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

Abstract

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 (E k ) 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/E k /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.

Approximate queue scheduling for rainfall synthesis over radio links in subtropical regions

“…Because of these unique extremities in the nature of typical queues, there exist certain parameters which govern the incidence of queue characteristics. In rainfall queues, these parameters in a First-Come, FirstServed (FCFS) process over Equatorial and subtropical locations, are described by Alonge and Afullo [12], [13] as service time, inter-arrival time and overlap time. The service time distribution, , of these arriving spikes is described as having several number of stages, k, thereby following an Erlangian process.…”

“…The service time distribution, , of these arriving spikes is described as having several number of stages, k, thereby following an Erlangian process. This non-Markovian distribution for rainfall service time was recently proposed by Alonge and Afullo [12] as:…”

“…From studies of Alonge and Afullo [12], [13] on this subject, steady state analysis of rainfall queues tend to therefore follow a semi-Markovian FCFS M/E k /s queue discipline over subtropical and tropical locations. The equivalent number of servers, s, which is the minimum ratio of service time to inter-arrival time, converges at 3.…”

“…Earlier researchers [9]- [11] have applied the Markov Chain (MC) approach, however, these methods have locationspecific transition matrices; making this approach seemingly incompatible elsewhere. This current work of rainfall synthesis over radio links is based on Queueing Theory Technique (QTT) proposed by Alonge and Afullo in [12], [13]. This technique applies Birth-Death (BD) process and queueing concepts from rainfall rate time series data collected over Durban between January 2009 and December 2010.…”

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

“…This is largely the consequence of the location-specific characteristics of rainfall across the world. Another approach that could be applied to grasp the underlying characteristics of time-varying rainfall is the consideration of this process as a queue-governed system [Alonge and Afullo, 2014;Alonge and Afullo, 2015]. Queueing systems are generally representative of processes where activities over a period of time possess fractal identities with self-similar behavior(s), in the counting domain [Bolch et al, 1998;Kleinrock, 1975;Hillier and Lieberman, 2001].…”