  This paper addresses the slicing of Radio Access Network (RAN) resources by
multiple tenants, e.g., virtual wireless operators and service providers. We
consider a criterion for dynamic resource allocation amongst tenants, based on
a weighted proportionally fair objective, which achieves desirable
fairness/protection across the network slices of the different tenants and
their associated users. Several key properties are established, including: the
Pareto optimality of user association to base stations, the fair allocation of
base stations resources, and the gains resulting from dynamic resource sharing
across slices, both in terms of utility gains and capacity savings. We then
address algorithmic and practical challenges in realizing the proposed
criterion. We show that the objective is NP-hard, making an exact solution
impractical, and design a distributed semi-online algorithm which meets
performance guarantees in equilibrium and can be shown to quickly converge to a
region around the equilibrium point. Building on this algorithm, we devise a
practical approach with limited computational, information, and handoff
overheads. We use detailed simulations to show that our approach is indeed
near-optimal and provides substantial gains both to tenants (in terms of
capacity savings) and end-users (in terms of improved performance).
