Computation Offloading Analysis in Clustered Fog Radio Access Networks with Repulsion

In this work, we leverage the clustered $\beta$ -Ginibre point process (GPP) and the queueing theory to analyse the delay performance in a large-scale repulsive fog radio access network (F-RAN) with computation offloading, which plays a key role on the delay performance. In particular, the average delay defined as the mean value of delay for executing the computing tasks and the task completion probability (TCP) defined as the probability of the delay for executing the computing task being smaller than a target delay, are derived in analytical forms and validated by Monte Carlo simulations. Based on these results, the optimal rate threshold, which affects the task offloading probability and the transmission delay, and the optimal cloud offloading probability to minimize the average delay and maximize the TCP are jointly analysed numerically. Moreover, an approximated result of the average delay is provided to reduce its computational complexity. The results show that the repulsion in the F-RAN significantly decreases the average delay and increases the TCP, but equipped with the optimal rate threshold and the cloud offloading probability, the effects of repulsion on the average delay and the TCP become trivial. Furthermore, with the optimal cloud offloading probability and rate threshold, the average delay and the TCP can be significantly reduced and improved in the hybrid processing mode compared with those in the local processing mode, respectively. The optimal rate thresholds lie in the range of 3 to 13 Mbps under our simulation environment, which can reduce a maximum of 60% of the average delay and increase a minimum of 0.17 of the TCP.