CAPT OF A DEHAVILLAND DHC8 TAXIED ON X'ED OUT TXWY WHILE TURNING OFF RWY AND CLRING THE RWY FOR LNDG TFC.

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WE WERE ASKED TO KEEP OUR SPD UP ON FINAL DUE TO A B737 BEHIND US. ON LNDG; I ASSUMED CTL OF THE ACFT PASSING THROUGH 80 KTS (PER NORMAL PROCS -- THE TILLER IS ONLY ON THE CAPT'S SIDE). TWR ASKED US TO EXPEDITE OFF THE RWY AS TFC WAS VERY SHORT FINAL BEHIND US. I WAS PLANNING ON EXITING AT TXWY P; BUT OUR SPD WAS STILL TOO HIGH TO MAKE THE TURN. I ADDED SOME PWR TO EXPEDITE TO THE NEXT EXIT AT TXWY N. UPON TURNING OFF ONTO TXWY N; I DISCOVERED THAT THE PORTION OF TXWY N WE WERE ON WAS X'ED OUT. WE WERE PASSING OVER THE X'S AND ONTO TXWY B; THE PARALLEL TO THE RWY TXWY WHEN I SAW THE X'S. TXWY B IS QUITE CLOSE TO THE RWY; SO THE TXWY EXITS ARE VERY SHORT. WE TURNED ONTO TXWY B WITHOUT INCIDENT AND CONTINUED TO OUR GATE. CONTRIBUTING FACTORS: 1) NO RWY EDGE LIGHTS ALONG THE NEWLY CLOSED PORTION OF TXWY N. LOOKED THE SAME AS BEFORE. 2) GND MARKINGS ARE IMPOSSIBLE TO SEE AT NIGHT UNTIL YOU ARE PASSING OVER THEM. 3) NO NOTAMS REGARDING THE CHANGE. THE COMMERCIAL ARPT DIAGRAM STILL SHOWS TXWY N AS BEING VERY WIDE COMPARED TO THE OTHER TXWYS. 4) NEW TO THE ACFT AND NEW AS CAPT AND TAXIING PLT. 5) FATIGUE -- WE WERE ON OUR THIRD NIGHT OF CONTINUOUS DUTY OVERNIGHTS.