The only thing more disturbing than thinking about Time Trax is thinking about Pointman, the most obscure of the 4 PTEN shows. 

It debuted the same month as DS9, so it wasn't inspired by that. Quantum Leap (1989) was probably more of a direct inspiration, with TNG being indirectly responsible (showing the strength of syndication for a sci-fi show).Probably the show's biggest problem was I remember it was dismissed as a Quantum Leap rip-off back in the day. Probably not fairly. As I recall it was one of a batch of made-for-syndicated dramas that flooded the market in the 1990s in the wake of the success of TNG and DS9, like Earth Final Conflict and the Xena/Hercules franchise, most of which were filmed on the cheap in places like Australia (which was the case for Time Trax, I know).