Scheduling and assignment on dynamic processor networks

Abstract

We address the problem of scheduling tasks characterized by dynamic completion time behavior. Existing scheduling methodologies reduce problems to using constant task durations and are therefore not suitable for problems with more complex completion time behavior. One such problem is scheduling applications on computer networks with time-varying communication channel capacities. We present a methodology that can be used to solve such problems. The specific contributions of this work are: (a) a novel representation for the completion time of tasks in scheduling problems, (b) a method for approximating that representation efficiently using an affine over-approximation, and (c) a mixed-integer programming-based formulation to solve a variety of scheduling problems using this representation and approximation. The resulting framework can be used to solve scheduling problems with time-varying task durations, and thus solve problems with time-varying communication links or resources. A case study is provided, in which we devise a scheduling scheme for computation on a computer network composed of processors onboard a satellite constellation. This example is an instance of scheduling applications on computer networks with known time-varying communication channel capacities and the results of the case study demonstrate the improvement of using the approximation method over existing methods.