Fractal analysis of rainfall event duration for microwave and millimetre networks: Rain queueing theory approach

Rain fade in radio networks is generated from random fluctuations of rainfall rates, within rain events of spatiotemporal dimensions. These events can be represented as a catenation of single rain spikes occurring as a possible three-stage process - birth, overlap and death. Using the queueing theory approach, the birth-death characteristics of single spikes are investigated as inter-arrival and service time distributions. A total of 548 spike samples from rainfall events in Durban (29°52'S, 30° 58'E), South Africa are examined based on distrometer measurements. Rainfall regime analysis of drizzle, widespread, shower and thunderstorm bounds is applied to determine the queue pattern. It is found that the queue patterns in Durban exhibit an Erlang-k distribution (E_k) for both the service and overlap times, while exponential distribution (M) is suitable for inter-arrival time. The mean error statistics for the regimes give root-mean-square errors of 0.64, 1.3 and 2.02% for the service, inter-arrival and overlap distribution, respectively, with acceptable Chi-Squared (X²) statistics. The M/E_k/s/∞ steadystate analysis is later undertaken to investigate the performance of the proposed queue system. Based on the overall data, a power-law relationship is found to exist between the service time and peak rain rate per spike.