  Massive molecular gas has been discovered in giant elliptical galaxies at the
centers of galaxy clusters. To reveal its role in active galactic nucleus (AGN)
feedback in those galaxies, we construct a semianalytical model of gas
circulation. This model especially focuses on the massive molecular gas
(interstellar cold gas on a scale of ~ 10 kpc) and the circumnuclear disk (~<
0.5 kpc). We consider the destruction of the interstellar cold gas by star
formation and the gravitational instability for the circumnuclear disk. Our
model can reproduce the basic properties of the interstellar cold gas and the
circumnuclear disk, such as their masses. We also find that the circumnuclear
disk tends to stay at the boundary between stable and unstable states. This
works as an 'adjusting valve' that regulates mass accretion toward the
supermassive black hole. On the other hand, the interstellar cold gas serves as
a 'fuel tank' in the AGN feedback. Even if the cooling of the galactic hot gas
is prevented, the interstellar cold gas can sustain the AGN activity for ~> 0.5
Gyr. We also confirm that the small entropy of the hot gas (~< 30 keV cm^2) or
the short cooling time (~< 1 Gyr) is a critical condition for the existence of
the massive amounts of molecular gas in the galaxy. The dissipation time of the
interstellar cold gas may be related to the critical cooling time. The galaxy
behavior is described by a simple relation among the disk stability, the cloud
dissipation time, and the gas cooling rate.
