  Finsler geometry is a natural and fundamental generalization of Riemann
geometry, and is a tool to research Lorentz invariance violation. We find the
connection between the most general modified dispersion relation and a
pseudo-Finsler structure, and then we calculate the arrival time delay of
astroparticles with different modified dispersion relations in the framework of
Finsler geometry. The result suggests that the time delay is irrelevant with
the exact form of the modified dispersion relation. If the modified term
becomes 0 when $E=p$, there is no arrival time difference, otherwise the time
delays only depend on the Lorentz violation scale and the order at which the
Lorentz invariance breaks.
