Completion Time Minimization in Multi-User Task Scheduling with Heterogeneous Processors and Budget Constraints

We study task scheduling and offloading in a cloud computing system with multiple users, where tasks have different processing times, release times, communication times, and weights. Each user may schedule a task locally or offload it to a finite-capacity shared cloud with heterogeneous processors by paying a price for the resource usage. Our work aims at identifying a task scheduling decision that minimizes the weighted sum completion time of all tasks, while satisfying the users' budget constraints. We propose an efficient solution framework for this NP-hard problem. As a first step, we solve an integer-relaxed problem and use a rounding technique to obtain an integer solution that is a constant factor approximation to the minimum weighted sum completion time. This solution violates the budget constraints, but the average budget violation decreases as the number of users increases. Thus, we develop a scalable Single-Task Unload for Budget Resolution (STUBR) algorithm, which resolves budget violations and orders the tasks to reduce the weighted sum completion time. Our trace-driven simulation shows that STUBR exhibits robust performance under practical scenarios and outperforms several alternatives.