OASS: A Mixed-Integer Programming Scheduling Model for Ordering and Allocating Parallel Jobs on Multi-Cluster Systems

Multi-cluster environments are composed of multiple clusters of computers that act collaboratively, thus allowing computational problems that require more resources than those available in a single cluster to be treated. However, the degree of complexity of the scheduling process is greatly increased by the heterogeneity of resources and the co-allocation process, which distributes the tasks of parallel jobs across cluster boundaries. In a previous work, the authors presented a new scheduling strategy made up of a job selection function and a linear programming model named PAS for Package Allocation Strategy. This strategy firstly selects a set of jobs from the system queue that fits the available resources, and then a MixedInteger Programming model (MIP) is responsible for finding the best possible allocation, considering both the computation and communication requirements of the applications. In this current study, the authors propose a one-step strategy based on an MIP model where all the jobs waiting in the system queue are treated together to determine their execution order and resource allocation to minimize the overall makespan. Keywords-Multiple-Job Scheduling; Co-Allocation; Mixed Integer Programming; Multi-Cluster Systems;