In this paper, we propose M/G/c/c+r queuing system as a model for performance evaluation of cloud server farms. Analytical resolution of this queuing system remains, to this day, an open and challenging issue because an exact analytical solution is difficult to reach. Therefore, we provide new approximate formulas to compute the transition-probability matrix of this system. In order to examine the accuracy of our approximate formulas, we test them numerically on some examples. Then, we compute the steady-state probabilities and some performance indicators such as blocking probability, mean response time, probability of immediate service and delay probability. Cloud Computing, Performance Analysis, M/G/c/c + r Queue, Embedded Markov Chain, Transition-probability Matrix.