This is really a question for an Arizona attorney familiar with traffic law cases. Contact the county Bar Association for the county in Arizona to get some referrals to local attorneys that can answer your questions. Often, state laws will provide that by driving in the state you will accept service of the violation by mail. Check with an Arizona attorney.
If you sign the waiver of service and mail it back, you validate the ticket. If you don't do that, some other service must occur.
"Summons and complaint may be served by first-class mail along with two copies of notice and acknowledgment of receipt of summons and complaint and postpaid return envelope, but service is not complete until the acknowledgment of receipt is executed." 16 A.R.S. Rules Civ.Proc., Rule 4.1(c), (c)(1, 2).
Essentially, that means the ticket -- which contains a court summons -- must be hand-delivered to you or a resident of your home if you do not validate it by mailing it back ( i.e. *service is not complete until the acknowledgment of reciept is executed.)
You need a lawyer. Check with an Arizona lawyer to discuss more of the details. I practice in Illinois.
Good luck to you.
NOTE: This answer is made available by the out-of-state lawyer for educational purposes only. By using or participating in this site you understand that there is no attorney client privilege between you and the attorney responding.