Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A Modeling and Optimization Framework for Fostering Modal Shift through the Integration of Tradable Credits and Demand-Responsive Autonomous Shuttles

Zenghao Hou, Ludovic Leclercq

TL;DR

This work develops a dynamic multimodal equilibrium framework that explicitly incorporates supply-side constraints (fleet size, capacity, and dispatch) and waiting times for public/shared transport under Tradable Credit Schemes (TCS). By integrating a trip-based multimodal MFD, station-level point queues, and a logit-based mode choice within a VI formulation, the paper captures feedback between demand shifts and service operations. A Demand-Responsive Autonomous Shuttle (DRAS) is introduced and optimized within a bi-level (MPEC) structure to jointly design credit allocation and DRAS deployment, demonstrating the importance of coordinating demand regulation with flexible supply. Case studies on a Paris-area corridor illustrate that DRAS can alleviate waiting-time bottlenecks and, when combined with TCS, yield the best system-wide performance, with non-monotonic interactions between policy tightness and supply that require careful, coordinated planning.

Abstract

Tradable Credit Schemes (TCS) promote the use of public and shared transport by capping private car usage while maintaining fair welfare outcomes by allowing credit trading. However, most existing studies assume unlimited public transit capacity or a fixed occupancy of shared modes, often neglecting waiting time and oversimplifying time-based costs by depending solely on in-vehicle travel time. These assumptions can overstate the system's performance with TCS regulation, especially when there are insufficient public or shared transport supplies. To address this, we develop a dynamic multimodal equilibrium model to capture operation constraints and induced waiting times under TCS regulation. The model integrates travelers' mode choices, credit trading, traffic dynamics, and waiting time, which depend on key operational features of service vehicles such as fleet size and capacity. Besides, most TCS studies assume fixed transport supply, overlooking supply-side responses triggered by demand shifts. Therefore, we further propose integrating adaptive supply management through the deployment of Demand-Responsive Autonomous Shuttles (DRAS) and developing a bi-level optimization framework that incorporates the equilibrium model to jointly optimize TCS design and operational strategies for the DRAS. We apply the framework to a section of the A10 highway near Paris, France, to examine demand-supply interactions and assess the potential benefits of jointly implementing TCS and DRAS. Numerical results demonstrate the importance of modeling operational features within multimodal equilibrium and incorporating flexible supply in TCS policies for mitigating overall generalized cost.

A Modeling and Optimization Framework for Fostering Modal Shift through the Integration of Tradable Credits and Demand-Responsive Autonomous Shuttles

TL;DR

This work develops a dynamic multimodal equilibrium framework that explicitly incorporates supply-side constraints (fleet size, capacity, and dispatch) and waiting times for public/shared transport under Tradable Credit Schemes (TCS). By integrating a trip-based multimodal MFD, station-level point queues, and a logit-based mode choice within a VI formulation, the paper captures feedback between demand shifts and service operations. A Demand-Responsive Autonomous Shuttle (DRAS) is introduced and optimized within a bi-level (MPEC) structure to jointly design credit allocation and DRAS deployment, demonstrating the importance of coordinating demand regulation with flexible supply. Case studies on a Paris-area corridor illustrate that DRAS can alleviate waiting-time bottlenecks and, when combined with TCS, yield the best system-wide performance, with non-monotonic interactions between policy tightness and supply that require careful, coordinated planning.

Abstract

Tradable Credit Schemes (TCS) promote the use of public and shared transport by capping private car usage while maintaining fair welfare outcomes by allowing credit trading. However, most existing studies assume unlimited public transit capacity or a fixed occupancy of shared modes, often neglecting waiting time and oversimplifying time-based costs by depending solely on in-vehicle travel time. These assumptions can overstate the system's performance with TCS regulation, especially when there are insufficient public or shared transport supplies. To address this, we develop a dynamic multimodal equilibrium model to capture operation constraints and induced waiting times under TCS regulation. The model integrates travelers' mode choices, credit trading, traffic dynamics, and waiting time, which depend on key operational features of service vehicles such as fleet size and capacity. Besides, most TCS studies assume fixed transport supply, overlooking supply-side responses triggered by demand shifts. Therefore, we further propose integrating adaptive supply management through the deployment of Demand-Responsive Autonomous Shuttles (DRAS) and developing a bi-level optimization framework that incorporates the equilibrium model to jointly optimize TCS design and operational strategies for the DRAS. We apply the framework to a section of the A10 highway near Paris, France, to examine demand-supply interactions and assess the potential benefits of jointly implementing TCS and DRAS. Numerical results demonstrate the importance of modeling operational features within multimodal equilibrium and incorporating flexible supply in TCS policies for mitigating overall generalized cost.

Paper Structure

This paper contains 30 sections, 46 equations, 15 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Problem Definition
  4. Modeling Framework
  5. Prelimnary settings
  6. Trip-based MFD in discrete time horizon
  7. Point queue model for station-based waiting
  8. TCS setting
  9. Utility function and Logit-Based Mode Choice
  10. Equilibrium Modeling
  11. Discussion on the solution existence and uniqueness
  12. Proof of existence
  13. Discussion on uniqueness
  14. Solving Algorithm
  15. Overall computation process
  16. ...and 15 more sections

Figures (15)

  • Figure 1: Bi-level framework linking DRAS operation with equilibrium dynamics.
  • Figure 2: An example of five DRAS schedules in a single OD scenario
  • Figure 3: Cumulative DRAS arrival and service curves illustrating passenger waiting times.
  • Figure 4: Interactions of major model components of TCS.
  • Figure 5: Flowchart for Computation process
  • ...and 10 more figures