ONE ENG QUIT DURING TAXI TO GATE DUE TO FUEL STARVATION ON A LTT ACR ACFT.

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DEPARTED HUN 2000 LBS FUEL; I FIGURED A 1100 LBS BURN. ITS FLT PLANNED AT 1:30 AND BURN OF 1050. I ALSO INCLUDED 600 LBS FOR VFR FUEL RESERVE AND 300 LBS CONT. WE HAD HEADWINDS AND A CHANGE OF FLT RTE. WE START THE APCH AND CIRCLE TO LAND IN VFR CONDITIONS. AFTER LNDG; WE TOOK THE HIGH SPD OFF OF RWY 30 IAD. TO THE PARALLEL TXWY TO W1 TO T1 TO THE GATE. THE LEFT ENG SHOT DOWN WHILE TAXIING. IT INDICATED 300 LBS OF FUEL ON THAT SIDE. THERE WERE NO LOW LEVEL WARNING LIGHTS THAT CAME ON. DURING THE TAXI MY R ENG LOW LEVEL LIGHTS CAME ON AT 250 LBS AND WE SHUT DOWN AT THE GATE. MY FO DIPPED THE TANKS. NO FUEL COULD BE MEASURED. (ZERO FUEL BOTH TANKS.) INDICATIONS; INDICATED WE HAD AT SHUT DOWN 400-450 LBS MAYBE 500 LBS TOTAL LEFT. COMPANY IRREGULARITIES WERE FILED ALONG WITH MECHANICAL INTERRUPTION RPT TO FAA. MAINT PERSONNEL ADVISED ME OF A FUEL SIT ON THIS AIR FRAME FOUR DIFFERENT ACCOUNTS. LOG SHOWS NO OPEN RECORD; DMI'S; OR PAST PROBS THAT INDICATE A FUEL INDICATION PROB. AC TYPE BAE-3100 SUPER; TPE 331- 10 ENGS.