  This paper proposes an analytic model for dimensioning OFDMA based networks
like WiMAX and LTE systems. In such a system, users require a number of
subchannels which depends on their \SNR, hence of their position and the
shadowing they experience. The system is overloaded when the number of required
subchannels is greater than the number of available subchannels. We give an
exact though not closed expression of the loss probability and then give an
algorithmic method to derive the number of subchannels which guarantees a loss
probability less than a given threshold. We show that Gaussian approximation
lead to optimistic values and are thus unusable. We then introduce Edgeworth
expansions with error bounds and show that by choosing the right order of the
expansion, one can have an approximate dimensioning value easy to compute but
with guaranteed performance. As the values obtained are highly dependent from
the parameters of the system, which turned to be rather undetermined, we
provide a procedure based on concentration inequality for Poisson functionals,
which yields to conservative dimensioning. This paper relies on recent results
on concentration inequalities and establish new results on Edgeworth
expansions.
