Anything else seems kind of alien to me. All 3 of the facilities I have worked in have operated in the same fashion. Call the answering service and tell them whether you need, "orders, results, or condition" and stat or routine call.
One physician, actually an intensivist/pulmonologist has given out his cell number so it is really fast to get him on the phone and get orders. If not careful it can be abused but he is not the kind of doctor that screams and shouts at people. If I were ever to be sick, he is the doctor I would want on my case!