SINR Meta Distribution for mmWave Heterogeneous Networks Under Varying Queue Status: A Spatio-Temporal Analysis

A fine-grained analysis of network performance is crucial for system design. In this paper, we focus on the meta distribution of the signal-to-interference-plus-noise-ratio (SINR) in the mmWave heterogeneous networks where the base stations (BS) in each tier are modeled as a Poisson point process (PPP). By utilizing stochastic geometry and queueing theory, we characterize the spatial and temporal randomness while the special characteristics of mmWave communications, including different path loss laws for line-of-sight and non-line-of-sight links and directional beamforming, are incorporated into the analysis. We derive the moments of the conditional successful transmission probability (STP). By taking the temporal random arrival of traffic into consideration, an equation on the meta distribution is formulated and its solution is obtained in a recursive manner. The critical arrival rate for a fraction of the queues at the BSs to be stable is provided. In addition, the mean delay is obtained. The numerical results reveal the impact of the key network parameters, such as the blockage parameter, the bias factor, the number of antenna elements and the BS density, on the network performance. Specifically, offloading the users from the macro BS tier to the small BS tier by biasing can reduce the performance fluctuation while only causing a slight degradation of the overall network performance.