Transformative technologies such as autonomous vehicles (AVs) create an opportunity to reinvent features of the traffic network to improve efficiency. The focus of this work is dynamic lane reversal: using AV communications and behavior to change the direction vehicles are allowed to travel on a road lane with much greater frequency than would be possible with human drivers. This work presents a novel methodology based on the linear programming formulation of dynamic traffic assignment using the cell transmission model for solving the system optimal (SO) problem. The SO assignment is chosen because the communications and behavior protocols necessary to operate AV intersection and lane reversal controls could be used to assign routes and optimize network performance. This work expands the model to determine the optimal direction of lanes at small space-time intervals. Model assumptions are outlined and discussed. Results demonstrate the model and explore the dynamic demand scenarios which are most conducive to increasing system efficiency with dynamic lane reversal.