Highlights • Bus substitution strategy with pooled standby fleet to control schedule deviations in multiline systems. • Stochastic dynamic program based on bus operation dynamics and substitution decisions • Approximate dynamic programming algorithm with offline simulations and estimation • Multi-period dynamic program to address fleet management in time-varying systems • Numerical examples demonstrate the performance and applicability of the proposed strategy

Abstract Traditional bus bunching control methods (e.g., adding slack to schedules, adapting cruising speed), in one way or another, trade commercial speed for better system stability and, as a result, may impose the burden of additional travel time on passengers. Recently, a dynamic bus substitution strategy, where standby buses are dispatched to take over service from late/early buses, was proposed as an attempt to enhance system reliability without sacrificing too much passenger experience. This paper further studies this substitution strategy in the context of multiple bus lines under either time-independent or time-varying settings. In the latter scenario, the fleet of standby buses can be dynamically utilized to save on opportunity costs. We model the agency’s substitution decisions and retired bus repositioning decisions as a stochastic dynamic program so as to obtain the optimal policy that minimizes the system-wide costs. Numerical results show that the dynamic substitution strategy can benefit from the “economies of scale” by pooling the standby fleet across lines, and there are also benefits from dynamic fleet management when transit demand varies over time. Numerical examples are presented to illustrate the applicability and advantage of the proposed strategy. The substitution strategy not only holds the promise to outperform traditional holding methods in terms of reducing passenger costs, they also can be used to complement other methods to better control very unstable systems.