Skewness-Based Min-Min Max-Min Heuristic for Grid Task Scheduling

Abstract

Skewness plays a very important role in task scheduling. It measures the degree of asymmetry in a data set. Moreover, the data set may be positively skewed or negatively skewed. The quartile coefficient of skewness lies in between -1 to 1. If the quartile coefficient is in between -1 to 0, then the data set is negatively skewed. Otherwise, it is positively skewed. Min-Min and Max-Min heuristic underperforms if the data set is positively skewed and negative skewed respectively. In order to overcome this problem, we have proposed a hybrid heuristic called Skewness-Based Min-Min Max-Min (SBM2). This heuristic selects one of the heuristics (Min-Min or Max-Min) based on the skewness value. It can be calculated using three factors: first quartile, second quartile (or median) and third quartile. Simulation results show that the proposed hybrid heuristic minimizes the make span and handle the skewed data set.