This problem is solved today by periodically forecasting a traffic matrix and (re designing the network to support the forecasted matrix.
The background (forecast) covariance matrix P b n is no longer a simple matrix product and must be approximated by other means, as described in Sec.
In addition, the models that we are considering are nonlinear, which implies that the background (forecast) covariance matrix P b n cannot be computed as a simple matrix product.
2.2, to find a low-rank approximation of the forecast covariance matrix P b n.
A second approach is the unscented Kalman filter, in which so-called "sigma points" are chosen about the ensemble mean and integrated with the model to estimate the forecast covariance matrix [ 20].
These filters use a limited-size ensemble representation of the forecast error covariance matrix.
However, a spatially-based filter localization provides a substantial moderation in the development of the forecast error covariance matrix, directly improving the forecast and also making it possible to further benefit from a simultaneous online inflow error estimation and correction.
Firstly, network costs can be globally bounded over correlated large scale variations of traffic, eliminating one of central weaknesses of classical network design (at least for planning purposes) — most traffic matrix forecasts are extremely error-prone.
This is achieved through observation of both the sensitivity matrix and forecast shifts in power and is based on (epsilon) decomposition (see [31] for an example of (epsilon) decomposition).
(2014) to generate "design-free" estimates of the general matrix of the forecast-error second-moment when there are relatively few forecast-error observations.
