  We constrain the uncertainty in waiting times for detecting the first
double-neutron-star (DNS) mergers by gravitational wave observatories. By
accounting for the Poisson fluctuations in the rate density of DNS mergers and
galaxy space density inhomogeneity in the local Universe, we define a detection
`zone' as a region in a parameter space constrained by the double neutron star
merger rate and two LIGO operations parameters: an observation horizon distance
and science run duration. Assuming a mean rate of about 80 DNS mergers per
Milky Way galaxy Myr^{-1}, we find a 1/20 chance of observing a merger by
Enhanced LIGO in only 1 yr of observation. The minimum waiting time and
temporal zone width for an Advanced LIGO sensitivity are much shorter and imply
that there is a 95% probability of detecting a DNS merger in less than 60 days
and a 1/20 chance of a first detection in about 1 day. At the 5% probability
threshold for a first detection, we find that the effect of galaxy clusters on
detection is smoothed out and may only influence detection rates after 5-10
years observation time.
