On the Mean Local Delay of Clustered Fog Radio Access Networks

Abstract

Uplink transmission delay has been considered as a main component of the end-to-end delay in the fog radio access networks (F-RAN). However, existing analysis of the transmission delay ignore the packet retransmission delay, i.e., mean local delay (MLD), which is the main component of transmission delay. In addition, the MLD has not been investigated in a clustered F-RAN. Therefore, in this work, we leverage the Matern cluster process (MCP) to analyse MLD in a large-scale F-RAN. To derive the MLD, we obtain the uplink coverage probability (CP) firstly. The MLD can be derived by the moment result of the CP, which is defined as the probability of received signal-to-interference-ratio (SIR) is larger than a threshold. To obtain the moment result of the CP, the analytical result of the CP and its approximation with a lower computational complexity are derived. However, the moment result of CP is difficult to be validated via simulations. Therefore, we derive the meta distribution, which is calculated directly from the moment result of the CP, and validate its correctness by Monte Carlo simulations. Equipped with this, the analytical results of MLD in closed-form are derived. Based on these results, the effect of UE activity factor and the uplink power control (PC) factor on the MLD are analysed. The results show that the fog access points (FAP) density has no effect on the MLD.