Just to complete this topic
My simulation was of course a rather rough one, even though I suppose that anybody could easily got the point unless he want just to make issues

However more sophisticated computer simulations have been proposed to confirm or refute Fermi's paradox
All of them led to absurd results

I quote one of them :

quote


Using a computer simulation of our own galaxy, the Milky Way, Rasmus Bjork, a physicist at the Niels Bohr institute in Copenhagen, proposed that a single civilisation might build eight intergalactic probes and launch them on missions to search for life. Once on their way each probe would send out eight more mini-probes, which would head for the nearest stars and look for habitable planets.

Mr Bjork confined the probes to search only solar systems in what is called the "galactic habitable zone" of the Milky Way, where solar systems are close enough to the centre to have the right elements necessary to form rocky, life-sustaining planets, but are far enough out to avoid being struck by asteroids, seared by stars or frazzled by bursts of radiation.

He found that even if the alien ships could hurtle through space at a tenth of the speed of light, or 30,000km a second, - Nasa's current Cassini mission to Saturn is plodding along at 32km a second - it would take 10bn years, roughly half the age of the universe, to explore just 4% of the galaxy. His study is reported in New Scientist today.

Like humans, alien civilisations could shorten the time to find extra-terrestrials by picking up television and radio broadcasts that might leak from colonised planets. "Even then, unless they can develop an exotic form of transport that gets them across the galaxy in two weeks it's still going to take millions of years to find us," said Mr Bjork.

unquote

For those who are interested the article can be downloaded from the " New Scientist today " web site
6 pages complete with graphics and pictures