  Recent observations show that the cosmic ray nuclei spectra start to harden
above 100 GeV, in contradiction with the conventional steady-state cosmic ray
model. We had suggested that this anomaly is due to the propagation effect of
cosmic rays released from local young cosmic ray sources, the total flux of the
cosmic ray should be computed with the myriad model, where contribution from
sources in local catalog is added to the background. However, while the
hardening could be elegantly explained in this model, the model parameters
obtained from the fit skew toward a region with fast diffusion and low
supernova rate in the Galaxy, in tension with other observations. In this
paper, we further explore this model in order to set up a concordant picture.
Two possible improvements related to the cosmic ray sources have been
considered. Firstly, instead of the usual axisymmetric disk model, we
considered a spiral model of source distribution. Secondly, for the nearby and
young sources which are paramount to the hardening, we allow for an
energy-dependent escape time. We find that major improvement comes from the
energy-dependent escape time of the local sources, and with both modifications,
not only the cosmic ray proton and helium anomalies are solved, but also the
parameters attain reasonable range values compatible with other analysis.
