The Ports of Los Angeles and Long Beach (San Pedro Bay Ports) are among the  busiest ports in America.  Although the economic recession has slowed some  of the cargo movement in the Ports, the rail system is still over  capacitated in certain portions of the network.  Rail traffic has already introduced congestion and threatened the accessibility and capacity of the  rail network system in the Los Angeles Basin and other locations.  Trains  operating in densely populated metropolitan areas typically encounter complex trackage configurations.  To make optimal use of the available rail capacity, some portions of the rail network may consist of single-track  lines while other locations may consist of double- or triple-track lines.   Because of varying local conditions, different points in the rail network  may have different speed limits. We formulate a graphical technique for  modeling such complex rail networks; and we use this technique to develop a  deadlock-free algorithm for dispatching each train to its destination with nearly minimal travel time while (a) abiding by the speed limits at each point on each train's route; and (b) maintaining adequate headways between trains.  We implemented this train-dispatching algorithm in a simulation  model of the movements of passenger and freight trains in Los Angeles County, and we validated the simulation as yielding an adequate  approximation to the current system performance.