Responsive bus dispatching strategy in a multi-modal and multi-directional transportation system: A doubly dynamical approach

Abstract This paper examines the time-dependent bus dispatching problem in a multi-modal context. Traditional studies along this line often optimize the bus frequency or schedule. However, they may fail as the realized bus frequency or schedule is constrained by the time-varying traffic congestion on the road. Adding more buses to service does not necessarily increase the service frequency. Given this, we look into the time-dependent bus dispatching (number of buses in service on road) when taking into account complex multimodal and multi-directional flow interactions on the road. In particular, the traffic dynamics over clock time is modeled through an aggregate traffic representation with flow interactions between cars and buses, and interactions between traffic in opposite moving directions. Instead of explicitly optimizing the size of dispatched bus fleet, we propose an adaptive fleet size adjustment mechanism where we have a target level of bus loading factor. This adaptive or responsive approach, by taking advantage of the doubly dynamical system proposed in Liu and Geroliminis (2017), adjusts the size of dispatched bus fleet over calendar time and accommodates day-to-day variations of mode choices and traffic patterns. Numerical studies show that the proposed approach can help bus operator to reduce operating cost and improve net benefit while maintaining comparable user costs for passengers. This study offers a new perspective for dynamic bus dispatching strategy and improves our understanding of multi-modal traffic dynamics.