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We consider a natural scheduling problem which arises in many distributed computing frameworks. Jobs with diverse resource requirements (e.g. memory requirements) arrive over time and must be served by a cluster of servers, each with a finite resource capacity. To improve throughput and delay, the scheduler can pack as many jobs as possible in the servers subject to their capacity constraints. Motivated by the ever-increasing complexity of workloads in shared clusters, we consider a setting where the jobs' resource requirements belong to a very large number of diverse types or, in the extreme, even infinitely many types, e.g. when resource requirements are drawn from an unknown distribution over a continuous support. The application of classical scheduling approaches that crucially rely on a predefined finite set of types is discouraging in this high (or infinite) dimensional setting. We first characterize a fundamental limit on the maximum throughput in such setting, and then develop oblivious scheduling algorithms that have low complexity and can achieve at least 1/2 and 2/3 of the maximum throughput, without the knowledge of traffic or resource requirement distribution. Extensive simulation results, using both synthetic and real traffic traces, are presented to verify the performance of our algorithms.

We study the problem of scheduling VMs (Virtual Machines) in a distributed server platform, motivated by cloud computing applications. The VMs arrive dynamically over time to the system, and require a certain amount of resources (e.g. memory, CPU, etc) for the duration of their service. To avoid costly preemptions, we consider non-preemptive scheduling: Each VM has to be assigned to a server which has enough residual capacity to accommodate it, and once a VM is assigned to a server, its service \textit{cannot} be disrupted (preempted). Prior approaches to this problem either have high complexity, require synchronization among the servers, or yield queue sizes/delays which are excessively large. We propose a non-preemptive scheduling algorithm that resolves these issues. In general, given an approximation algorithm to Knapsack with approximation ratio $r$, our scheduling algorithm can provide $r\beta$ fraction of the throughput region for $\beta < r$. In the special case of a greedy approximation algorithm to Knapsack, we further show that this condition can be relaxed to $\beta<1$. The parameters $\beta$ and $r$ can be tuned to provide a tradeoff between achievable throughput, delay, and computational complexity of the scheduling algorithm. Finally extensive simulation results using both synthetic and real traffic traces are presented to verify the performance of our algorithm., Comment: 29 pages