Quantitative static analysis of communication protocols using abstract Markov Chains

Abstract

In this paper we present a static analysis of communication protocols for inferring parametric bounds of performance metrics. Our analysis is formalized within the theory of abstract interpretation and soundly takes all possible executions into account. We model the concrete executions as Markov chains and we introduce a novel notion of Abstract Markov Chains that provides a finite and symbolic representation to over-approximate the (possibly unbounded) set of concrete behaviors. Our analysis operates in two steps. The first step is a classic abstract interpretation of the source code, using stock numerical abstract domains and a specific automata domain, in order to extract the abstract Markov chain of the program. The second step extracts from this chain particular invariants about the stationary distribution and computes its symbolic bounds using a parametric Fourier-Motzkin elimination algorithm. We present a prototype implementation of the analysis and we discuss some preliminary experiments on a number of communication protocols.