However, despite being crisp, the data available when considering the evaluation criteria of the different alternatives constitute a discrete approximation performed on a spatial grid of potential locations.
An analysis using the PDE model shows that a low-dimensional approximation performed by standard spatial discretization results in a spillover effect, which makes the behavior of the closed-loop system oscillatory.
In (c), the FMCI approximation performs very well throughout most of the support.
The large deviation approximation performs well in the right tail in all cases.
The FMCI approximation performs very well for the parameters tested here.
We give several numerical examples to verify that the frozen Gaussian approximation performs well in the presence of caustics and when the Gaussian beam spreads.
Both theoretical and numerical results show that, in the relative sense, the finite Markov chain imbedding approximation performs the best in the left tail and the large deviation approximation performs best in the right tail.
Lastly, since FDW provides great improvements on clean data, the approximation performed seems not to be robust to noise.
This is presented in Table 10 for traffic approximation performed using 24 discrete time periods in 1 day.
Theorem 3 (ii) implies that asymptotically (for fixed x and n→∞), the Poisson approximation performs poorly (in the relative sense) regardless of the value μ n used.
