Based on the transform function model of the observed citing process, the analytical expression of the age distribution of citations is deduced, and it is theoretically proved that the peak value of the citation distribution curve would fall and shift backward along with increasing the average publication delay and the peak age has a direct proportion relation with the pure delay and would be prolonged along with increasing the delay or decreasing the aging rate. The influence of the average publication delay on three ISI indicators impact factor, immediacy index and cited half-life are studied; in one subject discipline, the bigger the delay, the lower the three indicators of journals. Using the sensitivity theory, sensitivity formulae of the three indicators to publication delay parameters are deduced and it is found that responses of these indicators to changes of publication delays are different according to different time constant of the aging process; The faster the aging rate of a discipline literature is, the worse the influence of publication delays on the indicators of journals in the discipline.