  The next generation of mobile networks, namely 5G, and the Internet of Things
(IoT) have brought a large number of delay sensitive services. In this context
Cloud services are migrating to the edge of the networks to reduce latency. The
notion of Fog computing, where the edge plays an active role in the execution
of services, comes to meet the need for the stringent requirements. Thus, it
becomes of a high importance to elegantly formulate and optimize this problem
of mapping demand to supply. This work does exactly that, taking into account
two key aspects of a service allocation problem in the Fog, namely modeling
cost of executing a given set of services, and the randomness of resources
availability, which may come from pre-existing load or server mobility. We
introduce an integer optimization formulation to minimize the total cost under
a guarantee of service execution despite the uncertainty of resources
availability.
