ADS CTLR DESCRIBED MINIMALLY STAFFED SHIFT THAT RESULTED IN 5 HOURS ON POSITION.

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WHEN I RPTED FOR DUTY; I WAS INFORMED BY THE FACILITY MGR; MR X; THAT I WOULD BE WORKING THE LAST 5 HRS OF THE SHIFT BY MYSELF. I INFORMED MR X THAT I HAD EXPERIENCED INSOMNIA THE PREVIOUS NIGHT AND HAD ONLY APPROX 3 HRS OF BROKEN SLEEP IN THE PREVIOUS 36 HRS. I ALSO INFORMED MR X THAT I PHYSICALLY FELT EXHAUSTED DUE TO LACK OF SLEEP AND THE ONLY REASON I HAD NOT CALLED IN SICK WAS BECAUSE I HAD BEEN INFORMED BY THE FAA THAT LACK OF SLEEP IS NOT CONSIDERED A VALID REASON TO APPROVE SICK LEAVE. MR X TOLD ME THAT HE HAD NOT BEEN ABLE TO GET ANYONE FOR OVERTIME AND THAT I WOULD JUST HAVE TO WORK THE SHIFT ANYWAY. HE ALSO STATED THAT HE WOULD BE IN THE TWR TO HELP ME ALONG WITH A TRAINEE. MR X; WHO IS NOT CERTIFIED ON ANY POS OF OP; HAD HIMSELF SIGNED ON THE CIC POS FOR THE ENTIRE SHIFT. JUST PRIOR TO THE OTHER CPC DEPARTING AT THE END OF HIS SHIFT AROUND XA00; MR X AFFORDED ME A BREAK. FROM THAT TIME; I WORKED ON POS FOR 5 HRS. THERE WAS A TRAINEE WHO WAS CERTIFIED ON CLRNC DELIVERY AND GND CTL THAT DID WORK UNTIL XC00. THIS INDIVIDUAL WAS OF HELP AND WAS GIVEN BREAKS BY MR X. DURING THESE 5 HRS I WORKED VERY SLOWLY AND DELIBERATELY SO AS TO AVOID ANY MISTAKES. OCCASIONALLY; I WAS SHAKING FROM LACK OF REST. FOR THE FIRST 5 HRS OF MY SHIFT; I DID NOT DRINK ANY LIQUIDS SO THAT I WOULD NOT NEED A RESTROOM BREAK. I WOULD CHARACTERIZE THE TFC AS SLOW TO MODERATELY BUSY WITH A FEW SITS THAT REQUIRED MY INTENSE ATTN TO PREVENT ERROR. AT MY BUSIEST; I ENCOUNTERED A VFR OVERFLT PLT WHO HAD NO KNOWLEDGE OF THE DFW CLASS B AIRSPACE BOUNDARIES. THE PLT ENTERED THE ADS CLASS D AIRSPACE HEADED FOR CLASS B AIRSPACE BEFORE I COULD IDENT HIS POS AND ISSUE AN INSTRUCTION TO TURN AWAY FROM CLASS B AND TO CONTACT THE RADAR CTLR. AS STAFFING AT ADS IS AT ITS LOWEST IN YRS. I CAN ONLY EXPECT THAT THIS TYPE OCCURRENCE WILL CONTINUE AT LEAST OCCASIONALLY.