ACFT ON RWY TAXIES OFF ON OWN INITIATIVE AS APCHING ACFT PREPARES TO LAND. TWR UNAWARE OF ALL THIS.

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WE WERE HOLDING SHORT OF RWY 1L AT IAD ARPT; WHEN BOTH THE FO AND MYSELF HEARD A POS AND HOLD INSTRUCTION FROM TWR WITH OUR CALL SIGN AND NUMBER. THE FO RESPONDED WITH 'POS AND HOLD.' WE TOOK OUR POS ON THE RWY AND STOPPED; WAITING FOR TKOF CLRNC. AFTER APPROX 30 SECONDS A CITATION THAT WAS HOLDING SHORT ADVISED THE TWR THAT THERE IS AN ACFT ON THE RWY AND ONE ON SHORT FINAL. IMMEDIATELY I TAXIED OFF THE RWY WHILE THE FO ANNOUNCED OUR ACTIONS TO TWR. WHEN WE HAD CROSSED THE HOLD SHORT LINE I ANNOUNCED TO TWR THAT WE WERE CLR. AFTER TALKING WITH THE SUPVR AT IAD TWR; HE ADVISES ME THEY DID NOT ISSUE A POS AND HOLD CLRNC TO OUR ACFT AND THEY DID NOT HAVE ANY EVIDENCE OF OUR XMISSIONS ON THE TAPE UNTIL I ANNOUNCED CLR. MY FO AND I HAVE RECOUNTED THE INCIDENT MANY TIMES AND BELIEVE OUR ACTIONS WERE NORMAL FOR THE SIT. WE BOTH BELIEVE WE GOT THE CLRNC AND ACTED APPROPRIATELY. THERE MAY HAVE BEEN OTHER XMISSIONS BLOCKING OURS; BUT WE MOST DEFINITELY RESPONDED TO WHAT WE BELIEVED WERE INSTRUCTIONS FOR US. I THINK THE TFC SIGNAL LIGHTS BEING TESTED AT DIFFERENT ARPTS WOULD ELIMINATE THESE POSSIBLE INCURSIONS. THERE ARE MANY SIMILAR SOUNDING CALL SIGNS AND RWYS AT DIFFERENT SIDES OF THE ARPT WITH A COMMON CTLR; AND SOMETIMES L AND R ARE CONFUSED. SUPPLEMENTAL INFO FROM ACN 333428: CAPT TOOK IMMEDIATE ACTION TO VACATE THE RWY AND I RADIOED 'FLT XX LEAVING THE RWY.' THE TWR CTLR SAID THAT HE HAD NOT GIVEN US PERMISSION TO ENTER THE RWY. I REPLIED 'YES SIR; YOU DID AND WE ACKNOWLEDGED.' HE THEN SAID; 'NO I DID NOT.' CAPT THEN SAID; 'FLT XX IS CLR OF THE RWY.' IN THE MEANTIME; THE FALCON RADIOED 'GOING AROUND' AND DID SAME. AS A POSSIBLE CONTRIBUTING FACTOR THE TWR WAS HANDLING MULTIPLE OPS WITH 3 RWYS ACTIVE. THIS PERIOD AT IAD IS KNOWN AS 'PUSH TIME;' WHEN ACTIVITY IS AT ITS PEAK. THE TWR WAS NOT AWARE OF THE CONFLICTING TFC AND NEITHER WERE WE.