Quantitative Placement of Services in Hierarchical Clouds.

In this paper, we consider a hierarchical cloud topology and address the problem of optimally placing a group of logical entities according to some policy constraining the allocation of the members of the group at the various levels of the hierarchy. We introduce a simple group hierarchical placement policy, parametrized by lower and upper bounds, that is generic enough to include several existing policies such as collocation and anti-collocation, among others, as special cases. We present an efficient placement algorithm for this group hierarchical placement policy and demonstrate a six-fold speed improvement over existing algorithms. In some cases, there exists a degree of freedom which we exploit to quantitatively obtain a placement solution, given the amount of group spreading preferred by the user. We demonstrate the quality and scalability of the algorithm using numerical examples.