A generic queueing network model of a Web services environment is introduced. The behavior of a service is abstracted in three phases: serial, parallel and dormant, thus yielding a Serial Parallel Queueing Network (SPQN) model with a small number of parameters. A method is provided for estimated the parameters of the model that is based on stochastic approximation techniques for solving stochastic optimization problems. The parameter estimation method is shown to perform well in a noisy environment, where performance data is obtained through measurements or using approximate model simulations.