  Although public clouds still occupy the largest portion of the total cloud
infrastructure, private clouds are attracting increasing interest from both
industry and academia because of their better security and privacy control.
According to the existing studies, the high upfront cost is among the most
critical challenges associated with private clouds. To reduce cost and improve
performance, virtual machine placement (VMP) methods have been extensively
investigated, however, few of these methods have focused on private clouds.
This paper proposes a heterogeneous and multidimensional clairvoyant dynamic
bin packing (CDBP) model, in which the scheduler can conduct more efficient VMP
processes using additional information on the arrival time and duration of
virtual machines to reduce the datacenter scale and thereby decrease the
upfront cost of private clouds. In addition, a novel branch-and-bound algorithm
with a divide-and-conquer strategy (DCBB) is proposed to effectively and
efficiently handle the derived problem. One state-of-the-art and several
classic VMP methods are also modified to adapt to the proposed model to observe
their performance and compare with our proposed algorithm. Extensive
experiments are conducted on both real-world and synthetic workloads to
evaluate the accuracy and efficiency of the algorithms. The experimental
results demonstrate that DCBB delivers near-optimal solutions with a
convergence rate that is much faster than those of the other search-based
algorithms evaluated. In particular, DCBB yields the optimal solution for a
real-world workload with an execution time that is an order of magnitude
shorter than that required by the original branch-and-bound (BB) algorithm.
