GA JET PLTS DECLARE MINIMUM FUEL WHEN UNABLE TO COMPLY WITH APCH CTLR RADAR VECTORING.

Narrative

AT APPROX 230 NM E OF SFO. CTR REQUESTED DSCNT TO 390; THEN 350. I REQUESTED TO STAY AT 450 WITH DISCRETION TO DSND. THIS WAS DENIED. I ADVISED CTR THE POSSIBILITY OF HAVING MINIMUM FUEL WITH AN EARLY DSCNT. AFTER NUMEROUS VECTORS OFF COURSE WE WERE CLRED TO MOD AND TO CONTINUE THE MOD 2 ARR AT FL240. BTWN MOD AND CEDES INTXN BAY APCH SAID WE WERE NOT ANSWERING RADIO CALLS. THE FIRST TIME WE WERE AWARE OF THIS WAS WHEN WE REQUESTED DSCNT FROM 240 NEAR CEDES INTXN. THE CTLR SAID HE HAD CALLED AND WE WERE NOT LISTENING. HE GAVE US A PHONE NUMBER TO CALL. WE TOLD BAY APCH WE WERE APCHING MINIMUM FUEL. THEY PROCEEDED TO GIVE US VECTORS AWAY FROM SFO; ONE TO A HDG OF 030 DEGS. I UNDERSTOOD AFTER 030 DEGS CLRED DIRECT TO CEDES. HE SAID HE HAD NOT CLRED ME TO DO THAT AND CLRED ME BACK TO 030 DEGS. HE THEN GAVE ME A R TURN. HE THEN ASKED ME TO DO A 360 DEG TURN. I REFUSED. DECLARING MINIMUM FUEL. I HAD GONE FROM 28 NM TO ALMOST 45 NM FROM SFO. THEY THEN CLRED ME TO THE SFO ARPT FOR THE QUIET BRIDGE VISUAL TO RWY 28R. THE SUPVR SAID THEY HAD CALLED 7 TIMES AND WE DID NOT ANSWER. THERE IS NO WAY WE COULD MISS 7 CALLS UNLESS THEY WERE CALLING ON A FREQ WE WERE NOT ON. I HAVE NOTICED IN RECENT YRS ATC IS LOSING REALITY WITH FLYING. SUPPLEMENTAL INFO FROM ACN 280368: A RADIO HDOF WAS EITHER NOT GIVEN OR MISSED AND WE REMAINED AT FL240 WHEN WE WERE GETTING TOO CLOSE IN. I CALLED ATC AND ASKED FOR LOWER; I WAS THEN INFORMED THAT WE HAD BEEN HANDED OFF. WE HAD 1/5 MINIMUM (VFR MINIMUMS) OR 950 LBS OF FUEL ON BOARD. WE TALKED WITH THE FAA AND CALLED 2 CTR SUPVRS TO RESOLVE THE MISUNDERSTANDINGS.