Optimal design of skip-stop transit service in a corridor under heterogeneous demand

Abstract

Skip-stop service, also termed "limited-stop service", is a transit service with more than one transit route operating simultaneously on the same line and each route only visiting a subset of the stops. Compared to the conventional all-stop service (where a transit vehicle visits each and every stop along the line), the skip-stop service has higher commercial speed and patrons can enjoy reduced in-vehicle travel time. This service scheme has long been both studied in the literature and implemented in real cities. The majority of the previous studies have formulated discrete models for optimizing the skip-stop routing plan only; i.e., they optimize the selection of stops to be visited by each skip-stop route from a given set of stops. Hence, they fail to jointly optimize the skip-stop routing plan and stop locations. In addition, those discrete models were often solved by heuristic methods. Thus evaluating the solution quality, in terms of the optimality gap between the heuristic solution and the global optimum, is difficult. To address these deficiencies, this thesis has developed continuum approximation (CA) models to optimize various forms of skip-stop services designs under spatially heterogeneous demand. Efficient solution algorithms are also proposed and tested via extensive numerical examples. Specifically, the following three forms of skip-stop services are considered: i) AB-type service; ii) local-express service; and iii) a general form of skip-stop service. In an AB-type service, different skip-stop routes visit the non-transfer stops in a rotating fashion. If there are only two routes named route A and route B, then the non-transfer stops will be placed in an "ABABAB…" fashion; hence the term AB-type service. Each transfer stop will be visited by all the skip-stop routes. We have formulated CA models for jointly optimizing the stop spacings, the number of skip-stop routes, and the transfer stop spacings under any heterogeneous demand patterns. Near-optimal solutions to the CA formulation are obtained via an efficient solution approach, employing the calculus of variations method in an iterative algorithm. A discretization recipe is also proposed to convert the CA solution to a real design plan. Numerical case studies confirm the practicality of the models, the efficiency of the solution approach, and the advantages of the AB-type design over the conventional all-stop design under various heterogeneous demand patterns. A local-express service consists of an express route and a local route. The express route only visits the express stops (which are also transfer stops between the express and local routes), and the local route visits all the stops. CA models are again formulated for optimally designing the express and local stop spacings under heterogeneous demand. The models explicitly account for passengers' choices between different route options (for example, taking the local route only or taking the local route as feeder to access the express route). Numerical case studies compared the optimal local-express design with other corridor designs. Finally, a more general skip-stop service is also studied in this thesis, where the non-transfer stops of different routes and the transfer stops can both be distributed along the line in an arbitrary fashion. A novel formulation for optimizing this general design has been developed in this thesis, which is discrete in nature but inspired by the conventional CA models. Specifically, our model allows the stops to be located anywhere along the line, with stop densities instead of individual stop positions employed as decision variables. Efficient solution methods for this new formulation yielding near-optimal solutions under various heterogeneous demand patterns are presented. Comparison between different skip-stop design forms shows that the general skip-stop design is a generalization of the AB-type design and under some demand patterns the general design can significantly outperform AB-type and local-express designs.