Timetable-Based Transit Assignment Using Branch and Bound Techniques

Abstract

Transit assignment procedures need to reflect the constraints imposed by line routes and timetables. They require specific search algorithms that consider transfers between transit lines with their precise transfer times. Such an assignment procedure is presented for transit networks using a timetable-based search algorithm. In contrast to existing timetable-based search methods employing a shortest-path algorithm, the described procedure constructs connections using branch and bound techniques. This approach significantly reduces computing time, thus facilitating the use of timetable-based assignment for large networks. At the same time, it produces better results in cases where slow but cheap or direct connections compete with fast connections that are more expensive or require transfers.

A General Multi-agent Modelling Framework for the Transit Assignment Problem – A Learning-Based Approach

“…Although much attention has been given to auto-traffic assignment models, it is well addressed in the literature that the transit assignment process is more complicated than auto-traffic assignment [1,2]. This complexity is due to:…”

“…For instance, some of these assumptions are necessary to speed up the solution algorithm to a reasonable running time, such as the assumption that waiting times at boarding stops or at transfer stops depend only on the headway of the following transit line [2]. While it speeds up computation, it fails to consider the coordination of the timetables, an important feature of the transit network.…”

“…The complexity of the assignment process increases more than linearly with the transit line frequencies, because this implies the growth of graph's dimensions. When schedule-based procedures use a shortest path algorithm, they unfortunately have two more weaknesses [2]:…”

Operational route choice methodologies for practical applications

“…Different heuristics have been proposed to generate subsets of paths, commonly referred to as consideration sets (e.g. Ben-Akiva et al, 1984;Azevedo et al, 1993;de la Barra et al, 1993;van der Zijpp and Fiorenzo Catalano, 2005;Friedrich et al, 2001;Hoogendoorn-Lanser, 2005;Prato and Bekhor, 2006), to which the observed path is subsequently added . The values of the parameter estimates are dependent on the definition of the choice sets (Frejinger et al, 2009) and may vary significantly for different instances of sampled sets.…”

Stochastic user equilibrium with equilibrated choice sets: Part I – Model formulations under alternative distributions and restrictions

“…Bovy (2009) argues for the behavioural realism of models in which only a subset of all paths is permitted, stating that people do not choose their path from the full Universal Choice Set of alternatives, but rather from a Master Choice Set of paths considered relevant. To this end, several studies have developed methods to pre-generate a fixed Master Choice Set, such as distance-bounded enumeration (Leurent, 1997), constrained enumeration (Friedrich et al, 2001;Prato and Bekhor, 2006), probabilistic generation techniques (Cascetta and Papola, 2001;Frejinger et al, 2009) and various deterministic or stochastic shortest path algorithms (e.g., Dijkstra, 1959;Sheffi and Powell, 1982;Ben-Akiva et al, 1984).…”