Date: 201312
Local time of day: 0601-1200
Location: ZMA.ARTCC, FL
Flight conditions: Mixed
Weather elements / visibility: 10
Light: Daylight
Aircraft: Small Aircraft; Low Wing; 2 Eng; Retractable Gear
Operator: Personal
Operating under: Part 91
Flight plan: IFR
Mission: Passenger
Flight phase: Descent
Airspace: Class E ZMA
ATC / advisory: Center ZMA
Reporter organization: Personal
Reporter function: Pilot Flying
Reporter qualification: Flight Crew Multiengine; Flight Crew Commercial; Flight Crew Instrument
Human factors: Distraction; Workload; Situational Awareness; Communication Breakdown
Second reporter function: Pilot Not Flying
Anomaly: ATC Issue All Types; Conflict NMAC
Detector: Automation Aircraft TA; Person Flight Crew
When detected: In-flight
Result: Flight Crew Took Evasive Action
Contributing factors: Airspace Structure; Environment - Non Weather Related; Procedure
Primary problem: Ambiguous

Narrative: We were flying to F45.  We had filed (and had been cleared) IFR for 8;000 and a route of SABOT PHK F45.  We had departed to the east; eventually being cleared direct PHK.  We had been cruising direct to PHK with the Departure Controller.  He turned us over to a ZMA Controller on 132.25.  As soon as we checked on; we noticed it start to get busy.  We even remarked (internally) about how busy it was and the lack of English comprehension some of the trainees seem to have in and around the TRV/VRB area.  There were numerous airplanes requesting practice approaches; along with multiple missed calls; etc.  While still roughly 60-70 miles north of PHK; we were instructed to descend to 4;000.  We found it odd; as that normally doesn't happen until further along the route (closer to PHK).  Normally; we like to stay high to avoid the 'bee hive' of traffic below.  In any case; roughly 47-48 miles NE of PHK [estimated] we got an onboard traffic advisory from the installed ADS-B (Garmin's GDL-88).  When it first appeared; the traffic was 600 FT below our present altitude and climbing; as we were descending.  It was approaching from our 11 o'clock position.  I watched the trend and we (the two pilots on our plane) decided to shallow our descent.  Had we not done this; we feel as if a collision was likely.  When we flew over the other aircraft; we estimate we were 300-400 FT vertically and 100 feet horizontally.  Once the conflict cleared; we continued the descent to 4;000.  We tried once to contact the ZMA Controller after this and were unsuccessful.  The frequency utilization was nearly 100% for the 3-4 minutes prior and 5 minutes after the incident.  There were numerous VFR aircraft being denied services during our time on frequency and several IFR-pickups not being replied to.  Ultimately; we feel as if the other aircraft involved was VFR and unaware we were there.  The Controller didn't provide a traffic advisory to us and we feel that was because he was dealing with too much other traffic.  That sector is consistently busy with practice approaches; conducted by pilots with limited English skills.  The Sector is also very large from what we can tell by routinely flying through it.  A good fix to avoid this in the future would be to split the approaches at VRB and FPR into another sector.


Second narrative: [Report narrative contained no additional information.]


Synopsis: A light twin approaching PHK IFR had a near miss with a VFR aircraft while ZMA was extremely busy with English as a second language pilots on training missions.