Spatio-Temporal Analysis of SINR Meta Distribution for mmWave Heterogeneous Networks Under Geo/G/1 Queues

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 the meta distribution can be obtained in a recursive manner. The numerical results reveal the impact of the key network parameters, such as the SINR threshold and the blockage parameter, on the network performance.