How the Path-Loss with Log-Normal Shadowing Impacts the Quality of Service in Cellular Networks: Why Blocking Probability is Not Always Increasing in the Shadowing Variance - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2011

How the Path-Loss with Log-Normal Shadowing Impacts the Quality of Service in Cellular Networks: Why Blocking Probability is Not Always Increasing in the Shadowing Variance

Résumé

Using a spatial version of the Erlang's loss formula and the Kaufman-Roberts algorithm we show how the blocking probability of a constant bit-rate traffic depends on the variance of the log-normal shadowing and on the path-loss exponent in regular, hexagonal networks. Both functions exhibit a lack of monotonicity. In order to explain these observations, we study the mean path-loss with respect to the serving base station (BS) and the mean interference factor, defined as the ratio of the sum of the path-gains form interfering BS to the path-gain from the serving BS. We also compare them to those obtained for irregular (Poisson) networks. We observe, as commonly expected, that a strong variance of the shadowing increases the mean path-loss with respect to the serving BS, which in consequence increases the blocking probability. However, we also obtain a more surprising result saying that in some cases an increase of the variance of the shadowing can significantly reduce the mean interference factor and, in consequence, also the blocking probability. We confirm our findings by a mathematical analysis of the respective models. We also obtain fully explicit, analytical results for the mean path-loss and interference factors in the case of the infinite Poisson network with an arbitrary distribution of the shadowing.
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Dates et versions

inria-00562462 , version 1 (03-02-2011)
inria-00562462 , version 2 (03-10-2011)
inria-00562462 , version 3 (18-06-2012)
inria-00562462 , version 4 (02-04-2013)

Identifiants

  • HAL Id : inria-00562462 , version 1

Citer

Bartlomiej Blaszczyszyn, Mohamed Kadhem Karray. How the Path-Loss with Log-Normal Shadowing Impacts the Quality of Service in Cellular Networks: Why Blocking Probability is Not Always Increasing in the Shadowing Variance. 2011. ⟨inria-00562462v1⟩
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