Online Job Scheduling with Resource Packing on a Cluster of Heterogeneous Servers

Jobs in modern computing clusters have highly diverse processing durations and heterogeneous resource requirements. In this paper, we consider the problem of online job scheduling for a computing cluster comprised of multiple servers with heterogeneous computation resources, while taking the diversity of resource demands for different 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 notion of fractional job flowtime as a surrogate objective for minimization. We apply Online Convex optimization (OCO) techniques to design the corresponding online scheduling algorithm. More importantly, 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 of our online convex optimization formulation with the corresponding switching costs.