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The cosmic far-infrared background (CFIRB) is expected to be generated byfaint, dusty star-forming galaxies during the peak epoch of galaxy formation.The anisotropy power spectrum of the CFIRB captures the spatial distribution ofthese galaxies in dark matter halos and the spatial distribution of dark matterhalos in the large-scale structure. Existing halo models of CFIRB anisotropypower spectrum are either incomplete or lead to halo model parameters that areinconsistent with the galaxy distribution selected at other wavelengths. Herewe present a conditional luminosity function approach to describe the far-IRbright galaxies. We model the 250 um luminosity function and its evolution withredshift and model-fit the CFIRB power spectrum at 250 um measured by theHerschel Space Observatory. We introduce a redshift dependent duty-cycleparameter so that we are able to estimate the typical duration of the dustystar formation process in the dark matter halos as a function of redshifts. Wefind the duty cycle of galaxies contributing to the far-IR background is 0.3 to0.5 with a dusty star-formation phase lasting for \sim0.3-1.6 Gyrs. This resultconfirms the general expectation that the far-IR background is dominated bystar-forming galaxies in an extended phases, not bright starbursts that aredriven by galaxy mergers and last \sim10-100 Myrs. The halo occupation numberfor satellite galaxies has a power-law slope that is close to unity over 0<z<4.We find that the minimum halo mass for dusty, star-forming galaxies withL_250>10^{10} L_Sun is 2\times10^{11}M_Sun and 3\times 10^{10}M_Sun at z=1 and2, respectively. Integrating over the galaxy population with L_250>10^{9}L_Sun, we find that the cosmic density of dust residing in the dusty,star-forming galaxies responsible for the background anisotropies\Omega_{dust}\sim3\times10^{-6} to 2\times10^{-5}.

A Conditional Luminosity Function Model of the Cosmic Far-Infrared Background Anisotropy Power Spectrum