Advantage of using higher luminosity accelerator If two accelerators operate at the same energy but different luminosity, is the only advantage of accelerator with a higher luminosity that there will be more events in a given amount of time, thus it can operate for a shorter amount of time to observe same number of events? 
Or is there some fundamental advantage in which some processes can only be studied by the accelerator with higher luminosity?
 A: In most cases we are looking for a small signal on a large background and the usual signal-to-noise rules apply. If we do $N$ observations we expect the signal strength to be proportional to $N$ while the noise is proportional to $\sqrt{N}$. So the signal to noise ratio is proportional to $\sqrt{N}$. The higher the luminosity the greater the value of $N$ so the better the signal to noise ratio.
A: You are right saying that the only advantage of the higher lumi accelerator will be to operate for a shorter amount of time. Indeed you can build up the same statistics just running longer at a lower lumi.
But if you contextualize this, you find out important consequences. With physics programmes that already extend over decades, a factor 10 less luminosity means going into centuries!! Then the fixed costs of operating the facility (people, spare parts and maintenance, background power consumption, ...) are a factor 10 higher. Moreover as a machine gets older and older the performances and reliability can easily become an issue. You also have to take into account that physicists, and people in general, are not very happy to work for a lifetime already knowing that they won't be able to see the results of their efforts.
So in the end, if you don't get enough luminosity you just miss the physics.
