Delay-Optimal Scheduling for Integrated mmWave Sub-6 GHz Systems with Markovian Blockage Model

Abstract

Millimeter wave (mmWave) communication has the potential to achieve very high data rates but is highly vulnerable to blockage. In this paper, we provision an integrated mmWavesub-6 GHz architecture to combat blockage and intermittent connectivity of the mmWave communications. To this end, we model the mmWave channel as a two-state Markov channel and investigate the problem of scheduling packets across the mmWave and sub-6 GHz interfaces such that the long-term average delay of system is minimized. We prove that the optimal policy is of a threshold-type with state-dependent thresholds, i.e., packets should always be routed to the mmWave interface as long as the number of packets in the system is smaller than the state-dependent threshold. Numerical results demonstrate that under heavy traffic, integrating sub-6 GHz with mmWave can reduce the average delay by over 70%. Moreover, considering the difficulty of tracking the mmWave channel state in practice, we develop heuristics of substituting a single fixed threshold (state-independent) for two state-dependent thresholds. Our simulation results indicate that the replacement only incurs a slight increase in average delay. Moreover, when system parameters are not known, we propose a certainty-equivalence threshold-based learning algorithm, and provide an upper bound on its regret.