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Cloud computing is emerging as an important platform for business, personaland mobile computing applications. In this paper, we study a stochastic modelof cloud computing, where jobs arrive according to a stochastic process andrequest resources like CPU, memory and storage space. We consider a model wherethe resource allocation problem can be separated into a routing or loadbalancing problem and a scheduling problem. We study thejoin-the-shortest-queue routing and power-of-two-choices routing algorithmswith MaxWeight scheduling algorithm. It was known that these algorithms arethroughput optimal. In this paper, we show that these algorithms are queuelength optimal in the heavy traffic limit.

Heavy Traffic Optimal Resource Allocation Algorithms for Cloud Computing Clusters