Characteristics of rainfall queues for rain attenuation studies over radio links at subtropical and equatorial Africa

Attenuation due to precipitation remains an important design factor in the future deployment of terrestrial and earth-space communication radio links. Largely, there are concerted efforts to understand the dynamics of precipitation in attenuation occurrence at subtropical, tropical, and equatorial region of Africa. In this deliberate approach, rainfall spikes pertaining to rain cells are conceptualized as distinct rain spike traffic over radio links, by applying queueing theory concepts. The queue distributions at Durban (29°52'S, 30°58'E) and Butare (2°36'S, 29°44'E)-respectively, of subtropical and equatorial climates-are investigated from distrometer measurements. The data sets at both sites are observed over four rain regimes: drizzle, widespread, shower, and thunderstorm. The queue parameters of service time and inter-arrival of rain spikes traffic at both regions are found to be Erlang-k distributed (Ek) and exponentially distributed (M), respectively. It is established that the appearance of rain rates over radio links invariably follows a First Come, First Served (FCFS), multi-server (s), infinite queue, and semi-Markovian process, designated as M/Ek/s/∞/FCFS discipline. Modeled queue parameters at both regions are found to vary significantly over different regimes. However, these queue parameters over the entire data set suggest similar queue patterns at both sites. More importantly, power law relationships describing other queue-related parameters are formulated. The paper concludes by demonstrating an application of queueing theory for rainfall synthesis. The proposed technique will provide an alternative method of estimating rain cell sizes and rain attenuation over satellite and terrestrial links.