  The observation of high-energy extraterrestrial neutrinos at IceCube
represents the beginning of the era of neutrino astronomy. In this paper, we
study the cosmic neutrino flavor ratios against the Dirac CP-violating phase at
neutrino telescopes, taking into account the charged-current and
neutral-current interactions at the detectors. We then demonstrate how to probe
mass hierarchy at future neutrino telescopes by the precise measurements of the
cosmic neutrino flavor ratios. We show that the sensitivity of our scheme is
independent of the undetermined values of the Dirac CP-violating phase. We also
explore the possible effects of active-sterile mixing, neutrino decay and
pseudo-Dirac nature of neutrinos.
