—Recent advances in virtualization technology have made it a common practice to consolidate virtual machines(VMs) into a fewer number of servers. An efficient consolidation scheme requires that VMs are packed tightly, yet receiving resources commensurate with their demands. On the other hand, measurements from production data centers show that the network bandwidth demands of VMs are dynamic, making it difficult to characterize the demands by a fixed value and to apply traditional consolidation schemes. In this work, we capture VM bandwidth demand by random variables following probabilistic distributions. We study how VMs should be consolidated with bandwidth limit imposed by network devices such as Ethernet adapters and edge switches. We formulate a Stochastic Bin Packing problem and propose an online packing algorithm by which the number of servers required is within (1+ )( √ 2+1) of the optimum for any > 0. In a special case that there are finite number of possibilities f...