Divisible load scheduling on a hypercube cluster with finite-size buffers and granularity constraints

Abstract

In this paper we address the problem of scheduling a large size divisible load on a hypercube cluster of processors. Unlike in earlier studies in the divisible load theory (DLT) literature, here, we assume that the processors have finite-size buffers. Further we impose constraints on the extent to which the load can be divided, referred to as granularity constraint. We first present the closed-form solutions for the case with infinite-size buffers. For the case with load granularity constraint, we propose a simple algorithm to find the sub-optimal solution and then we analyze the case when these buffer are of finite size. For this case, we present an elegant strategy, referred to as incremental balancing strategy (IBS), to obtain an optimal load distribution. Based on the rigorous mathematical analysis, a number of interesting and useful properties exhibited by the algorithm are proven. Numerical examples are presented for the ease of understanding.