Speculative execution is one of the key issues to boost the performance of future generation microprocessors. In this paper, we introduce a novel approach to evaluate the effects of branch and value prediction, which allow the processor to execute instructions beyond the limits of control and true data dependences. Until now, almost all the estimations of their performance potential under different scenarios have been obtained using trace-driven or execution-driven simulation. Occasionally, some simple deterministic models have been used. We employ an analytical model based on recently introduced Fluid Stochastic Petri Nets (FSPNs) in order to capture the dynamic behavior of an ILP processor with aggressive use of prediction techniques and speculative execution. Here we define the FSPN model, derive the state equations for the underlying stochastic process and present performance evaluation results to illustrate its usage in deriving measures of interest. Our implementation-independent stochastic modeling framework reveals considerable potential for further research in this area using numerical solution of systems of partial differential equations and/or discrete-event simulation of FSPN models.