  By acquiring cloud-like capacities at the edge of a network, edge computing
is expected to significantly improve user experience. In this paper, we
formulate a hybrid edge-cloud computing system where an edge device with
limited local resources can rent more from a cloud node and perform resource
allocation to serve its users. The resource procurement and allocation
decisions depend not only on the cloud's multiple rental options but also on
the edge's local processing cost and capacity. We first propose an offline
algorithm whose decisions are made with full information of future demand.
Then, an online algorithm is proposed where the edge node makes irrevocable
decisions in each timeslot without future information of demand. We show that
both algorithms have constant performance bounds from the offline optimum.
Numerical results acquired with Google cluster-usage traces indicate that the
cost of the edge node can be substantially reduced by using the proposed
algorithms, up to $80\%$ in comparison with baseline algorithms. We also
observe how the cloud's pricing structure and edge's local cost influence the
procurement decisions.
