Cloud computing technology has been a game changer in recent years. Cloud computing providers promise cost-effective and on-demand resource computing for their users. Cloud computing providers are running the workloads of users as virtual machines (VMs) in a large-scale data center consisting a few thousands physical servers. Cloud data centers face highly dynamic workloads varying over time and many short tasks that demand quick resource management decisions. These data centers are large scale and the behavior of workload is unpredictable. The incoming VM must be assigned onto the proper physical machine (PM) in order to keep a balance between power consumption and quality of service. The scale and agility of cloud computing data centers are unprecedented so the previous approaches are fruitless. We suggest an analytical model for cloud computing data centers when the number of PMs in the data center is large. In particular, we focus on the assignment of VM onto PMs regardless of their current load. For exponential VM arrival with general distribution sojourn time, the mean power consumption is calculated. Then, we show the minimum power consumption under quality of service constraint will be achieved with randomize assignment of incoming VMs onto PMs. Extensive simulation supports the validity of our analytical model.