Optimal Job Scheduling With Resource Packing for Heterogeneous Servers

Abstract

Jobs in modern computing clusters have highly diverse processing duration and heterogeneous resource requirements. In this paper, we consider the problem of job scheduling for a computing cluster comprised of multiple servers with heterogeneous computation resources, while taking the different resource demands of the jobs into account. Our focus is to achieve a low overall job response time for the system (which is also referred to as the job flowtime) while providing fairness between small and large jobs. Since the job flowtime minimization problem under multiple (even homogeneous) servers are known to be NP-hard, we propose an approximation algorithm to tackle the original online scheduling problem by adopting the recently-proposed notion of fractional job flowtime as a surrogate objective for minimization. For the general online job arrival case with multi-dimensional resource requirements, we apply Online Convex Optimization (OCO) techniques to design the corresponding scheduling algorithm with performance guarantees. In the single-dimensional resource setting, we show that the dynamic fit of the online version of our approximate algorithm grows only sublinearly with respect to time and derive a bound for its dynamic regret when comparing to its offline counterpart. While the baseline version of our proposed scheduling algorithm assumes the possibilities of job preemption and job migration across different servers, we show that the extent of job preemption and migration can be well controlled by augmenting the objective function with the corresponding switching costs.