Time series rainfall spike modelling from Markov chains and queueing theory approach for rainfall attenuation over terrestrial and earth-space radio wave propagation in Jimma, Ethiopia

Rainfall attenuation over radio wave propagation originates from the stochastic turbulence of rainfall intensity on wireless networks, especially at higher operating frequencies. Basically, three parameters characterize a stochastic process of rainfall: rainfall spike, rainfall rate regimes and the sojourn time of a rainfall spike in each rain rate regime. In this paper, the characteristics of rainfall spikes are investigated as a randomly varying in four rainfall rate states in Jimma, Ethiopia using Markov chain model and queueing theory approach. From the first model the spikes transition probability matrix among regimes is determined and found to be ergodic and, applying the second approach the sojourns time distribution of spike is modelled and the result shows Erlang-K probability distribution not the common exponential distribution for all regimes with very minimum fitting errors.