Fuel pump relay chattering

As described in the subject my sons 1996 Lumina PD has been experiencing some weird problem with the fuel pump relay, located under the hood in the fuse block. Every once and a while it starts chattering, and when it does the car apppears to stumble as if starving for fuel. Any ideas? I have replaced the relay and cleaned the contacts on all the fuses located in that fuse box. Also what controls and provides power to this relay, is it a sensor in the fuel system or is it the computer, or a combination of both. Thanks. Jim