Heavy Traffic Limits for GI/H/n Queues: Theory and Application

We consider a GI/H/n queueing system. In this system, there are multiple servers in the queue. The inter-arrival time is general and independent, and the service time follows hyper-exponential distribution. Instead of stochastic differential equations, we propose two heavy traffic limits for this system, which can be easily applied in practical systems. In applications, we show how to use these heavy traffic limits to design a power efficient cloud computing environment based on different QoS requirements.