The original Nintendo DSi cannot connect to any router—it lacks Wi-Fi hardware for internet access. It only supports local wireless (DS Download Play).
The DSi XL (larger screen model) does have Wi-Fi (802.11b/g) and connects to any standard router—including Arris—via WPA2-PSK (AES). Router brand is irrelevant; the DSi XL joins the network like a phone or laptop.
If you have a standard DSi (not XL), internet features (Shop, Browser, WFC) are hardware-impossible.