We study in detail the effect of different particle release times from sources on the cosmic ray (CR) spectrum below 10¹⁵ eV in the Galaxy. We discuss different possible forms of particle injection such as burst-like injection, continuous injection for a finite time, injection from a stationary source and energy-dependent injection. When applied to the nearby known supernova remnants, we find that the observed CR anisotropy data favour the burst-like particle injection model for the CR diffusion coefficient D(E) ∝E^a with a= 0.3 –0.6 in the local region. In this study we have also found that the contribution of the sources G114.3+0.3 and Monogem dominate if the observed anisotropy is a result of the effect of the nearby sources. Further study shows that we should not neglect the contribution of the undetected old sources to the local CR anisotropy.