Analytical resolution of complex queuing systems remains nowadays an open and challenging issue and may be extensively used in modeling and representing dynamic behavior of sophisticated systems. This is particularly the case of M/G/c/c+r queue where exact analytical solution is difficult to reach. In this paper, we propose a new approximate analytical model in order to evaluate the performance of cloud computing center using M/G/c/c+r queuing system. The adopted modeling approach combines two models. The first one is a transform-based analytical model whereas the second relies on an approximate Markov chain. This combination enables to compute the one-step transition probabilities for the system M/G/c/c+r.