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Theoretical studying of the very inner structure of faint satellite galaxyrequires very high-resolution hydro-dynamical simulations with realistic modelsfor star formation, which are beginning to emerge recently. In this work wepresent an analytical description to model the inner kinematic of satellites inthe Milky Way (MW). We use a Monte-Carlo method to produce merger trees for MWmass halo and analytical models to produce stellar mass in the satellitegalaxies. We consider two important processes which can significantly modifythe inner mass distribution in satellite galaxy. The first is baryonic feedbackwhich can induce a flat inner profile depending on the star formationefficiency in the galaxy. The second is the tidal stripping to reduce andre-distribute the mass inside satellite. We apply this model to MW satellitegalaxies in both CDM and thermal relic WDM models. It is found that tidalheating must be effective to produce a relatively flat distribution of thesatellite circular velocities, to agree with the data. The constraint on WDMmass depends on the host halo mass. For a MW halo with dark matter mass lowerthan $2\times 10^{12}M_{\odot}$, a 2 keV WDM model can be safely excluded asthe predicted satellite circular velocities are systematically lower than thedata. For WDM with mass of 3.5 keV, it requires the MW halo mass to be largerthan $1.5\times 10^{12}M_{\odot}$, otherwise the 3.5 Kev model can also beexcluded. Our current model can not exclude the WDM model with mass larger than10 Kev.

Warm dark matter model with a few keV mass is bad for the too-big-to-fail problem