processes have a bandwidth limit?

Hello,

My question is the bandwidth allocated to a process.

1) prog.pl is a perl script which continuously carries out an exchange on a TCP port xxx as a client (so the server to upload and download TCP's response to this server continues)
2) The shell jutilise (as root) is this: nice -19 perl prog. pl
3) When does jeffectue exchange loop 100 via TCP, I see no difference on a server that offers a lower bandwidth than a server B, which offers at least 2 times more than BP.

questions: why no difference in speed? BP dedicated in limited?
Hoping to have formulated the question and find assistance to better understand it. I read the word several times Qos but is not sure if that is bound. Is there a way to say that I want to take advantage of any bandwidth up to run my order?
Thank you very much for your help.