Résumé : Fair resource allocation is usually studied in a static context, in which a fixed amount of resources is to be shared. In dynamic resource allocation one usually tries to assign resources instantaneously so that the average share of each user is split fairly. The exact definition of the average share may depend on the application, as different applications may require averaging over different time periods or time scales. In this paper we address the question of defining and computing resource allocation in such situations. We examine how the constraints on the averaging durations impact the amount that each user gets.