  We develop a semi-analytical model that determines the evolution of the mass,
position and internal structure of dark matter substructures orbiting in dark
matter haloes. We apply this model to the case of the Milky Way. We focus in
particular on the effects of mass loss, dynamical friction and
substructure--substructure interactions, the last of which has previously been
ignored in analytic models of substructure evolution. Our semi-analytical
treatment reproduces both the spatial distribution of substructures and their
mass function as obtained from the most recent N-body cosmological calculations
of Gao et al. (2004). We find that, if mass loss is taken into account, the
present distribution of substructures is practically insensitive to dynamical
friction and scatterings from other substructures.
  Implementing these phenomena leads to a slight increase (~5%) in the number
of substructures at r<0.35 r_vir, whereas their effects on the mass function
are negligible. We find that mass loss processes lead to the disruption of
substructures before dynamical friction and gravitational scattering can
significantly alter their orbits. Our results suggest that the present
substructure distribution at r>0.35 r_vir reflects the orbital properties at
infall and is, therefore, purely determined by the dark matter environment
around the host halo and has not been altered by dynamical evolution.
