As the future of autonomous vehicles (AVs) becomes more certain, transport network managers may seek ways to reinvent elements of the traffic network to improve efficiency. One possibility is dynamic lane reversal, in which the network operator makes use of AV communications and behavior to change the direction of flow on a road link at smaller time intervals than would be possible with human drivers. Although there is much research into the mechanical details of AVs, this study motivates the need for future research by focusing on a planning application in which AVs are already present. A novel extension to an established system optimal dynamic traffic assignment model based on the cell transmission model was examined. The model determined the optimal lane configuration at small space-time intervals. Results demonstrate the model on a single link and a grid network and explore the dynamic demand scenarios that are most conducive to increasing system efficiency with dynamic lane reversal.