This paper develops a novel approximate analytical model to evaluate the performance of active virtual machines in IaaS clouds using an M/G/m/m+K queue. The proposed model, combined with the transform-based analytical approach, enables the computation of the probability distribution of the number of jobs in the system and subsequently a set of performance measures, including the mean number of jobs in the system, the mean response time, the probability of immediate service, and the blocking probability. Compared to the existing Markov models of cloud data centers, our approach can reflect the system behavior more accurately even when the service-time distribution has a large coefficient of variation (> 1.5) in a medium-sized IaaS cloud. Numerical results obtained from the proposed analytical model are verified through extensive simulations under various system parameter settings, and compared with the results from existing models.

The virtual network embedding (VNE) problem has been receiving significant research interest lately. A realistic scenario might entail embedding multiple VN requests (MVNE) that arrive simultaneously (batch arrivals). The existing MVNE approaches either did not consider the coordination among multiple VNR embeddings or embedded all the arriving VNRs simultaneously without considering the substrate network state. This paper considers the MVNE problem in the scenarios where the available physical resources may not be sufficient to satisfy the physical resource demands of all the VNRs in the batch. We formulate the problem as mixed integer programs, which not only provide optimal MVN embedding but also improve the network service provider's long-term revenue. Simulation results validate the revenue gains of the proposed approach over the existing exact and heuristic MVNE approaches.