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We revisit the eccentric neutron star (NS)-white dwarf (WD) binary model forthe periodic activity of fast radio burst (FRB) sources, by including theeffects of gravitational wave (GW) radiation. In this model, the WD fills itsRoche lobe at the periastron and mass transfer occurs from the WD to the NS.The accreted materials can be fragmented and arrive at the NS episodically,resulting in multiple bursts through curvature radiation. Consequently, the WDmay be kicked away owing to the conservation of angular momentum. To initiatethe next mass transfer, the WD has to refill its Roche lobe through GWradiation. In this scenario, whether the periodic activity can show up relieson three timescales, i.e., the orbital period $P_{\rm orb}$, the timescale$T_{\rm GW}$ for the Roche lobe to be refilled, and the time span $T_{\rmfrag}$ for all the episodic events corresponding to each mass transfer process.Only when the two conditions $T_{\rm GW} \gtrsim P_{\rm orb}$ and $T_{\rm frag}< P_{\rm orb}$ are both satisfied, the periodic activity will manifest itselfand the period should be equal to $P_{\rm orb}$. In this spirit, the periodicactivity is more likely to show up for relatively long periods ($P_{\rm orb}\gtrsim$ several days). Thus, it is reasonable that FRBs 180916 and 121102, theonly two sources having been claimed to manifest periodic activity, bothcorrespond to relatively long periods.

Effects of Gravitational Wave Radiation of Eccentric Neutron Star-White Dwarf Binaries on the Periodic Activity of Fast Radio Burst Sources