Date: 201506
Local time of day: 1201-1800
Location: MIA.Airport, FL
Flight conditions: VMC
Weather elements / visibility: Thunderstorm
Aircraft: Large Transport; Low Wing; 2 Turbojet Eng
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Cruise
Airspace: Class A ZMA
ATC / advisory: Center ZMA
Reporter organization: Air Carrier
Reporter function: Pilot Flying; Check Pilot; Captain
Reporter qualification: Flight Crew Air Transport Pilot (ATP)
Human factors: Distraction; Confusion; Communication Breakdown; Situational Awareness; Workload
Second reporter function: Pilot Not Flying; First Officer
Anomaly: ATC Issue All Types; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter Weather / Turbulence
Detector: Person Flight Crew
When detected: In-flight
Result: Air Traffic Control Issued New Clearance; Flight Crew FLC complied w / Automation / Advisory; Flight Crew Requested ATC Assistance / Clarification
Contributing factors: Procedure; Weather
Primary problem: Procedure

Narrative: While in Cuban airspace; we had to deviate for weather. Havana asked us to fly direct to MAXIM which was not on our clearance. Our clearance was to fly to TADPO and then G448 to MTH and the Curso2 Arrival. We asked Havana for the rest of the clearance and they said that MIA Center would provide that. 10 minutes prior to MAXIM; we began trying to reach MIA Center on 132.2. They would not answer. We could hear other aircraft as well as MIA; but they would not answer us. As we approached MAXIM we had no clearance and were on a routing that was different from our filing. Twice we 'idented' attempting to get the controllers attention. We transmitted 'in the blind' several times. Still; nothing back from MIA. At that point; as we were crossing into US airspace; without positive contact from MIA; we elected to squawk 'no comm' on the transponder and proceed to waypoint CURSO. In our haste; we set 7500 rather than 7600. For the next several minutes we continued to try to reach MIA and yet we still heard nothing from ATC. The observer pilot noticed that we were squawking 7500 rather than 7600. I looked; and he was right. We presumed that by now someone had surely noticed our squawk so we went back to our assigned squawk and continued to call MIA. Finally MIA responded but STILL did not give us a clearance. We kept trying to get one and then MIA put us on a heading for sequencing. Additional radio calls from us to MIA went unanswered with that controller. After we were handed off to the next controller; everything was normal.There were several contributing factors that caused this event. I believe that the primary factor was that the controller was over loaded and completely task saturated. There were several radio calls where he only partially acknowledged our transmissions and numerous calls that simply went unanswered. I'm not sure how ATC staffs or trains; but up until the point where we entered the wrong code; we believed that we were operating in compliance with SOP. It seems that there should be some monitoring of a controller when he is approaching a point of saturation so that radio calls; for more than 10 minutes; do not go unanswered; especially when entering US airspace. For us; the lesson is clear and well learned through this event - slow down; be more careful with your key strokes.


Second narrative: I wish MIA would have responded in some way to our calls in some way; like 'stand by.'


Synopsis: A US carrier in Cuban airspace deviated for weather and was placed a route not in the original flight plan. An apparently task saturated ZMA Controller did not respond to calls for a clearance after entering US airspace.