ACR CAPT LAMENTS THE LACK OF COORDINATION BETWEEN ARTCC SECTORS AND IS UNABLE TO ACCEPT HOLDING AFTER COMPLYING WITH BEST FORWARD SPEED REQUEST FROM PREVIOUS CONTROLLER.

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AFTER BEING TOLD TO COMPLY WITH MAX FORWARD AIRSPD BY ATC; THE CTLR SLAMMED THE DOOR SHUT ON US JUST A FEW SECONDS FROM ABC INTXN. WE HAD NO ADVANCE PLANNING; NOTICE; TIME; DISTANCE OR REASON FOR THE HOLD. WE HAD BURNED INTO OUR PLANNED HOLDING FUEL ON A CLR NON-WX DAY JUST TO HELP OUT THE ATC SYS. (ZZZ WAS USING 1 RWY AND IT HAS 4.) MY FO PARROTED BACK THE HOLDING INSTRUCTIONS AS I WAS SAYING IN HIS OTHER EAR 'NO WE DON'T HAVE GAS TO HOLD.' AS SOON AS I COULD BREAK BACK INTO THE FREQ I TOLD THE CTLR THAT WE WOULD NOT BE ABLE TO COMPLY WITH THE LAST REQUEST; AS ABC WAS NOW A FEW MI BEHIND US. IN AN ATTEMPT TO STAY AT LEAST ON THE DEPICTED SIDE OF THE HOLDING PATTERN I BEGAN A R TURN. WE WERE THEN COUNTERMANDED TO MAKE A L TURN TO A 320 DEG HDG. AS I LOOKED AT OUR FUEL STATE; FUEL BURN; SPD; ALTERNATE; MISSED APCH PROBABILITY; TFC; ALT; LOCATION; ATC'S SELF-IMPOSED IDIOCY; WX; SCHEDULE; RWY CONDITIONS; APCH BRIEFING; LENGTH OF TIME SINCE WAKING; FATIGUE; ACFT CONDITION; BLOOD SUGAR LEVEL; EMOTIONAL STATE; PHYSIOLOGICAL NEEDS; AND A FEW OTHER THINGS. I TOLD THE CTLR THAT WE WERE 'MINIMUM FUEL.' I DID NOT HAVE THE ABILITY TO HOLD; FLY A 30 MI FINAL AT 160 KTS; MISS THE APCH; GAR AND IMPART MY FIDUCIARY DUTY OF SAFE OP OF A COMMERCIAL JETLINER FULL OF PEOPLE. SHE SAID AFTER A FEW EXCHANGES AND SEMANTICS CHALLENGES THAT SHE WOULD DECLARE AN EMER 'FOR US.' A HDOF TO THE NEXT CTLR OCCURRED AND WE LANDED AT ZZZ. AS PLTS WE ALWAYS TRY TO COMPLY WITH REASONABLE REQUESTS BUT WE CANNOT FIX A BROKEN SYS OR CTLR'S PROB WITH JUST THE PUSH OF A BUTTON. NEXT TIME I THINK INSTEAD OF ANSWERING THE QUESTION OF 'HOW MANY MINS OF FUEL ARE REMAINING' I WILL SAY; 10 MINS UNTIL I BECOME UNCOMFORTABLE; 20 MINS UNTIL ONE OR THE OTHER ENG FLAMES OUT DUE TO MANEUVERING; OR FAULTY FUEL PROBES; 30 MINS UNTIL THE PUMPS START TO CAVITATE AND 40 MINS UNTIL GRAVITY CONTINUES ITS EARTHLY PULL AND WINS. WE EITHER NEED TO HAVE 20000 LBS ARR FUEL FOR ZZZ; OR GET OVER TO THE TRACON AND CTL TWRS WITH GIFT BASKETS OF FRUIT; CHEESE; WINE AND SPIRITS AS WELL AS A FEW COMPANY LOGO T-SHIRTS; HATS; BUTTONS; FLY FREE TICKETS; AND BROWN PAPER BAGS OF CASH IN ORDER TO APPEASE THE SYSTEM'S APPARENT RESPONSE TO OUR INCREASE OF FLYING AT ZZZ.