Focusing on elasticity, this paper tackles the problem of optimum allocation of elastic services on virtualized physical resources by incorporating a probabilistic approach in terms of availability guarantees. The proposed approach relies on the actual probabilities of needing extra computational requirements during runtime, which are incorporated into the admission control test, allowing for reducing the number of physical computational resources that need to be booked for elasticity reasons. The output of the optimization problem is the set of the admitted services, as well as the allocated computing capacity for each service component that comprise them on the physical hosts that have been selected in the optimal allocation pattern. The ...