The next generation of mobile networks, namely SG, together with the Internet of Things (IoT) come with a large number of delay sensitive services. To meet their requirements, 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 needs for the stringent requirements. Thus, it becomes of a high importance to address the problem of mapping services demands to infrastructure resources supply. This work addresses it taking into account the randomness of resource availability in a fog infrastructure. We introduce an integer optimization formulation to minimize the total cost under a guarantee of service execution despite the uncertainty of resources availability. Our results illustrate the effect of various system parameters, such as the diversity of the infrastructure server set, the availability of different infrastructure servers in the set, and the probability of service completion required by each service.