A Stochastic Knapsack Model for Energy Efficient Management of Multi-Server Queues

We consider multiple bursty flows characterized by different statistical parameters and performance requirements, which generate packets that require some form of processing at the network edge. We model the processing resources as multiple servers that can be activated/deactivated on a longer time scale with respect to the packet dynamics. Packets awaiting service are queued in an infinite buffer, and the queueing model adopted is of the $M^{\mathrm{X}} / \mathrm{D} / \mathrm{C}$ type; the flow dynamics is instead represented by a birth-death model on a much longer time scale. By exploiting a time-scale decomposition, we describe possible Call Admission Control (CAC) strategies that are based on a Stochastic Knapsack model over the space of flows that satisfy packet-level delay constraints. We compare a Complete Partitioning and a Complete Sharing CAC scheme in terms of energy efficient implementation.