Spatio-Temporal Analysis of Meta Distribution for Cell-Center/Cell-Edge Users

Emergence of various types of wireless applications has brought about fast growing and diversified traffic in cellular networks. To gain a comprehensive understanding of the influences caused by the differentiated and dynamic traffic is vital for the design of the next-generation wireless networks. In this paper, we develop a mathematical framework for meta-distribution analysis by utilizing queueing theory and stochastic geometry to capture the spatial (geographical location) and temporal randomness (queue status) of traffic. We derive the k-th moment of the conditional successful transmission probability (STP) and the closed-form expressions of the meta distribution for the cell-center users (CCUs) and the cell-edge users (CEUs), respectively. The results are further extended to obtain the analytical expression of the meta distribution by taking the temporal random arrival of traffic into consideration. Moreover, the mean local delays for the CCUs and CEUs are derived. Finally, the impact of key network parameters on the meta distribution and the corresponding mean local delay is investigated.