Rainfall time series synthesis from queue scheduling of rain event fractals over radio links

Rainfall attenuation over wireless networks stems from random fluctuations in the natural process of arriving rainfall rates over radio links. This arrival process results in discernible rainfall traffic pattern which manifests as naturally scheduled and queue-generated rain spikes. Hence, the phenomenon of rainfall process can be approached as a semi-Markovian queueing process, with event characteristics dependent on queue parameters. However, a constraint to this approach is the knowledge of the physical characteristics of queue-generated rain spikes. Therefore, this paper explores the probability theory and descriptive mathematics of rain spikes in rainfall processes. This investigation presents the synthesis of rainfall queue with rain spikes at subtropical and equatorial locations of Durban (29°52′S, 30°58′E) and Butare (2°36′S, 29°44′E), respectively. The resulting comparative analysis of rainfall distributions, using error analysis at both locations, reveals that queue-generated rainfall compares well with measured rainfall data set. This suggests that the time-varying process of rainfall, though stochastic, can be synthesized via queue scheduling with the application of relevant queue parameters at any location. Key Points Rain spikes are the smallest units of semi-Markovian rainfall queues over radio links Rainfall queues are applicable in rainfall time series synthesis by applying queue parameters Rain rate distributions from queue scheduling compare well with actual data.