A Transit Bottleneck Model for Optimal Control Strategies and its Use in Traffic Assignment in Paris

Control strategies are of crucial importance in operations of saturated transit lines. At a given bottleneck, delay propagates due to an excess of demand over supply. Operators therefore use optimal strategies (e.g. holding, fast-running, train-canceling etc.) in order to recover the level of service. While toolbox for train operation control system has thrived in past years, few traffic assignment models for large-scale transit networks on the planning side have touched on the impact of control dynamics: static macroscopic models perform quite well in simulating platform/vehicle saturation, but less so with bottleneck delay; dynamic models deal with dynamic passenger behavior under congestion, yet single vehicle runs are not explicitly considered either. The objective of this paper is to (1) capture the dynamic control features in a bottlenecked rail system; (2) provide a computation-friendly simulation approach to optimize the control; and finally (3) fit the bottleneck model in a static capacitated assignment model to improve its performance. The paper first provides mathematical formulae to describe bottleneck phenomena in a high-demand high-frequency transit line. Formulae are then cast into a control problem of dynamic system, to which we apply dynamic programming to reduce the dimension of decision variables. A numerical application to the Line RER A in Paris is followed, in which control strategies are optimized at key stations in a rolling horizon; on-platform passenger activities are simulated accordingly. Results are compared with both static model and real-life data, showing the effectiveness of the control-based assignment.