Every time you run your program, you get a different sequence of (pseudo-)random numbers. But you want a reproducible sequence, useful when running a simulation, so you need Perl to produce the same set of random numbers each time.
Use Perl's srand function:
srand EXPR; # use a constant here for repeated sequences
Making random numbers is hard. The best that computers can do, without special hardware, is generate "pseudo-random" numbers, which are evenly distributed in their range of values. These are generated using a mathematical formula, which means that given the same seed (starting point), two programs will produce identical pseudo-random numbers.
The srand function creates a new seed for the pseudo-random number generator. If given an argument, it uses that number as the seed. If no argument is given, srand uses a value that's reasonably difficult to guess as the seed.
If you call rand without first calling srand yourself, Perl calls srand for you, choosing a "good" seed. This way, every time you run your program you'll get a different set of random numbers. Ancient versions of Perl did not call srand, so the same program always produced the same sequence of pseudo-random numbers every time the program was run. Certain sorts of programs don't want a different set of random numbers each time; they want the same set. When you need that behavior, call srand yourself, supplying it with a particular seed:
srand( 42 ); # pick any fixed starting point
Don't call srand more than once in a program, because if you do, you'll start the sequence again from that point. Unless, of course, that's what you want.
Just because Perl tries to use a good default seed does not necessarily guarantee that the numbers generated are cryptographically secure against the most intrepid crackers. Textbooks on cryptography are usually good sources of cryptographically secure random number generators.
The srand function in perlfunc(1) and Chapter 29 of Programming Perl; Recipe 2.6 and Recipe 2.8; Bruce Schneier's excellent Applied Cryptography (John Wiley & Sons)