Linksys Router BEFSR11

I have had this set up for some time and have always wondered why I have almost continuous activity on my cable modem. Here is my setup. Roadrunner cable modem (surfboard sb3100) connected to my router which is connected to a simple hub to connect to my two desktop computers. Currently I have the router running with DHCP enabled and desktops with dynamic ip. I believe I have run with DHCP disabled and didn't notice any change. The activity light blinks constantly even when the computers are shutdown.

My question here is is this normal or am I wasting bandwith?

The traffic in your local cable segment reflects to your cable modem. It is normal for the lights to blink even if your router is unplugged. DHCP on/off will not make a difference if you lease the IP from your router.