  The realistic simulation of variable star populations is fundamental to
determine the selection function and contamination in existing and upcoming
multi-epoch surveys. We present \ellisa, a simulator that produces an ensemble
of mock light curves for a population of eclipsing binaries obtained from
physical and orbital parameters consistent with different galactic populations,
and which considers user-supplied time sampling and photometric errors to
represent any given survey. We carried out a search for eclipsing binaries in
the QUEST low-galactic latitude catalogue of variable stars, spanning an area
of 476 sq. deg at $-25^\circ \la b \la 30^\circ$ and $190^ \circ \leqslant l
\leqslant 230^ \circ$ towards the galactic anti-centre, and use \ellisa~to
characterise the completeness of the resulting catalogue in terms of amplitudes
and periods of variation as well as eclipsing binary type. The resulting
catalogue consists of $1,125$ eclipsing binaries, out of which $179$, $60$ and
$886$ are EA, EB and EW types respectively. We estimate, on average, $30\%$
completeness in the period range $0.25 \la P/d \la 1$ for EB+EW binaries and
$15\%$ completeness for EA binaries with periods $2 \la P/d \la 10$, being the
time sampling the primary factor determining the completeness of each type of
eclipsing binary. This is one of few eclipsing binary catalogues reported with
an estimate of the selection function. Mock eclipsing binary light curve
libraries produced with \ellisa~can be used to estimate the selection function
and optimise eclipsing binary searches in upcoming multi-epoch surveys such as
Gaia, the Panoramic Survey Telescope and Rapid Response System, the Zwicky
Transient Factory or the Large Synoptic Survey Telescope.
