Joint design of multimodal transit networks and shared autonomous mobility fleets

Highlights

• Integrates shared autonomous vehicle service with conventional public transit.

• Method to jointly determine autonomous vehicle fleet size and transit route frequencies.

• Develops best allocation of resources to provide mobility to urban residents.

• Bi-level problem formulation explicitly considers user response (demand) in the design process.

• Methodology applied to Chicago multimodal transit network.

Abstract

Providing quality transit service to travelers in low-density areas, particularly travelers without personal vehicles, is a constant challenge for transit agencies. The advent of fully-autonomous vehicles (AVs) and their inclusion in mobility service fleets may allow transit agencies to offer better service and/or reduce their own capital and operational costs. This study focuses on the problem of allocating resources between transit patterns and operating (or subsidizing) shared-use AV mobility services (SAMSs) in a large metropolitan area. To address this question, a joint transit network redesign and SAMS fleet size determination problem (JTNR-SFSDP) is introduced, and a bi-level mathematical programming formulation and solution approach are presented. The upper-level problem modifies a transit network frequency setting problem (TNFSP) formulation via incorporating SAMS fleet size as a decision variable and allowing the removal of bus routes. The lower-level problem consists of a dynamic combined mode choice-traveler assignment problem (DCMC-TAP) formulation. The heuristic solution procedure involves solving the upper-level problem using a nonlinear programming solver and solving the lower-level problem using an iterative agent-based assignment-simulation approach. To illustrate the effectiveness of the modeling framework, this study uses traveler demand from Chicago along with the region’s existing multimodal transit network. The computational results indicate significant traveler benefits, in terms of improved average traveler wait times, associated with optimizing the joint design of multimodal transit networks and SAMS fleets compared with the initial transit network design.

Introduction

Designing public transit networks to efficiently serve heterogeneous travelers subject to various constraints (e.g. budgetary, political, equity) is a challenging problem for transit agencies. Residents of low-density areas and employees working outside of central business districts tend to experience low-quality transit service (e.g. long walk distances to or from a transit stop, long wait times due to infrequent transit service, circuitous routes, and multi-transfer trips) due to the difficulty of serving these areas in a cost-effective manner.

Autonomous vehicles (AVs) and their inclusion in mobility service fleets may offer transit agencies a potential solution to this problem. Agencies could replace inefficient transit routes/patterns operating in certain regions, and during certain times of the day, and reallocate those resources to operate (or subsidize) shared-use AV mobility services (SAMSs). Given the considerable operational and capital cost advantages of SAMSs over fixed-route transit services and driver-operated mobility services (e.g. flex-transit, ridesourcing, and taxi service), it is conceivable that reallocating resources from less cost-efficient transit patterns may produce better service for travelers and/or reduce overall transit agency costs. This study uses an agent-based modeling approach that captures the system-level impacts of redesigning transit networks and operating (or subsidizing) SAMSs taking into account traveler behavior and the interactions between traveler agents in the system. In their cost-based analysis of future transport systems, Bösch et al. (2018) indicate that there is an opportunity for SAMSs to replace bus service in low-density areas and allow transit agencies to focus their resources on mass transit in dense urban areas.

To help achieve the Pareto-improving outcome of better service for travelers and lower costs for agencies, this study presents a modeling framework to optimize the joint design of transit networks and SAMS fleets. Specifically, the objective is to formulate and solve the joint transit network redesign and SAMS fleet size determination problem (JTNR-SFSDP) subject to user-equilibrium constraints at the mode and route choice levels.

This study presents conceptual, theoretical, and methodological contributions. First, as far as the authors are aware, there are no other studies that define, model, or solve a joint transit network redesign and mobility service fleet size determination problem. The study models the problem using a bi-level mathematical programming formulation. The problem definition and modeling framework represent a timely contribution to the existing literature, especially with the emergence of AVs, rapid growth of mobility services, and their interaction with transit services. The second and third contributions relate to the formulation of the upper- and lower-level problems in the bi-level JTNR-SFSDP, respectively. This study modifies a transit network frequency setting problem (TNSFP) formulation for the upper-level problem via allowing transit frequencies to be set to near-zero and incorporating SAMS fleet size as a decision variable. For the lower-level problem, this study employs a dynamic combined mode choice—traveler assignment problem (DCMC-TAP) formulation. This appears to be the first study to incorporate time-dependent mode (and route) choice in the lower-level problem of a transit network design problem. Hence, the modeling framework captures the modal split response to the frequency setting of transit patterns and operation/subsidization of SAMS fleets. The fourth contribution is the use of a detailed agent-based simulation tool with three components to address the lower-level problem. The three component models include a multinomial logit mode choice model, a transit traveler assignment-simulation model, and a SAMS fleet simulation model. Although data-intensive, the agent-based model for the lower-level provides information about individual travelers, the transit network, and the SAMS fleet. This information is valuable for model verification, model validation, and understanding the complex interactions between design decisions and travel behavior.

Relative to the small but growing literature modeling the intersection and integration of SAMSs with public transit, the modeling framework in this paper imposes fewer restrictions. For example, this study makes no a priori assumptions about efficient joint designs of transit networks and SAMSs; whereas, existing studies define scenarios in which SAMSs (i) replace specific transit routes (Pinto et al., 2018, Winter et al., 2018), (ii) replace transit systems (Basu et al., 2018), (iii) are implemented instead of new transit lines (Mendes et al., 2017), or (iv) act as a transit feeder mode (Meyer et al., 2017, Scheltes and de Almeida Correia, 2017). Similarly, the modeling framework in the current study endogenously determines modal flows (demand) for SAMSs and public transit based on the performance of the two systems, rather than exogenously (e.g. Shen et al., 2018).

The remainder of the paper is structured as follows. Section 2 presents an overview of the bi-level mathematical programming modeling framework and reviews relevant literature. The Nomenclature section displays the mathematical notation used in the paper. Section 3 presents the mathematical formulation of the bi-level JTNR-SFSDP. Section 4 presents the heuristic solution procedure designed to solve the bi-level JTNR-SFSDP. Section 5 describes the experimental design and Section 6 presents the computational results. Section 7 concludes the paper.