ZJX Controller described a very busy/complex traffic period when only a small transitioning corridor was available for enroute aircraft; the reporter listing TMU inaction and lack of staffing as contributing factors in this event.

Narrative

After working Albany/Ashburn for some time; I was asked to give the sector to the Talahasse controller. We combined those sectors because our staffing was critically low. Upon completing the transfer to the TLH sector; I was asked to relieve the RADAR Controller at Sector 30. There was a line of precipitation extending from the Gulf of Mexico up over the state of Florida; then up into the Carolinas and into the Atlantic Ocean. There was a small approximate 20NM break in the precipitation. At the time I assumed the sector; the traffic was busy but manageable. Shortly after I had more aircraft than I could keep track of. I did not take some hand offs; but that did not prevent them from flying into my sector. My airspace was violated multiple times; and I am fairly certain that I violated other airspace multiple times as well; though I cannot remember enough to cite details. During this time I also had at least two aircraft incidents where separation was almost lost. One involved an Air Carrier that I assigned FL 290; I recall nothing about the other aircraft. The other was an Air Canada and an Airtran. I am not sure what specifically happened with the Airtran; but my D-Side says we took a point out on him but Sector 17 then decided to hand him off to us. Upon taking the hand off; the aircraft was never switched to our frequency. The Air Canada flight was at FL320; Northbound; and on our frequency. The Airtran began a decent right in the face of the Air Canada flight. Upon seeing the Conflict Alert; I assigned the Air Canada flight a 270 heading and used the word 'immediately' in the clearance. I do not think separation was lost; but it was close. Over the course of the 36 minutes I was sitting at this sector I cannot say how many times I told the supervisor that I needed a tracker; that the sector was UNSAFE; and that something needed to be done to temper the flow of aircraft heading for the gap in the precipitation. No help was given; no tracker provided; no flow was put out to help us. I also cannot say how many times my airspace was violated; how many times I violated others. Nor can I say how many near misses occurred with aircraft to aircraft separation. If Conflict Alert had not gone off; I am fairly sure that I would have missed the above incident with the Air Canada and Airtran flights. The entire situation was completely unsafe. I do not know how or why this was allowed to occur; but the system totally failed in this case. Recommendation; I would first recommend that our staffing issues be addressed. If we are critically staffed; safety should not be compromised like it was in this instance. We need to have overtime called in when we take as many sick outs as we did. Our staffing; or lack thereof; was definately a contributing factor in this incident. By the end of my session; I had been on position for over 3 hours. I was fatigued beyond what mere words can describe. Secondly; I would recommend that the Eastern portion of this sector be designated as a separate sector; with separate frequencies. The North East corner of this sector gets so congested at certain times; that this seems like it would be an obvious fix. It would allow us to zoom in more to see all the aircraft that are transitioning the area; rather than being forced to work on a 175 mile range. Thirdly; I would recommend that our TMU be investigated and/or retrained. They did nothing to help us; so I can only assume that it was that they did not know what to do.