Divisible Load Scheduling Strategies on Arbitrary Graphs

In this paper, we consider the problem of scheduling divisible loads on arbitrary graphs with the objective to minimize the total processing time of the entire load submitted for processing. We consider an arbitrary graph network comprising heterogeneous processors interconnected via heterogeneous links in an arbitrary fashion. The divisible load is assumed to originate at any processor in the network. We transform the problem into a multi-level unbalanced tree network and schedule the divisible load. We design systematic procedures to identify and eliminate any redundant processor–link pairs (those pairs whose consideration in scheduling will penalize the performance) and derive an optimal tree structure to obtain an optimal processing time, for a fixed sequence of load distribution. Since the algorithm thrives to determine an equivalent number of processors (resources) that can be used for processing the entire load, we refer to this approach as resource-aware optimal load distribution (RAOLD) algorithm. We extend our study by applying the optimal sequencing theorem proposed for single-level tree networks in the literature for multi-level tree for obtaining an optimal solution. We evaluate the performance for a wide range of arbitrary graphs with varying connectivity probabilities and processor densities. We also study the effect of network scalability and connectivity. We demonstrate the time performance when the point of load origination differs in the network and highlight certain key features that may be useful for algorithm and/or network system designers. We evaluate the time performance with rigorous simulation experiments under different system parameters for the ease of a complete understanding.