  In an earlier paper, the effect of the nearby known supernova remnants (SNRs)
on the local cosmic-rays (CRs) was studied, considering different possible
forms of the particle injection time. The present work is a continuation of the
previous work, but assumes a more realistic model of CR propagation in the
Galaxy. The previous work assumed an unbounded three-dimensional diffusion
region, whereas the present one considers a flat cylindrical disc bounded in
both the radial and vertical directions. The study has found that the effect of
the vertical halo boundary $H$ on the local SNR contribution to the observed CR
anisotropy is negligible as long as $H\gtrsim 2kpc$. Considering the values of
the halo height $H\gtrsim 2kpc$ obtained by different authors, the present work
suggests that the study of the effect of local sources on the CR anisotropy can
be carried out without having much information on $H$ and hence, using the much
simpler three-dimentional unbounded solution. Finally, the present work
discusses about the possibility of explaining the observed anisotropy below the
knee by a single dominant source with properly chosen source parameters, and
claims that the source may be an \textit{undetected} old SNR with a
characteristic age of $\sim 1.5\times 10^5 yr$ located at a distance of $\sim
0.57 kpc$ from the Sun.
