  In order to meet the performance/privacy requirements of future
data-intensive mobile applications, e.g., self-driving cars, mobile data
analytics, and AR/VR, service providers are expected to draw on shared
storage/computation/connectivity resources at the network "edge". To be
cost-effective, a key functional requirement for such infrastructure is
enabling the sharing of heterogeneous resources amongst tenants/service
providers supporting spatially varying and dynamic user demands. This paper
proposes a resource allocation criterion, namely, Share Constrained Slicing
(SCS), for slices allocated predefined shares of the network's resources, which
extends the traditional alpha-fairness criterion, by striking a balance among
inter- and intra-slice fairness vs. overall efficiency. We show that SCS has
several desirable properties including slice-level protection, envyfreeness,
and load driven elasticity. In practice, mobile users' dynamics could make the
cost of implementing SCS high, so we discuss the feasibility of using a simpler
(dynamically) weighted max-min as a surrogate resource allocation scheme. For a
setting with stochastic loads and elastic user requirements, we establish a
sufficient condition for the stability of the associated coupled network
system. Finally, and perhaps surprisingly, we show via extensive simulations
that while SCS (and/or the surrogate weighted max-min allocation) provides
inter-slice protection, they can achieve improved job delay and/or perceived
throughput, as compared to other weighted max-min based allocation schemes
whose intra-slice weight allocation is not share-constrained, e.g., traditional
max-min or discriminatory processor sharing.
