  We present a new theoretical framework to predict average histograms of
line-of-sight velocities over pairs of galaxies and galaxy clusters. Since the
histogram can be measured at different galaxy-cluster separations, this
observable is commonly referred to as the stacked phase-space density. We
formulate the stacked phase density based on a halo-model approach so that the
model can be applied to real samples of galaxies and clusters. We examine our
model by using an actual sample of massive clusters with known weak-lensing
masses and spectroscopic observations of galaxies around the clusters. A simple
likelihood analysis with our model enables us to infer the three-dimensional
velocity dispersion of observed galaxies in massive clusters. We find the
velocity bias of galaxies surrounding clusters with their masses of
$\sim10^{15}\, h^{-1}M_{\odot}$ to be $1.09\pm0.245$ at the 68\% confidence
level (including systematic errors associated with our model uncertainties).
Our results confirm that the relation between the galaxy velocity dispersion
and the host cluster mass in our sample is consistent with the prediction in
dark-matter-only N-body simulations. We measure the line-of-sight velocity
dispersions of 16701 galaxies around 23 clusters on scales of $<6\,
h^{-1}\mathrm{Mpc}$ with a 10\% level precision. Our measurement of the
line-of-sight velocity dispersion is in good agreement with the standard
$\Lambda$CDM prediction. Possible directions for improvement in the analysis
are also discussed.
