In this paper, we model the infrastructure of cloud computing systems to evaluate the power consumption and performance measures using stochastic activity networks (SANs). In the proposed model, servers run different numbers of virtual machines (VMs) and tasks are divided into two categories, namely low and high, demonstrating their priorities to run. Furthermore, both servers and VMs can fail during their operation. We consider the shutting down and the dynamic voltage and frequency scaling (DVFS) techniques for decreasing the power consumption in the proposed model. These techniques can also affect the performance of cloud systems. By evaluating the results obtained from the proposed SAN model in different scenarios, we conclude that the scenario in which servers run different numbers of VMs compared to scenarios at which servers run the same number of VMs is optimal in terms of both power and performance measures. Furthermore, the obtained results represent that failures do not much affect the power consumption, but the failure of servers, in comparison with the failure of VMs, has a great impact on the performance of the system under study. We also cross-validate the results obtained from the proposed analytical model, by applying the Mobius modeling tool, with the simulation results gained from the CloudSim framework.