A B36TC PILOT RAN OUT OF FUEL NEAR HIS DESTINATION IN PART BECAUSE THE JPI FUEL FLOW INDICATOR WAS MALFUNCTIONING. HE MANAGED A SAFE DEAD STICK LANDING AT HIS DESTINATION.

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AFTER ESTIMATING THE WT AND BAL; I ADDED THE MINIMUM FUEL PLUS RESERVE THAT I THOUGHT I WOULD NEED FOR THE 1 HR 15 MIN FLT FROM ZZZ1 TO ZZZ. THIS EXTRA FUEL PUT MY TOTAL TO 40 GALLONS ACCORDING TO THE JPI FUEL FLOW DIGITAL DISPLAY. AFTER LOADING UP THE PEOPLE AND BAGS; WE TOOK OFF EASIER THAN EXPECTED. MY FIRST CLUE THAT SOMETHING WAS NOT NORMAL WAS THE 'GALLONS USED' INDICATION FROM THE JPI AFTER LEVELING OFF AT 11000 FT. THE JPI INDICATED WE HAD USED 39 GALLONS ON CLBOUT. WE ONLY CLBED FOR 17 MINS OR SO AND WE BURN ABOUT 33 GPH ON CLBOUT. SOMEHOW THE JPI DID NOT RESET THE 'GALLONS USED' COUNTER ON THE LAST PWR OFF AND ON AS IT USUALLY DOES. THE 'GALLONS REMAINING;' HOWEVER; STILL SEEMED CORRECT SO I CONTINUED. ABOUT 30 MINS INTO THE FLT; I NOTICED THE L TANK FUEL GAUGE WAS VERY CLOSE TO EMPTY. SOMETIMES THE NEEDLES WILL MOVE ERRATICALLY SO I DISMISSED IT AS A POSSIBLE GAUGE ERROR. NEVERTHELESS; BECAUSE I WAS NOT 100% CERTAIN; I LET ATC KNOW THAT I WAS ON 'MINIMUM FUEL' TO AVOID ANY UNNECESSARY VECTORING. ATC WAS VERY HELPFUL AND UPDATED ME WITH WINDS ALOFT FOR BETTER DSCNT PLANNING. AT THIS POINT I SHOULD HAVE LANDED AT THE NEAREST ARPT FOR SAFETY; BUT BECAUSE I WAS RUNNING A LITTLE LATE AND THE JPI SAID I HAD ABOUT 18 GALLONS LEFT; I CONTINUED BECAUSE I REQUIRED ONLY ABOUT 9 GALLONS TO REACH ZZZ. IT WAS ONLY A FEW MOMENTS LATER WHEN THE L TANK RAN DRY. I SWITCHED TO THE R TANK IMMEDIATELY WITH THE FIRST SIGNS OF ENG FUEL STARVATION. AGAIN; I LET ATC KNOW THAT I WAS DRY ON ONE SIDE AND I NEEDED PRIORITY IN LNDG. AT THIS POINT I WAS ABOUT 12 NM S OF ZZZ4 AND ABOUT 24 NM N OF ZZZ3. MY R TANK GAUGE SHOWED 1/4 TANK AND THE JPI METER SHOWED 16 'GALLONS REMAINING.' I PWRED DOWN THE AIRPLANE TO 22 INCHES MANIFOLD PRESSURE AND 2200 RPM. I ALSO LEANED IT AS MUCH AS I COULD TO CONSERVE FUEL. I WAS NOW FLYING OVER AN OVCST AREA THAT COVERED MOST OF CENTRAL AND WESTERN STATE. THERE WAS NO TERRAIN VISIBLE AS FAR AS I COULD SEE. THE CEILINGS RPTED IN THE AREA WERE ABOUT 3000-4000 FT AGL. I WAS AT ABOUT 11000 FT MSL; AND THE OVCST TOP WAS AT ABOUT 5500 FT MSL. THE TIME WAS NOW ABOUT XA30Z. BECAUSE OF THESE FACTORS; I WAS NOT EAGER TO TRY AND LAND AT AN UNFAMILIAR ARPT IN THE IMMEDIATE AREA. IF I DID RUN DRY ANYTIME SOON; I WANTED TO APCH A FAMILIAR ART; WHICH IN THIS CASE WAS ZZZ. SO I CONTINUED TO ZZZ. I STARTED A STEEP DSCNT INTO ZZZ; ABOUT 23 NM FROM ZZZ. WHEN I REACHED AN ALT OF ABOUT 8000 FT AND ABOUT 13 NM FROM ZZZ; THE ENG STARTED RUNNING ROUGH; SO I SWITCHED THE FUEL SELECTOR 'OFF;' SQUAWKED 7700; AND NOTIFIED ATC (CTR) THAT I RAN OUT OF FUEL AND WAS GOING TO ATTEMPT A GLIDE APCH INTO ZZZ. THEY CLRED ME FOR THE VISUAL APCH RWY 5 AT ZZZ. I SET THE PLANE TO ITS BEST GLIDE SPD OF 105 KIAS. I STAYED THE COURSE USING GPS AND ENTERED THE CLOUDS ABOUT 5500 FT MSL; AND BROKE OUT AT ABOUT 4000 FT MSL. I LOCATED THE FIELD ALMOST IMMEDIATELY AND WAS CONFIDENT THAT I COULD MAKE IT THAT FAR. I RPTED THE FIELD IN SIGHT TO ATC; THEY APPROVED THE FREQ CHANGE; AND I MADE A QUICK CALL ON THE ZZZ CTAF. WHEN I WAS ABSOLUTELY CONFIDENT I WOULD MAKE IT; I PUT FLAPS TO APCH AND THE LNDG GEAR DOWN. I LANDED IN THE LNDG ZONE. THERE WERE EMER VEHICLES AND A TUG WAITING. ONCE WE ROLLED TO A STOP JUST A LITTLE OFF THE RWY; I CALLED CTR AND LET THEM KNOW WE WERE SAFE ON THE GND. THEY CLOSED MY IFR FLT PLAN AND WE SHUT DOWN ALL ELECTRICAL SYSTEMS WHILE THE TUG TOOK US TO THE PARKING RAMP. AFTER PARKING I TURNED ON THE PWR TO CHK THE 'FUEL REMAINING' READING ON THE JPI. ACCORDING TO IT; I HAD 10.2 GALLONS LEFT. NOW LOOKING BACK; I SHOULD HAVE LANDED OR TURNED BACK TO ZZZ1 AT THE FIRST SIGN OF UNCERTAIN FUEL QUANTITIES. AND I SHOULD HAVE NOT ALLOWED THE LATE SCHEDULE TO BE A FACTOR IN THE 'GO; NO-GO' DECISION-MAKING PROCESS.