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