This paper presents a syntax-directed non-uniform static analysis of the stochastic π-calculus to safely approximate the amount of time required before name substitutions occur in a process. Name substitutions form the basis for defining security properties, like information leakage. The presence of the quantitative and qualitative information in the results of the analysis allows us to reason about the speed at which sensitive information is leaked in a computing environment with malicious mobile code. We demonstrate the applicability of the analysis through a simple example of firewall breaches.