I shall talk about two systems: (i) file swarming and (ii) mobile users. In the first part, the context is that of p2p file dissemination that follows file swarming paradigm, where a file is sliced into pieces and these are replicated by users. An example file swarming system is widely-used BitTorrent. The obtained results are a first study based on analysis that elucidates issues such as performance criticality of the replication strategy and of user altruism in offering pieces for free. The second part introduces random trip, a generic class of mobility models that includes mobility models used by many in performance evaluation of mobile (ad-hoc) networks. The results include a proof of existence and uniqueness of a time-stationary distribution and a new perfect simulation algorithm that enables running stationary simulations of mobility, which are free of initial transient. As time would permit, the talk will close with a few recent results obtained in other projects.