The Jovian polar magnetosphere has relativistic particle accelerations with quasi-periodicity (hereafter QP accelerations) that are accompanied by periodic auroral emissions and low-frequency radio bursts called quasi-periodic (QP) bursts. Some previous observations suggested a possible physical relationship between the QP accelerations and QP radio bursts. However, the cause of the QP accelerations has not been revealed yet. This study investigated the generation process of QP radio bursts that constrain the QP acceleration process. The statistical features of QP bursts' periodicity were investigated by applying Lomb-Scargle periodogram analysis to the variations of the QP bursts' spectral densities observed by the Galileo and Ulysses spacecraft. The Lomb-Scargle analysis revealed remarkable characteristics: QP bursts have statistically large amplitudes with periods of 30–50 min at all latitudes. This result suggests that 30–50 min is an “eigenfrequency” of the QP accelerations which is close to the 45 min periodicity of the pulsating X-ray hot spot in the polar cap region. In addition, it was also revealed that successive pulses sometimes exhibit periodicity transition. We discussed one possible scenario which links Jovian periodic accelerations to those in the terrestrial magnetosphere. The scenario is that particles are energized within the period of the dispersive Alfvén waves with field-aligned electric fields that obliquely propagate between the northern and southern ionospheres. The observed eigenfrequency and periodicity transition of QP bursts are consistent with the Alfvénic acceleration scenario.