  An improved Tsallis statistics is implemented in a multisource thermal model
to describe systematically pseudorapidity spectra of charged particles produced
in relativistic nucleon-nucleon ($pp$ or $p\overline{p}$) collisions at various
collision energies and in relativistic nucleus-nucleus ($AA$) collisions at
different energies with different centralities. The results with Tsallis
statistics using the two-cylindrical multisource thermal model are in good
agreement with the experimental data measured at RHIC and LHC energies. It is
found that the rapidity shifts of longitudinal sources increase linearly with
collision energies and centralities in the framework. According to the laws, we
also give a prediction of the pseudorapidity distributions in
$pp$($\overline{p}$) collisions at higher energies.
