1. Conflict-resolving train control apparatus for a railroad, which railroad includes a plurality of potentially conflicting routes and railroad traffic controlling equipment, said equipment operating in response to signals communicated thereto by a central station, said equipment further communicating information respecting the condition of said equipment and the location of railroad traffic thereon to said central station, said conflict-resolving apparatus comprising: storage means for storing information as to the railroad configuration, status of traffic controlling equipment, location of traffic, nominal schedule of said traffic, and for further storing of information respecting potential conflicts which require resolution in light of actual railroad traffic on said railroad, processor means operating in response to said storage means for initiating a heuristic search for resolution of said conflicts, said processor assigning to each potential conflict resolution, a cost related to the delay required by said resolution, said processor searching for a successful resolution through a path of potential conflict resolution on the basis of said cost, and means responsive to discovery of a successful resolution for storing a desired order of conflicting railroad traffic to eliminate said conflicts, said equipment for controlling said railroad traffic being responsive to said order of trains to control said traffic to eliminate said conflicts.