  We consider a hierarchical edge-cloud architecture in which services are
provided to mobile users as chains of virtual network functions. Each service
has specific computation requirements and target delay performance, which
require placing the corresponding chain properly and allocating a suitable
amount of computing resources. Furthermore, chain migration may be necessary to
meet the services' target delay, or convenient to keep the service provisioning
cost low. We tackle such issues by formalizing the problem of optimal chain
placement and resource allocation in the edge-cloud continuum, taking into
account migration, bandwidth, and computation costs. Specifically, we first
envision an algorithm that, leveraging resource augmentation, addresses the
above problem and provides an upper bound to the amount of resources required
to find a feasible solution. We use this algorithm as a building block to
devise an efficient approach targeting the minimum-cost solution, while
minimizing the required resource augmentation. Our results, obtained through
trace-driven, large-scale simulations, show that our solution can provide a
feasible solution by using half the amount of resources required by
state-of-the-art alternatives.
