A scenario for a periodic filling and emptying of the accretion disc of the microquasar GRS 1915+105 is proposed, by computing the mass transfer rate from the evolving low mass red giant donor (Greiner at al. 2001) and comparing it with the observed accretion rate onto the primary black hole. We propose a duty-cycle with (5-10)(eta/0.1) per cent active ON-state where eta is the efficiency of converting accretion into radiation. The duration of the quiescent recurrent OFF-state is identified as the viscosity time scale at the circularization radius and equals 370(alpha/0.001)^(-4/5) years, where alpha is the viscosity parameter in the alpha-prescription of a classical disc. If the viscosity at the outer edge of the disc is small and eta is close to the maximum available potential energy (per rest mass energy) at the innermost stable orbit, the present active phase may last another 10 - 20 years.
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