A multi-criteria approach to time cheating in the divisible load scheduling

The divisible load scheduling (DLS) can be considered as a special class of scheduling model in the area of distributed and parallel systems. According to the DLS, the computations and communications can be divided into some arbitrarily independent fragments in which each fragment can be computed independently by a processor. The basic assumptions of the traditional DLS models are wj≤wj+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$w_j\le w_{j+1}$$\end{document} and zj≤zj+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_j\le z_{j+1}$$\end{document} for all j≤m\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$j\le m$$\end{document}(zj\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_j$$\end{document} and wj\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$w_j$$\end{document} are the rates of communication and computation of the jth processor, respectively). These presumptions are not acceptable if the processors do not report their real rates of communication or computation. The problem that a processor may not report its real rates of communication or computation is called cheating problem. This paper has a multi-criteria approach to the time cheating problem in the area of the DLS. The multi-criteria DLS model is a new paradigm in the area of DLS and its applications. The main contribution of this paper is to reduce the effects of time cheating in a DLS scheduling model.