How not to lag on xbox live?

When i'm playing call of duty 4, my connection goes from green to yellow to green to red to green to yellow etc.. when im in the yellow or red, it's like if I freeze and my player just stops moving and teleports a couple of yards away. I close my router for 5 seconds and then re-open it; before it worked for a couple of hours but then the next day i'd end up with the same situation... Now when i close it i still lag. Having an ethernet cable plugged in doesn't work, it does the same thing. It's really weird. If somebody has an answer to this i'd extremely appreciate it. Thanks!