  We have determined the currently allowed regions of the parameter spaces of
two representative models of diffuse neutrino flux from active galactic nuclei
(AGN): one by Koers & Tinyakov (KT) and another by Becker & Biermann (BB). Our
observable has been the number of upgoing muon-neutrinos expected in the
86-string IceCube detector, after 5 years of exposure, in the range 10^5 <
E/GeV < 10^8. We have used the latest estimated discovery potential of the
IceCube-86 array at the 5-sigma level to determine the lower boundary of the
regions, while for the upper boundary we have used either the AMANDA upper
bound on the neutrino flux or the more recent preliminary upper bound given by
the half-completed IceCube-40 array (IC40). We have varied the spectral index
of the proposed power-law fluxes, alpha, and two parameters of the BB model:
the ratio between the boost factors of neutrinos and cosmic rays,
Gamma_nu/Gamma_{CR}, and the maximum redshift of the sources that contribute to
the cosmic-ray flux, zCRmax. For the KT model, we have considered two
scenarios: one in which the number density of AGN does not evolve with redshift
and another in which it evolves strongly, following the star formation rate.
Using the IC40 upper bound, we have found that the models are visible in
IceCube-86 only inside very thin strips of parameter space and that both of
them are discarded at the preferred value of alpha = 2.7 obtained from fits to
cosmic-ray data. Lower values of alpha, notably the values 2.0 and 2.3 proposed
in the literature, fare better. In addition, we have analysed the capacity of
IceCube-86 to discriminate between the models within the small regions of
parameter space where both of them give testable predictions. Within these
regions, discrimination at the 5-sigma level or more is guaranteed.
