Linear Switching State Space (LS3) Model for Task Scheduling: An Analytical Approach

Task Scheduling (TS) poses a challenging problem in distributed systems such as multiprocessor systems, flow-shop scheduling, and project management problems in which there are multiple tasks and processors (resources), and the problem is to efficiently assign tasks to processors. The importance of this problem includes several aspects such as heterogeneity of processors, computational complexity of reaching a solution as well as theoretical performance analysis. In this paper, control theory is used to construct a modeling paradigm. The approach which is basically a switching state space model opens a possibility of using the extensive theoretical developments that have taken place in this field within the past several decades. In this study, first we show the role of nonlinear state space equations in modeling the standard TS, a suitable transformation is then devised to convert this model to linear switching state space (LS3) equations with nonlinear constraints, and then the most important aspects of a control-based system – the stability, controllability, observability and stabilizability – for the proposed method is analytically proven. Finally we inspected the robustness of the proposed model in a similar way at the presence of the changes in processing power and link failure.