  Upcoming radio telescopes will allow to study the radio sky at low
frequencies with unprecedent sensitivity and resolution. New surveys are
expected to discover a large number of new radio sources. Here we investigate
the abundance of radio relics, i.e. steep-spectrum diffuse radio emission
coming from the periphery of galaxy clusters, which are believed to trace shock
waves induced by cluster mergers. With the advent of comprehensive relic
samples a framework is needed to analyze statistically the relic abundance. To
this end, we introduce the probability to find a relic located in a galaxy
cluster with given mass and redshift allowing us to relate the halo mass
function of the Universe with the radio relic number counts. Up to date about
45 relics have been reported and we compile the resulting counts, N(>S_1.4). In
principle, the parameters of the distribution could be determined using a
sufficiently large relic sample. However, since the number of known relics is
still small for that purpose we use the MareNostrum Universe simulation to
determine the relic radio power scaling with cluster mass and redshift. Our
model is able to reproduce the recently found tentative evidence for an
increase in the fraction of clusters hosting relics, both with X-ray luminosity
and redshift, using an X-ray flux limited cluster sample. Moreover, we find
that a considerable fraction of faint relics (S_1.4 < ~10 mJy) reside in
clusters with an X-ray flux below ~3e-12 erg/s/cm^2. Finally, we estimate the
number of radio relics which await discovery by future low frequency surveys
proposed for LOFAR and WSRT. We estimate that the WODAN survey proposed for
WSRT may discover 900 relics and that the LOFAR-Tier 1-120 MHz survey may
discover about 2500 relics. However, the actual number of newly discovered
relics will crucially depend on the existence of sufficiently complete galaxy
cluster catalogues.
