Edge computing technologies and integrated architectures have been deployed to accommodate Internet traffic growth. These architectures include facilities (cloudlets, micro DCs) to cache and serve contents close to consumers. Resulting systems adapt to observed request/consumption patterns by allowing cloudlet coordination for content caching/dissemination. This paper presents a novel analytical model of transient dynamics of the cloudlets set. The model is used to study system convergence, stability and delivered content locality. Results from this model are validated via simulations.