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