|Fabio Cecchi||Eindhoven University of Technology, The Netherlands|
|Sem Borst||Eindhoven University of Technology, The Netherlands|
|Johan Van Leeuwaarden||Eindhoven University of Technology, The Netherlands|
|Philip Whiting||Macquarie University, Australia|
As the Internet-of-Things (IoT) emerges, connecting immense numbers of sensors and devices, the continual growth in wireless communications increasingly manifests itself in terms of a larger and denser population of nodes with intermittent traffic patterns. A crucial issue that arises in these conditions is how to set the activation rates as a function of the network density and traffic intensity. Depending on the scaling of the activation rates, dense node populations may either result in excessive activations and potential collisions, or long delays that may increase with the number of nodes, even at low load. Motivated by the above issues, we examine optimal activation rate scalings in ultra-dense networks with intermittent traffic sources. We establish stability conditions, and provide closed-form expressions which indicate that the mean delay is roughly inversely proportional to the nominal activation rate. We also discuss a multi-scale mean-field limit, and use the associated fixed point to determine the buffer content and delay distributions. The results provide insight in the scalings that minimize the delay while preventing excessive activation attempts. Extensive simulation experiments demonstrate that the mean-field asymptotics yield highly accurate approximations, even when the number of nodes is moderate.