  We study the fairness of dynamic resource allocation problem under the
$\alpha$-fairness criterion. We recognize two different fairness objectives
that naturally arise in this problem: the well-understood slot-fairness
objective that aims to ensure fairness at every timeslot, and the less explored
horizon-fairness objective that aims to ensure fairness across utilities
accumulated over a time horizon. We argue that horizon-fairness comes at a
lower price in terms of social welfare. We study horizon-fairness with the
regret as a performance metric and show that vanishing regret cannot be
achieved in presence of an unrestricted adversary. We propose restrictions on
the adversary's capabilities corresponding to realistic scenarios and an online
policy that indeed guarantees vanishing regret under these restrictions. We
demonstrate the applicability of the proposed fairness framework to a
representative resource management problem considering a virtualized caching
system where different caches cooperate to serve content requests.
