Cost estimation of a fixed network deployment over an urban territory

Abstract

This paper presents a methodology for fast and reliable cost estimation of fixed access network deployment on any urban area. It is based on theoretical results presented in former papers for distances and attenuation results, adding the most important part of cost estimation. In particular it is showed that good estimations can be obtained in a very short time. The territory to be deployed, the network architecture and the scenarios are defined by the user via two user-friendly prototypes. The first one helps defining the limit of the city and computes mathematical parameters representing its street system. The second one computes global information on the network deployment on this territory, namely the probability distributions of distances and attenuation from a node of the network to the final customer, and an evaluation of the deployment cost, once given an architecture and engineering rules. The results were compared on two real French urban territories (in Tours and Rouen) to those given by an optimization tool currently used by Orange.

Appendix: Retreiving model parameters from reality

A two levels network with a number N _H of high nodes HL and N _L of low nodes LL is to be deployed on a territory T of area A (km ²). Let us assume that the fitting process identified a PVT model of intensity γ (km⁻²) for the streets and recall that the corresponding morphological vector is

$$\mathcal{M}_{theo}^{PVT}(\gamma)=(2 \gamma,3 \gamma,\gamma,\tau= 2 \sqrt{\gamma}),$$

where τ (km⁻¹) is the average length of streets par unit area.

The averaged area of a HL serving zone is then A/N _H since everything is assumed homogeneous. It contains a mean length of streets L _s = τ A/N _H (km) and is assimilated to the area of the typical “Poisson-Cox-Voronoï” cell centred on HL. This typical cell also contains by construction a unique HL thus giving λ _{H L} = 1/L _s (km⁻¹) for the linear intensity of the random process that models HL locations on the streets. A key parameter is the dimensionless ratio κ = τ/λ _{H L} = 4γ A/N _H . A high (resp. low) value of κ describes a typical cell with a dense (resp. sparse) street system.

Using scaling arguments, Palm theory and statistical analysis of extensive simulation data, it is shown that for κ ≥ 1 the probability distribution of length ℓ (km) writes:

$$dis_{LH}^{PVT} (\gamma,\lambda_{HL},\ell)=\tau W_{t}(a(\kappa), b(\kappa),c(\kappa),\tau\ell) $$

where a, b, c are known polynomial functions and W _t is the truncated Weibull probability distribution

$$W_{t}(a,b,c,x)=\frac{a}{b} C^{a} (\frac{x}{b}+C)^{a-1} e^{(\frac{x}{b}+C)^{a}}$$

with C = (b c/a)^1/(a− 1). Explicit formulas exist for the cumulative function, quantile and average of W _t distribution. Theoretical considerations provide formulas for κ < 1. Similar expressions hold for the others PLT and PDT models, using the associated expression for τ.