Edge Computing Resource Allocation for Dynamic Networks: The DRUID-NET Vision and Perspective.

The potential offered by the abundance of sensors, actuators, and communications in the Internet of Things (IoT) era is hindered by the limited computational capacity of local nodes. Several key challenges should be addressed to optimally and jointly exploit the network, computing, and storage resources, guaranteeing at the same time feasibility for time-critical and mission-critical tasks. We propose the DRUID-NET framework to take upon these challenges by dynamically distributing resources when the demand is rapidly varying. It includes analytic dynamical modeling of the resources, offered workload, and networking environment, incorporating phenomena typically met in wireless communications and mobile edge computing, together with new estimators of time-varying profiles. Building on this framework, we aim to develop novel resource allocation mechanisms that explicitly include service differentiation and context-awareness, being capable of guaranteeing well-defined Quality of Service (QoS) metrics. DRUID-NET goes beyond the state of the art in the design of control algorithms by incorporating resource allocation mechanisms to the decision strategy itself. To achieve these breakthroughs, we combine tools from Automata and Graph theory, Machine Learning, Modern Control Theory, and Network Theory. DRUID-NET constitutes the first truly holistic, multidisciplinary approach that extends recent, albeit fragmented results from all aforementioned fields, thus bridging the gap between efforts of different communities.

Distance distribution in random graphs and application to network exploration.

We consider the problem of determining the proportion of edges that are discovered in an Erdos-Rényi graph when one constructs all shortest paths from a given source node to all other nodes. This problem is equivalent to the one of determining the proportion of edges connecting nodes that are at identical distance from the source node. The evolution of this quantity with the probability of existence of the edges exhibits intriguing oscillatory behavior. In order to perform our analysis, we introduce a different way of computing the distribution of distances between nodes. Our method outperforms previous similar analyses and leads to estimates that coincide remarkably well with numerical simulations. It allows us to characterize the phase transitions appearing when the connectivity probability varies.