© The Institution of Engineering and Technology
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 (Ek ) 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 (χ 2) statistics. The M/Ek /s/∞ steady-state 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.
References
-
-
1)
-
9. Bolch, G., Greiner, S., de Meer, H., Trivedi, K.S.: ‘Queueing networks and Markov chains’ (John Wiley and Sons, New York, 1998).
-
2)
-
8. Acosta, R.J.: ‘Rain fade compensation alternatives for Ka-band communication studies’. Third Ka-Band Utilization Conf., Sorrento, Italy, September 1997, pp. 15–18.
-
3)
-
13. Rodriguez, R.I.F., Prez, G.A.C., Werner, M., Castaño, A.G., Cano, A.M.: ‘Rainfall estimation by a signal attenuation analysis in mobile systems’. XV Symp. SELPER, November 2012.
-
4)
-
1. Foty, D., Smith, B., Sinha, S., Schröter, M.: ‘The wireless bandwidth crisis and the need for power-efficient bandwidth’. IEEE AFRICON Conf., Livingstone, Zambia, September 2011, pp. 1–6.
-
5)
-
20. Alonge, A.A., Afullo, T.J.: ‘Regime analysis of rainfall drop-size distribution models for microwave terrestrial network’, IET Microw. Antennas Propag., 2012, 6, (4), pp. 393–403 (doi: 10.1049/iet-map.2011.0411).
-
6)
-
2. ITU-R P.530-14: ‘Propagation data and prediction methods for the design of terrestrial line-of-sight systems’, ITU-R Record, Geneva, 2012.
-
7)
-
15. Begum, S., Nagaraja, C., Otung, I.: ‘Analysis of rain cell size distribution for application in site diversity’. .
-
8)
-
H.E. Green
.
Propagation impairment on Ka-Band SATCOM links in tropical and equatorial regions.
IEEE Antennas Propag. Mag.
,
2 ,
31 -
44
-
9)
-
16. Wingo, D.R.: ‘Computing maximum-likelihood parameter estimates of the generalized gamma distribution by numerical root isolation’, IEEE Trans. Reliab., 1987, R-36, (5), pp. 586–590 (doi: 10.1109/TR.1987.5222478).
-
10)
-
23. Abramowitz, M., Stegun, I.A. (Eds.): ‘Handbook of mathematical functions with formulas’, graphs and mathematical tables’, (Dover, New York, 1972, 9th printing), p. 880.
-
11)
-
17. Kreyszig, E.: ‘Engineering mathematics’ (John Wiley and Sons Inc., New York, 2006, 9th edn.).
-
12)
-
10. Hillier, S.F., Lieberman, J.G.: ‘Introduction to operations research’ (McGraw-Hill, 2001, 7th edn.).
-
13)
-
18. Kotek, M., Grieser, J., Beck, C., Rudolf, B., Rubel, F.: ‘World map of the Koppen–Geiger climate classification updated’, Meteorol. Z., 2006, 15, pp. 259–263 (doi: 10.1127/0941-2948/2006/0130).
-
14)
-
22. Adimula, I.A., Ajayi, G.O.: ‘Variation in raindrop size distribution and specific attenuation due to rain in Nigeria’, Ann. Telecommun., 1996, 51, (1–2), pp. 87–93.
-
15)
-
4. Owolawi, P.: ‘Rainfall rate probability density evaluation and mapping for the estimation of rain attenuation in south africa and surrounding island’, Prog. Electromagn. Res. B, 2011, 112, pp. 155–181.
-
16)
-
3. Ajayi, G.O., Feng, S., Radicella, S.M., Reddy, B.M. (Eds.): ‘Handbook on Radiopropagation Related to Satellite Communications in Tropical and Subtropical Countries’ (ICTP, 1996), pp. 7–14.
-
17)
-
19. Afullo, T.J.O.: ‘Raindrop size distribution modeling for radio link design along the eastern coast of South Africa’, Prog. Electromagn. Res. B, 2011, 34, pp. 345–366 (doi: 10.2528/PIERB11082005).
-
18)
-
J.S. Mandeep ,
K. Tanaka
.
Effect of atmospheric parameters on satellite link.
Int. J. Infrared Millim. Waves
,
10 ,
789 -
795
-
19)
-
14. Pawlina, A.: ‘No rain intervals within rain events: some statistics based on Milano radar and rain-gauge data’. COST Action 280, First Int. Workshop, July 2002.
-
20)
-
11. Kleinrock, L.: ‘Queueing systems volume I’, theory’ (John Wiley and Sons, New York, 1975), .
-
21)
-
7. Mämmela, A., Kolteba, A.: ‘Link budgets: how much energy is really received’, Vehicular technologies: increasing connectivity, InTech2011, pp. 433–448.
-
22)
-
6. ITU-R P.838-3: ‘Specific attenuation model for rain for use in prediction methods’, ITU-R Record, Geneva, 2005.
-
23)
-
12. Gross, D., Harris, C.M.: ‘Fundamentals of queueing theory’ (John Wiley and Sons Inc., NY, 1998, 3rd edn.).
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