Virtual machines are allocated on demand in virtualized cloud platforms to provide flexible and reliable services. The major difficulty lies in satisfying the conflicting objectives of reducing response time while lowering resource costs. In this paper, a mathematical multi-tier framework for virtual machine allocation is proposed, which can be used to capture the performance of the cloud platform. We first use simulations to derive virtual resource allocation policies, and later use real benchmarking applications to verify the effectiveness of this framework. Experimental results show that the model can be simply and effectively used to satisfy the response time requirement as well as lowering the cost of using the virtual machine resources. © 2011 IEEE.