Well, not knowing what you have (ie. cable/dsl vs. like actual fiber, T1's, or what), I'm presuming probably cable or dsl.
Tempe in that area was originally acquired by cox from some local podunk cable company that built it originally, and circa 2003 when I worked for cox, the cable was all craptastic in the asu/tempe area. A buddy that works there told me they fixed most of tempe already, but one never knows... DSL is highly variable on age as well, and that being an older hood, I can imagine it might be shaky. Centurylink never really fixes those on old 2-wire infrastructure, they just guarantee less quality.
If you have cox and a decent motorola/arris modem, you can probably monitor your own modem power levels off the modem's internal page if you look up how to, which will tell you if it's truly a service problem in your area or house and you can yell at them to (hopefully) fix. Calling cox and drilling them some, they can see and record modem levels historically too, so they know if someone there cares to look. DSL you're probably more stuck with Centurylink some asscrack tech looking at a point in time, which may or may not tell the whole story. Monitoring externally with pings and recording latency is probably all you can do there. Run an mtr (linux enhanced traceroute utility) to google over time and watch your per-hop latencies, see where it goes to hell.
Short of getting cox or CL to build fiber to your crib, you're mostly stuck with cox cable or centurylink dsl for residential or *business* service (which is just residential with better maintenance response times to roll a tech there). They'll make you pay the construction one form or another (higher monthly recurring cost over a long-term contract, or you pay construction up front of some tens of thousands of dollars), but then you can get 10mbps to 10gbps, again whatever you want to pay for.
-mb