Equational Reasonings in Wireless Network Gossip Protocols

Gossip protocols have been proposed as a robust and efficient method for disseminating information throughout large-scale networks. In this paper, we propose a compositional analysis technique to study formal probabilistic models of gossip protocols expressed in a simple probabilistic timed process calculus for wireless sensor networks. We equip the calculus with a simulation theory to compare probabilistic protocols that have similar behaviour up to a certain tolerance. The theory is used to prove a number of algebraic laws which revealed to be very effective to estimate the performances of gossip networks, with and without communication collisions, and randomised gossip networks. Our simulation theory is an asymmetric variant of the weak bisimulation metric that maintains most of the properties of the original definition. However, our asymmetric version is particularly suitable to reason on protocols in which the systems under consideration are not approximately equivalent, as in the case of gossip protocols

Weak simulation quasimetric in a gossip scenario

We propose the notion of weak simulation quasimetric as the quantitative counterpart of weak simulation for probabilistic processes. This is an asymmetric variant of the weak bisimulation metric of Desharnais et al. which maintains most of the properties of the original definition. However, our asymmetric version is particularly suitable to reason on protocols where the systems under consideration are not approximately equivalent. As a main application, we adopt our simulation theory in a simple probabilistic timed process calculus to derive an algebraic theory to evaluate the performances of gossip protocols

Probabilistic Semantics: Metric and Logical Character¨ations for Nondeterministic Probabilistic Processes

In this thesis we focus on processes with nondeterminism and probability in the PTS model, and we propose novel techniques to study their semantics, in terms of both classic behavioral relations and the more recent behavioral metrics. Firstly, we propose a method for decomposing modal formulae in a probabilistic extension of the Hennessy-Milner logic. This decomposition method allows us to derive the compositional properties of probabilistic (bi)simulations. Then, we propose original notions of metrics measuring the disparities in the behavior of processes with respect to (decorated) trace and testing semantics. To capture the differences in the expressive power of the metrics we order them by the relation `makes processes further than'. Thus, we obtain the first spectrum of behavioral metrics on the PTS model. From this spectrum we derive an analogous one for the kernels of the metrics, ordered by the relation `makes strictly less identification than'. Finally, we introduce a novel technique for the logical characterization of both behavioral metrics and their kernels, based on the notions of mimicking formula and distance on formulae. This kind of characterization allows us to obtain the first example of a spectrum of distances on processes obtained directly from logics. Moreover, we show that the kernels of the metrics can be characterized by simply comparing the mimicking formulae of processes