Real-time holding control for high-frequency transit with dynamics

• We formulate a holding optimization model that captures dynamics.
• We compare its effectiveness to that of a static model and two other strategies.
• The dynamic model outperforms the static model in high-demand cases with dynamics.
• The best holding strategies do not always lead to even headways.
• Computation times are suitable for real-time application.

Operations control is an important means of improving service quality for high-frequency transit. Past research on real-time control has focused on developing and evaluating the effectiveness of different control strategies, largely relying on running times and demand which are assumed to be static. We formulate a mathematical model for holding control optimization that reflects dynamic running times and demand. The model can be used to produce a plan of holding times that accounts not only for the current state of the system, but also for expected changes in running times and demand. We evaluate the effectiveness of the model within a simulation environment. The results show that control based on dynamic inputs outperforms its static equivalent in high demand cases where passengers can be left behind at stops, and to a lesser extent in low to moderate demand cases with time-varying running times.