Selective Fair Scheduling over Fading Channels

Imposing fairness in resource allocation incurs a loss of system throughput, known as the Price of Fairness ($PoF$). In wireless scheduling, $PoF$ increases when serving users with very poor channel quality because the scheduler wastes resources trying to be fair. This paper proposes a novel resource allocation framework to rigorously address this issue. We introduce selective fairness: being fair only to selected users, and improving $PoF$ by momentarily blocking the rest. We study the associated admission control problem of finding the user selection that minimizes $PoF$ subject to selective fairness, and show that this combinatorial problem can be solved efficiently if the feasibility set satisfies a condition; in our model it suffices that the wireless channels are stochastically dominated. Exploiting selective fairness, we design a stochastic framework where we minimize $PoF$ subject to an SLA, which ensures that an ergodic subscriber is served frequently enough. In this context, we propose an online policy that combines the drift-plus-penalty technique with Gradient-Based Scheduling experts, and we prove it achieves the optimal $PoF$. Simulations show that our intelligent blocking outperforms by 40$\%$ in throughput previous approaches which satisfy the SLA by blocking low-SNR users

Non-Equilibrium Phonon Transport Across Nanoscale Interfaces

Despite the ubiquity of applications of heat transport across nanoscale interfaces, including integrated circuits, thermoelectrics, and nanotheranostics, an accurate description of phonon transport in these systems remains elusive. Here we present a theoretical and computational framework to describe phonon transport with position, momentum and scattering event resolution. We apply this framework to a single material spherical nanoparticle for which the multidimensional resolution offers insight into the physical origin of phonon thermalization, and length-scale dependent anisotropy of steady-state phonon distributions. We extend the formalism to handle interfaces explicitly and investigate the specific case of semi-coherent materials interfaces by computing the coupling between phonons and interfacial strain resulting from aperiodic array of misfit dislocations. Our framework quantitatively describes the thermal interface resistance within the technologically relevant Si-Ge heterostructures. In future, this formalism could provide new insight into coherent and driven phonon effects in nanoscale materials increasingly accessible via ultrafast, THz and near-field spectroscopies.Comment: 6 pages, 3 figure