Real - Time Optimization Model for Dynamic Scheduling of Transit Operations

A new transit operating strategy is presented in which service vehicles operate in pairs with the lead vehicle providing an all-stop local service and the following vehicle being allowed to skip some stops as an express service. The underlying scheduling problem is formulated as a nonlinear integer programming problem with the objective of minimizing the total costs for both operators and passengers. A sensitivity analysis using a real-life example is performed to identify the conditions under which the proposed operating strategy is most advantageous. The design and operations of public transit services involve many complicated issues. On the one hand, transit routes are expected to have a fixed schedule or service interval (headway) and to provide broad coverage. On the other hand, the origin-destination (O-D) passenger demands along a route often vary significantly, with some stops, such as those downtown, having a relatively large number of passengers boarding and alighting and others having few passengers. Such an O-D pattern cannot be efficiently serviced by transit with fixed routes and schedules. Balancing the needs of delivering reliable and consistent services and the costs of providing such services has continuously been one of the major challenges facing the transit agencies. In the past 30 years, many operating strategies have been proposed with the goal of better matching services covered by transit routes with the O-D demand distribution along the routes. One of the central ideas has been flexible routing and scheduling that integrates express services (stop only at a few stops) with local services (stop at all stops). Flexible routing and scheduling strategies can be classified into four general categories (1): (a) zone scheduling, including restricted zonal service, semirestricted zonal service, and limited-stop zonal service ; (b) short turning; (c) deadheading; and (d) dynamic stop skipping. In zone scheduling, the whole route is divided into several zones. The inbound buses make all stops within a single zone and then run without stopping to the terminus, while outbound vehicles operate in the reverse manner. With this operating strategy, passenger travel time and the required numbers of vehicles and drivers may be reduced. This operating strategy, however, has two disadvantages, including reduced service frequency and increased waiting time and the possible requirement of cross-zone transfer. Turnquist (2, 3) was among the first to study the zone scheduling method with the objective of simultaneously determining the optimal zone division and vehicle allocation. This model was …