Connected to the experiment performed at the Stockholm electron beam ion trap, a systematic relativistic configuration-interaction calculation is carried out to compare with the experimental spectra. In particular, separate rate coefficients are calculated for dominant recombination and excitation processes in the range of the impact electron energy determined by the experiment. By means of the relevant experimental parameters, the presently calculated dielectronic recombination rate coefficients for and S14+ ions and electron-impact excitation ones for S15+, S14+, and S13+ ions are employed further to synthesize overall theoretical spectra for comparison with the experimentally measured spectra. Overall, very good agreements with the experimental results are found except for one missing excitation peak around the impact electron energy 2.52 keV, which cannot be explained by the present calculations and thus remains open.