A RWY INCURSION AND TFC CONFLICT AT SAV; GA.

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I ASKED FOR PROGRESSIVE TAXI. WAS TOLD TO 'TAXI TO RWY 36' AND TO 'GIVE WAY TO GRUMMAN...ENTERING PARKING AREA.' MY INTERNAL COMPASS CAUSED ME TO MISTAKE RWY 9/27 FOR RWY 18/36. I BEGAN TAXIING IN DIRECTION GRUMMAN CAME FROM. THE GND CTLR CALLED AND ASKED IF I WAS TAXIING N 'ON THE RAMP.' I LOOKED AT MY COMPASS AND REALIZED I WAS. AFTER SOME DISCUSSION HE TOLD ME TO MAKE A L TURN THEN TAXI TO THE END OF TXWY B. TXWY B IS ACTUALLY PART OF THE RAMP AT THAT POINT. HE SHOULD HAVE SAID 'DO A 180 DEG TURN AND TAXI TO RWY 36 VIA TXWY B.' I WAS AT AN INTXN AND TURNED L. I HEADED FOR WHAT I THOUGHT WAS A PARALLEL TXWY. IT WAS RWY 36. AS SOON AS I SAW THE RWY MARKINGS; I REALIZED ANOTHER ACFT WAS ON THE RWY AND I NEEDED TO EXIT ASAP. I GUNNED THE ENG AND COASTED ONTO A CLOSED TXWY. LATER I WAS CLRED TO CROSS RWY 36 AND ORDERED TO PHONE THE CTLR. I HAVE LEARNED TO STUDY THE ARPT DIAGRAM BETTER; AND TO INSIST ON PROGRESSIVE TAXI WHEN UNFAMILIAR WITH ARPT. SAV NEEDS BETTER SIGNAGE. CTLRS COULD HELP BY SAYING TXWY B IS PART OF THE RAMP.