We propose a data-driven linear programming model to compute energy-optimal timetables for networks operating under communications-based train control (CBTC); the model was developed in collaboration with Hitachi Rail Canada, the largest provider of CBTC systems worldwide. Our model minimizes the network’s effective energy consumption, defined as the total traction energy consumed by the trains minus the regenerative braking energy transferred from braking trains to nearby accelerating trains. Our main modeling contribution is to show that the signed overlap between a braking and an accelerating phase is concave in the event times, so maximizing the transferred energy is a convex problem that can be reformulated into a linear program via hypograph constraints. In contrast, prior work either captures this synchronization structure with binary variables or other non-convex constraints, or relies on multiple stages interleaved with simulation. Our model computes an energy-optimal timetable subject to the operational constraints of the railway network in under a second on a laptop for every instance studied and predicts the effective energy consumption of the network without requiring time-consuming simulations. We demonstrate the effectiveness of our model on two real-world CBTC networks. First, on 11 full-day operational instances of Shanghai Metro Line 8 with 1,000–1,332 active trains, the model computes energy-optimal timetables in under 0.7 seconds per instance and predicts 19.5%–28.2% reductions in effective energy consumption relative to the existing operational timetables; the industrial physics-based simulator SPSIM independently corroborates these reductions. Second, on 17 real-world instances of the Docklands Light Railway with 108–336 active trains, the model predicts reductions of 19.3%–28.8%, solving each instance in under 0.11 seconds. Our model is being integrated into Hitachi Rail Canada’s industrial timetable compiler.