We consider the problem of scheduling VMs (Virtual Machines) in a multi-server system motivated by cloud computing applications. VMs arrive dynamically over time and require various amounts of resources (e.g., CPU, Memory, Storage, etc.) for the duration of their service. When a VM arrives, it is queued and later served by one of the servers that has sufficient remaining capacity to serve it. The scheduling of VMs is subject to: (i) packing constraints, i.e., multiple VMs can be be served simultaneously by a single server if their cumulative resource requirement does not violate the capacity of the server, and (ii) non-preemption, i.e., once a VM is scheduled in a server, it cannot be interrupted or migrated to another server. To achieve maximum throughput, prior results hinge on solving a hard combinatorial problem (Knapsack) at the instances that all the servers become empty (the so-called global refresh times which require synchronization among the servers). The main contribution of this paper is that it resolves these issues. Specifically, we present a class of randomized algorithms for placing VMs in the servers that can achieve maximum throughput without preemptions. The algorithms are naturally distributed, have low complexity, and each queue needs to perform limited operations. Further, our algorithms display good delay performance in simulations, comparable to delay of heuristics that may not be throughput-optimal, and much better than the delay of the prior known throughput-optimal algorithms.
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