TAXI ACROSS ACTIVE RWY NO CLRNC.

Narrative

AT LAS VEGAS MCCARRAN ARPT THE NORMALLY USED RWY FOR AIR TAXI OPERATORS; 90 PERCENT OF THE TIME; IS 19L. ON THE DAY OF THE OCCURRENCE; I CALLED FOR TAXI; GND CTRL WAS VERY BUSY; AND ASKED; 'WHO CALLED FOR TAXI?' I AGAIN CALLED FOR TAXI CLRNC AND WAS CERTAIN GND CLRED ME TO 19L. I WAS ALSO CERTAIN I READ BACK CLRED TO 19L. TAXIING TO 19L REQUIRES XING 19R AND 1L. AS I TAXIED OUT; I CHKED BOTH DIRECTIONS BEFORE XING 19R AND 1L. IT APPEARED CLR. I TAXIED ACROSS AND THEN NOTICED AN ACFT HAD JUST TOUCHED DOWN ON 1L ABUT 4000 FT DOWN ON THE RWY. I THEN ASKED GND TO VERIFY 19L OR 1L. THEY SAID; 'AFFIRMATIVE 1L.' I THEN TAXIED TO 1L VIA THE PARALLEL TXWY. I THEN REALIZED I WAS THE ACTIVE RWY. WHEN I REACHED THE HOLD SHORT LINE FOR 1L; I CONTACTED TWR FOR TKOF CLRNC; THEY INFORMED ME TO CONTACT THEM WHEN I ARRIVED TO MY DEST. WHEN I ARRIVED AT MY DEST; I CALLED LAS TWR; THEY INFORMED ME THAT I HAD CROSSED AN ACTIVE RWY WITHOUT CLRNC. I FEEL CONTRIBUTING FACTORS TO THIS OCCURRENCE WERE CONGESTION ON GND CTRL AND THE HVY WORKLOAD ON GND CTRL WHICH LIMITS ABILITY TO MONITOR GND MOVEMENTS.