I would tend to disagree, that 3 (or even a few more) isolated calls would cause the rescue response system to become overwhelmed. Yes, in a regional/state disaster situation, rescue resources can and do become overwhelmed at times. That is why transfer/fill-in, mutual aid, emergency management agency compacts (EMACs) and memos of understanding (MOUs) charters/agreements are in place. Whenever there is an activation of the emergency response system, a backup system/agency is physically moved, placed on alert or moved up within the computer assisted dispatch systems (CAP) to handle the next due call.
This occurs daily in many jurisdictions, an ambulance is dispatched, and another call(s) comes in at the same time or just after. If the station does not have another ambulance, then the next closest unit is dispatched. If resources in a particular area are exhausted on a call(s), such as a high-life hazard incident, then resources are alerted/moved up to cover/fill-in those stations that are depleted.
If a particular aviation (or other rescue resource) rescue resource is tied up, then the next due unit is alerted, dispatched or moved to cover the area. The increase in cell phone use has certainly increased the calls coming into emergency/dispatch communication centers, but the increase in actually emergencies is determined more by population density and life style then cell phone use. Likewise, the increase in use of PLBs might lead to more activation of emergency services by this specific method, but the same PLB user may have previously activated the system by phone, radio, cell phone or runner in the past. A substantial increase in the activation of rescue resources solely due to an increase in the number of PLBs users is unlikely.
Pete